% --------------------------------------------------------------------------
% This Prover9 input file produces a proof that Candidate C5,
%
%    f(f(y, f(y, f(z, x))), f(x, f(y, z))) = x # label("Candidate C5").
%
% from the paper
%
%    Short Single Axioms for Boolean Algebra
%    W. McCune, R. Veroff, B. Fitelson, K. Harris, A. Feist and L. Wos
%    Journal of Automated Reasoning 29(1):1-16, 2002.
%
% is a single axiom for Boolean algebra in terms of the Sheffer Stroke.
%
% We believe that this result was already shown using Waldmeister, but
% we have not seen that proof and don't know the details of how that
% proof was found.
%
% See http://www.cs.unm.edu/~veroff/BA/ for a discussion of the original
% problem, and note that Candidate C5 is Equation 8 from the original
% candidates list.
%
% This proof makes use of the defined function G(),
%
%    G(x) = f(x, f(x, x))
%
% and derives the known system
%
%    f(x, y) = f(y, x)             # label("Commutativity").
%    f(f(x, y), f(x, f(y, z))) = x # label("Equation 26a").
% 
% --------------------------------------------------------------------------

assign(order, kbo).
set(lex_order_vars).

lex([G,f]).

assign(max_megs,8000).

set(para_units_only).
set(para_from_small).

clear(back_demod).
set(restrict_denials).

assign(backsub_check,-1).
assign(sos_limit,-1).

assign(max_weight,  5 ).

formulas(assumptions).

   f(f(y,f(y,f(z,x))),f(x,f(y,z))) = x # label("Candidate C5").
   f(x,f(x,x)) = G(x).

end_of_list.

formulas(goals).

   f(x,y) = f(y,x)           # label("Commutativity").
   f(f(x,y),f(x,f(y,z))) = x # label("Equation 26a").

end_of_list.

%
% Hints extracted from previously found proofs.
%

formulas(hints).

f(x,y) = f(y,x).
f(f(x,f(x,f(y,z))),f(z,f(x,y))) = z.
f(x,f(x,x)) = G(x).
f(c1,c2) != f(c2,c1).
f(c2,c1) != f(c1,c2).
f(f(x,f(x,y)),f(f(y,f(z,u)),f(x,f(z,f(z,f(u,y)))))) = f(y,f(z,u)).
f(f(f(x,f(x,f(y,z))),z),f(f(x,y),f(f(x,f(x,f(y,z))),z))) = f(x,y).
f(f(f(x,f(x,f(y,z))),f(f(x,f(x,f(y,z))),f(f(z,f(x,y)),u))),f(u,z)) = u.
f(f(x,f(x,f(f(y,z),f(y,f(y,f(z,x)))))),x) = f(y,f(y,f(z,x))).
f(f(x,f(x,G(y))),f(f(y,y),f(x,y))) = f(y,y).
f(f(x,G(x)),f(x,f(x,x))) = x.
f(G(f(x,y)),f(y,f(f(x,y),x))) = y.
f(f(x,f(x,f(f(x,x),y))),f(y,G(x))) = y.
f(f(x,G(x)),G(x)) = x.
f(f(x,f(x,y)),f(G(y),f(x,f(y,G(y))))) = G(y).
f(f(G(f(x,y)),y),f(f(f(x,y),x),f(G(f(x,y)),y))) = f(f(x,y),x).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(y,f(f(x,y),x)),z))),f(z,y)) = z.
f(f(x,f(x,f(f(f(y,x),y),G(f(y,x))))),x) = G(f(y,x)).
f(f(f(x,f(x,f(f(x,x),y))),y),f(G(x),f(f(x,f(x,f(f(x,x),y))),y))) = G(x).
f(f(f(x,f(x,f(f(x,x),y))),f(f(x,f(x,f(f(x,x),y))),f(f(y,G(x)),z))),f(z,y)) = z.
f(f(f(x,f(x,G(y))),f(y,y)),f(f(x,y),f(f(x,f(x,G(y))),f(y,y)))) = f(x,y).
f(f(x,G(x)),f(G(f(x,x)),f(x,f(f(x,x),G(f(x,x)))))) = G(f(x,x)).
f(G(x),f(G(x),f(x,f(x,G(x))))) = G(x).
f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(G(x),G(x)))) = f(x,f(x,G(x))).
f(f(G(x),f(G(x),f(f(x,f(x,G(x))),G(x)))),G(x)) = G(x).
f(G(G(f(x,y))),f(y,f(f(f(y,f(y,f(f(f(x,y),x),G(f(x,y))))),y),f(y,f(y,f(f(f(x,y),x),G(f(x,y)))))))) = y.
f(f(x,f(x,G(y))),f(G(y),f(x,f(G(y),f(G(y),f(f(y,f(y,G(y))),G(y))))))) = G(y).
f(f(G(x),f(G(x),f(x,f(x,G(x))))),f(f(f(x,f(x,G(x))),f(G(x),G(x))),G(G(x)))) = f(f(x,f(x,G(x))),f(G(x),G(x))).
f(f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(f(f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(G(x),G(x))),f(G(f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(G(x),G(x))))),f(f(x,f(x,G(x))),f(G(x),G(x)))))) = f(f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(G(x),G(x))).
f(f(f(x,f(x,y)),f(y,f(z,u))),f(f(x,f(z,f(z,f(u,y)))),f(f(x,f(x,y)),f(y,f(z,u))))) = f(x,f(z,f(z,f(u,y)))).
f(f(f(x,f(y,z)),f(f(x,f(y,z)),f(f(u,f(y,f(y,f(z,x)))),f(u,f(u,x))))),f(x,f(y,z))) = f(u,f(u,x)).
f(G(x),f(f(x,f(y,z)),f(x,f(y,f(y,f(z,x)))))) = f(x,f(y,z)).
f(f(G(x),f(x,f(y,z))),f(f(x,f(y,f(y,f(z,x)))),f(G(x),f(x,f(y,z))))) = f(x,f(y,f(y,f(z,x)))).
f(G(f(x,x)),f(f(f(x,x),f(y,x)),f(f(x,x),f(y,f(y,G(x)))))) = f(f(x,x),f(y,x)).
f(f(f(f(x,f(x,f(y,z))),z),f(x,y)),f(f(f(x,f(x,f(y,z))),z),f(f(f(x,f(x,f(y,z))),z),f(x,y)))) = f(f(x,f(x,f(y,z))),z).
f(f(f(f(x,f(x,f(y,z))),z),f(f(f(x,f(x,f(y,z))),z),f(f(f(x,y),f(f(x,f(x,f(y,z))),z)),u))),f(u,f(x,y))) = u.
f(f(f(x,y),f(f(x,y),f(f(f(x,f(x,f(y,z))),z),f(f(x,f(x,f(y,z))),z)))),f(x,y)) = f(f(x,f(x,f(y,z))),z).
f(G(x),f(f(G(x),f(x,f(x,G(x)))),f(f(G(x),f(G(x),f(f(x,f(x,G(x))),G(x)))),G(x)))) = f(G(x),f(x,f(x,G(x)))).
f(f(f(x,f(x,f(y,f(z,u)))),f(f(y,f(z,u)),f(y,f(z,f(z,f(u,y)))))),f(f(x,G(y)),f(f(x,f(x,f(G(y),f(f(y,f(z,u)),f(y,f(z,f(z,f(u,y)))))))),f(f(y,f(z,u)),f(y,f(z,f(z,f(u,y)))))))) = f(x,G(y)).
f(f(f(G(x),f(x,f(y,z))),f(x,f(y,f(y,f(z,x))))),f(f(G(x),f(x,f(y,z))),f(f(G(x),f(x,f(y,z))),f(x,f(y,f(y,f(z,x))))))) = f(G(x),f(x,f(y,z))).
f(f(x,f(x,f(y,f(y,z)))),f(f(z,f(u,w)),f(x,f(f(z,f(u,w)),f(f(z,f(u,w)),f(f(y,f(u,f(u,f(w,z)))),f(y,f(y,z)))))))) = f(z,f(u,w)).
f(G(G(f(x,y))),f(y,f(G(f(x,y)),f(y,f(y,f(f(f(x,y),x),G(f(x,y)))))))) = y.
f(G(x),f(f(G(x),f(x,f(x,G(x)))),G(x))) = f(G(x),f(x,f(x,G(x)))).
f(f(G(x),f(G(x),f(x,f(x,G(x))))),f(G(x),f(G(x),f(G(x),f(x,f(x,G(x))))))) = G(x).
f(f(G(x),f(G(x),f(f(G(x),f(G(x),f(x,f(x,G(x))))),f(G(x),f(G(x),f(x,f(x,G(x)))))))),G(x)) = f(G(x),f(G(x),f(f(G(x),f(x,f(x,G(x)))),G(x)))).
f(G(x),f(G(x),f(G(x),f(G(x),f(x,f(x,G(x))))))) = G(x).
f(G(x),f(G(x),G(x))) = G(x).
f(f(x,f(x,G(y))),f(f(G(y),G(y)),f(x,G(y)))) = f(G(y),G(y)).
f(f(G(x),f(G(x),f(f(G(x),G(x)),y))),f(y,G(x))) = y.
G(x) = G(G(x)).
G(G(x)) = G(x).
f(G(x),f(f(G(x),f(y,z)),f(G(x),f(y,f(y,f(z,G(x))))))) = f(G(x),f(y,z)).
f(f(x,f(x,G(y))),f(G(y),f(x,f(G(y),G(G(y)))))) = G(G(y)).
f(G(f(x,y)),f(y,f(G(f(x,y)),f(y,f(y,f(f(f(x,y),x),G(f(x,y)))))))) = y.
f(f(G(x),f(G(x),f(f(G(x),G(x)),f(x,G(x))))),x) = f(x,G(x)).
f(f(f(G(x),f(G(x),f(f(G(x),G(x)),y))),f(f(G(x),f(G(x),f(f(G(x),G(x)),y))),G(f(y,G(x))))),f(f(f(y,G(x)),f(y,G(x))),y)) = f(f(y,G(x)),f(y,G(x))).
f(f(G(x),f(G(x),f(f(G(x),G(x)),f(G(x),f(G(x),f(f(x,f(x,G(x))),G(x))))))),G(x)) = f(G(x),f(G(x),f(f(x,f(x,G(x))),G(x)))).
f(f(x,f(x,G(y))),f(G(y),f(x,f(G(y),G(y))))) = G(G(y)).
f(f(x,f(x,G(y))),f(G(y),f(x,f(G(y),G(y))))) = G(y).
f(f(G(x),f(G(x),f(f(y,f(G(x),G(x))),f(y,f(y,G(x)))))),G(x)) = f(y,f(y,G(x))).
f(f(G(x),f(G(x),f(y,z))),f(f(G(x),f(y,f(y,f(z,G(x))))),f(G(x),f(G(x),f(y,z))))) = f(G(x),f(y,f(y,f(z,G(x))))).
f(G(x),f(f(f(x,f(x,G(x))),f(G(x),G(x))),G(G(x)))) = f(f(x,f(x,G(x))),f(G(x),G(x))).
f(G(x),f(f(f(x,f(x,G(x))),f(G(x),G(x))),G(x))) = f(f(x,f(x,G(x))),f(G(x),G(x))).
f(G(x),f(f(y,f(y,f(y,f(f(G(x),G(x)),G(x))))),f(f(y,f(y,G(x))),f(G(x),f(y,f(G(x),G(x))))))) = f(y,f(y,f(y,f(f(G(x),G(x)),G(x))))).
f(f(f(f(x,f(x,f(f(y,z),u))),u),f(f(f(x,f(x,f(f(y,z),u))),u),f(f(f(x,f(y,z)),f(f(x,f(x,f(f(y,z),u))),u)),f(y,f(y,f(z,x)))))),x) = f(y,f(y,f(z,x))).
f(f(f(x,f(y,z)),f(f(x,f(y,z)),f(f(u,f(f(x,f(y,z)),f(f(x,f(y,z)),f(f(w,f(y,f(y,f(z,x)))),f(w,f(w,x)))))),f(u,f(u,f(w,f(w,x))))))),f(x,f(y,z))) = f(u,f(u,f(w,f(w,x)))).
f(f(G(x),f(G(x),f(G(x),f(G(x),f(G(x),f(x,f(x,G(x)))))))),G(x)) = f(G(x),f(G(x),f(f(G(x),f(x,f(x,G(x)))),G(x)))).
f(f(G(x),G(x)),G(x)) = f(G(x),f(G(x),f(f(G(x),f(x,f(x,G(x)))),G(x)))).
f(G(x),f(G(x),f(f(G(x),f(x,f(x,G(x)))),G(x)))) = f(f(G(x),G(x)),G(x)).
f(G(x),f(G(x),f(x,f(x,G(x))))) = f(f(G(x),G(x)),G(x)).
f(f(G(x),G(x)),G(x)) = G(x).
f(f(G(x),f(G(x),f(G(x),G(f(G(x),G(x)))))),G(x)) = G(f(G(x),G(x))).
f(f(f(G(x),G(x)),G(x)),f(f(G(x),f(y,z)),f(f(G(x),G(x)),f(y,f(y,f(z,G(x))))))) = f(G(x),f(y,z)).
f(f(f(G(x),G(x)),G(x)),f(G(x),f(f(G(x),G(x)),f(G(x),f(G(x),f(f(x,f(x,G(x))),G(x))))))) = G(x).
f(G(x),f(f(y,f(y,f(y,G(x)))),f(f(y,f(y,G(x))),f(G(x),f(y,f(G(x),G(x))))))) = f(y,f(y,f(y,f(f(G(x),G(x)),G(x))))).
f(G(x),f(G(x),f(f(G(x),G(x)),f(G(x),f(G(x),f(f(x,f(x,G(x))),G(x))))))) = G(x).
f(G(x),G(x)) = f(G(x),f(G(x),f(f(x,f(x,G(x))),G(x)))).
f(G(x),f(G(x),f(f(x,f(x,G(x))),G(x)))) = f(G(x),G(x)).
f(f(x,f(x,f(G(y),G(y)))),f(f(G(y),f(f(y,f(y,G(y))),G(y))),f(x,G(y)))) = f(G(y),f(f(y,f(y,G(y))),G(y))).
f(f(G(x),f(G(x),f(f(f(x,f(x,G(x))),G(x)),G(x)))),f(G(x),G(x))) = G(x).
f(G(x),f(f(G(x),f(y,z)),f(f(G(x),G(x)),f(y,f(y,f(z,G(x))))))) = f(G(x),f(y,z)).
f(G(x),f(f(G(x),G(y)),f(f(G(x),G(x)),f(f(G(y),G(y)),f(f(G(y),G(y)),f(G(y),G(x))))))) = f(G(x),f(f(G(y),G(y)),G(y))).
f(f(f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(G(x),f(f(x,f(x,G(x))),G(x)))),f(f(f(x,f(x,G(x))),G(x)),G(x))) = f(f(x,f(x,G(x))),G(x)).
f(f(G(x),G(x)),f(f(G(x),f(f(x,f(x,G(x))),G(x))),f(G(x),G(x)))) = f(G(x),f(f(x,f(x,G(x))),G(x))).
f(G(x),f(f(y,f(y,f(y,G(x)))),G(x))) = f(y,f(y,f(y,f(f(G(x),G(x)),G(x))))).
f(G(x),f(f(y,f(y,f(y,G(x)))),G(x))) = f(y,f(y,f(y,G(x)))).
f(f(G(x),f(y,f(y,f(y,G(x))))),f(G(x),f(G(x),f(y,f(y,f(y,G(x))))))) = G(x).
f(G(x),f(f(G(x),G(x)),f(f(G(x),G(x)),G(f(G(x),G(x)))))) = f(G(x),f(f(G(x),G(x)),G(x))).
f(G(x),f(f(G(x),G(x)),f(f(G(x),G(x)),G(f(G(x),G(x)))))) = f(G(x),G(x)).
f(G(x),f(f(f(x,f(x,G(x))),G(x)),G(x))) = f(f(x,f(x,G(x))),G(x)).
f(f(G(x),f(f(x,f(x,G(x))),G(x))),f(G(x),G(x))) = G(x).
f(f(G(x),G(x)),G(x)) = f(G(x),f(f(x,f(x,G(x))),G(x))).
f(G(x),f(f(x,f(x,G(x))),G(x))) = f(f(G(x),G(x)),G(x)).
f(G(x),f(f(x,f(x,G(x))),G(x))) = G(x).
f(f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x)))),G(x)) = G(x).
f(G(x),f(G(x),f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x))))))) = f(G(x),f(f(x,f(x,G(x))),G(x))).
f(f(G(x),f(G(x),f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x))))))),G(x)) = f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x)))).
f(G(x),f(G(x),f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x))))))) = G(x).
f(G(x),G(x)) = f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x)))).
f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x)))) = f(G(x),G(x)).
f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))))),f(f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))),f(f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))),f(f(x,f(x,f(y,f(y,x)))),f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))))))) = f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))).
f(f(f(x,f(x,f(y,f(z,u)))),f(f(y,f(z,u)),f(y,f(z,f(z,f(u,y)))))),f(f(x,G(y)),f(f(x,f(x,f(y,f(z,u)))),f(f(y,f(z,u)),f(y,f(z,f(z,f(u,y)))))))) = f(x,G(y)).
f(f(f(x,f(x,x)),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))),f(f(f(x,f(x,x)),G(x)),f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(x,f(x,x)))))),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(G(x),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))),f(f(f(x,f(x,x)),G(x)),f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(x,f(x,x)))))),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(G(x),f(f(x,f(x,G(x))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))),f(f(f(x,f(x,x)),G(x)),f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(x,f(x,x)))))),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(G(x),f(f(x,f(x,G(x))),f(x,f(x,f(x,f(G(x),x)))))),f(f(f(x,f(x,x)),G(x)),f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(x,f(x,x)))))),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(x,f(x,G(x))),f(f(f(x,f(x,x)),G(x)),f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(x,f(x,x)))))),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(f(f(x,f(x,x)),f(f(x,f(x,x)),f(x,f(x,f(x,f(x,x)))))),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(f(G(x),f(f(x,f(x,x)),f(x,f(x,f(x,f(x,x)))))),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(f(G(x),f(G(x),f(x,f(x,f(x,f(x,x)))))),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(f(G(x),f(G(x),f(x,f(x,G(x))))),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(G(x),f(f(x,f(x,f(x,f(x,x)))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(G(x),f(f(x,f(x,G(x))),f(x,f(x,f(x,f(f(x,f(x,x)),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(G(x),f(f(x,f(x,G(x))),f(x,f(x,f(x,f(G(x),x)))))))) = f(f(x,f(x,x)),G(x)).
f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(x,f(x,G(x))))) = f(f(x,f(x,x)),G(x)).
f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(x,f(x,G(x))))) = f(G(x),G(x)).
f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x))))) = f(x,f(x,G(x))).
f(f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x))))),f(f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x))))))) = f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(x,f(x,G(x))))))).
f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(G(x),G(x))) = f(x,f(x,G(x))).
f(f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(x,f(x,G(x)))),f(G(x),f(f(f(x,f(x,G(x))),f(G(x),G(x))),G(x)))) = G(x).
f(f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(G(x),G(x)))) = G(x).
f(f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(G(f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(G(x),G(x))))),f(f(x,f(x,G(x))),f(G(x),G(x)))))) = f(f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(G(x),G(x))).
f(f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(G(x),G(x)))))) = f(f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(G(x),G(x))).
f(f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(G(x),G(x)))))) = f(f(x,f(x,G(x))),f(G(x),G(x))).
f(f(G(f(x,f(x,G(x)))),f(G(x),G(x))),f(f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x))))))) = f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(x,f(x,G(x))))))).
f(f(G(f(x,f(x,G(x)))),f(G(x),G(x))),f(f(G(x),G(x)),f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x))))))) = f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(x,f(x,G(x))))))).
f(f(G(f(x,f(x,G(x)))),f(G(x),G(x))),f(f(G(x),G(x)),f(G(f(x,f(x,G(x)))),f(G(x),G(x))))) = f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(f(G(x),G(x)),f(x,f(x,G(x))))))).
f(f(G(f(x,f(x,G(x)))),f(G(x),G(x))),f(f(G(x),G(x)),f(G(f(x,f(x,G(x)))),f(G(x),G(x))))) = f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x)))).
f(f(G(f(x,f(x,G(x)))),f(G(x),G(x))),f(f(G(x),G(x)),f(G(f(x,f(x,G(x)))),f(G(x),G(x))))) = f(G(x),G(x)).
f(f(x,f(x,f(y,f(y,x)))),f(f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))),f(f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))),f(f(x,f(x,f(y,f(y,x)))),f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))))))) = f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))).
f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))),f(f(x,f(x,f(y,f(y,x)))),f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))))))) = f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))).
f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))))))) = f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))).
f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))) = f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))))))).
f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))) = f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(x,f(x,f(y,f(y,x)))))).
f(f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(f(x,f(x,f(y,f(y,x)))),f(f(x,f(x,f(y,f(y,x)))),f(f(y,f(x,f(x,f(f(y,f(y,x)),x)))),f(y,f(y,x)))))),f(x,f(x,f(y,f(y,x))))))),f(x,f(x,f(y,f(y,x))))) = G(f(x,f(x,f(y,f(y,x))))).
G(f(x,f(x,f(y,f(y,x))))) = f(x,f(x,f(y,f(y,x)))).
G(f(x,f(x,G(x)))) = f(x,f(x,f(x,f(x,x)))).
f(x,f(x,f(x,f(x,x)))) = G(f(x,f(x,G(x)))).
f(x,f(x,G(x))) = G(f(x,f(x,G(x)))).
G(f(x,f(x,G(x)))) = f(x,f(x,G(x))).
f(f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x)))),f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(G(x),G(x)))))) = f(f(x,f(x,G(x))),f(G(x),G(x))).
f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(f(G(x),G(x)),f(G(f(x,f(x,G(x)))),f(G(x),G(x))))) = f(G(x),G(x)).
f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(f(G(x),G(x)),f(f(x,f(x,G(x))),f(G(x),G(x))))) = f(G(x),G(x)).
f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(x,f(x,G(x)))) = f(G(x),G(x)).
f(f(G(x),G(x)),f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(G(f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(G(x),G(x)))))) = f(f(x,f(x,G(x))),f(G(x),G(x))).
f(f(G(x),G(x)),f(f(f(x,f(x,G(x))),f(G(x),G(x))),f(f(x,f(x,G(x))),f(f(x,f(x,G(x))),f(G(x),G(x)))))) = f(f(x,f(x,G(x))),f(G(x),G(x))).
f(f(G(x),G(x)),f(x,f(x,G(x)))) = f(f(x,f(x,G(x))),f(G(x),G(x))).
f(f(x,f(x,G(x))),f(G(x),G(x))) = f(f(G(x),G(x)),f(x,f(x,G(x)))).
f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,f(x,G(x))))) = f(x,f(x,G(x))).
f(f(f(f(G(x),G(x)),f(x,f(x,G(x)))),f(x,f(x,G(x)))),f(f(x,f(x,G(x))),f(G(x),G(x)))) = G(x).
f(f(f(G(x),G(x)),f(x,f(x,G(x)))),f(x,f(x,G(x)))) = f(G(x),G(x)).
f(f(f(f(G(x),G(x)),f(x,f(x,G(x)))),f(x,f(x,G(x)))),f(f(G(x),G(x)),f(x,f(x,G(x))))) = G(x).
f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,f(x,G(x))))) = G(x).
G(x) = f(x,f(x,G(x))).
f(x,f(x,G(x))) = G(x).
f(f(f(x,G(x)),G(x)),f(f(x,x),f(f(x,f(x,f(x,G(x)))),G(x)))) = f(x,x).
f(f(f(x,x),f(f(x,x),f(f(f(x,G(x)),G(x)),f(f(x,f(x,f(x,G(x)))),G(x))))),f(x,x)) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(G(x),f(f(G(x),G(x)),f(x,G(x)))) = f(G(x),G(x)).
f(f(f(f(x,G(x)),G(x)),f(x,x)),f(f(f(x,f(x,f(x,G(x)))),G(x)),f(f(f(x,f(x,f(x,G(x)))),G(x)),f(x,x)))) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(G(x),G(f(G(x),G(x)))) = f(G(x),G(x)).
f(f(G(x),f(G(x),f(G(x),G(x)))),G(x)) = G(f(G(x),G(x))).
f(f(G(x),f(G(x),G(x))),x) = f(x,G(x)).
f(G(x),x) = f(x,G(x)).
f(f(x,f(x,f(y,G(y)))),f(y,f(x,G(y)))) = y.
f(f(G(f(x,y)),f(f(x,y),G(f(x,y)))),f(y,f(G(f(x,y)),x))) = y.
f(f(x,f(x,f(f(y,G(y)),f(G(y),f(G(y),f(y,x)))))),x) = f(G(y),f(G(y),f(y,x))).
f(f(f(x,f(x,f(f(x,x),x))),f(f(x,f(x,f(f(x,x),x))),f(f(G(x),x),y))),f(y,x)) = y.
f(f(G(x),G(x)),G(x)) = G(f(G(x),G(x))).
G(f(G(x),G(x))) = G(x).
f(G(x),f(f(f(G(x),G(x)),f(y,z)),f(f(G(x),G(x)),f(y,f(y,f(z,f(G(x),G(x)))))))) = f(f(G(x),G(x)),f(y,z)).
f(G(x),f(f(f(G(x),G(x)),f(y,G(x))),f(f(G(x),G(x)),f(y,f(y,G(G(x))))))) = f(f(G(x),G(x)),f(y,G(x))).
f(x,f(f(x,x),f(f(x,f(x,f(x,G(x)))),G(x)))) = f(x,x).
f(x,f(f(x,x),f(f(x,G(x)),G(x)))) = f(x,x).
f(x,f(f(x,x),x)) = f(x,x).
f(f(f(x,f(x,x)),f(f(x,f(x,f(f(x,x),x))),f(f(G(x),x),y))),f(y,x)) = y.
f(f(G(x),f(f(x,f(x,f(f(x,x),x))),f(f(G(x),x),y))),f(y,x)) = y.
f(f(G(x),f(f(x,f(x,x)),f(f(G(x),x),y))),f(y,x)) = y.
f(f(G(x),f(G(x),f(f(G(x),x),y))),f(y,x)) = y.
f(f(G(x),f(G(x),f(f(x,G(x)),y))),f(y,x)) = y.
f(G(x),f(f(f(G(x),G(x)),f(y,G(x))),f(f(G(x),G(x)),f(y,f(y,G(x)))))) = f(f(G(x),G(x)),f(y,G(x))).
f(G(x),f(f(f(G(x),G(x)),f(x,G(x))),f(f(G(x),G(x)),G(x)))) = f(f(G(x),G(x)),f(x,G(x))).
f(G(x),f(f(f(G(x),G(x)),f(x,G(x))),G(x))) = f(f(G(x),G(x)),f(x,G(x))).
f(f(f(x,x),f(f(x,x),f(x,f(f(x,f(x,f(x,G(x)))),G(x))))),f(x,x)) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(f(f(x,x),f(f(x,x),f(x,f(f(x,G(x)),G(x))))),f(x,x)) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(f(f(x,x),f(f(x,x),f(x,x))),f(x,x)) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(G(f(x,x)),f(x,x)) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(f(x,f(x,f(x,G(x)))),G(x)) = f(G(f(x,x)),f(x,x)).
f(f(x,f(x,f(x,G(x)))),G(x)) = f(f(x,x),G(f(x,x))).
f(f(x,G(x)),G(x)) = f(f(x,x),G(f(x,x))).
f(f(x,x),G(f(x,x))) = f(f(x,G(x)),G(x)).
f(f(x,x),G(f(x,x))) = x.
f(f(x,G(x)),f(G(f(x,x)),f(x,x))) = G(f(x,x)).
f(f(x,x),x) = G(f(x,x)).
f(f(x,x),f(f(x,x),f(x,x))) = f(f(x,x),x).
f(f(x,G(x)),f(f(x,x),G(f(x,x)))) = G(f(x,x)).
f(f(x,G(x)),x) = G(f(x,x)).
f(f(x,f(x,x)),f(f(f(x,f(x,f(x,G(x)))),G(x)),f(f(f(x,f(x,f(x,G(x)))),G(x)),f(x,x)))) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(G(x),f(f(f(x,f(x,f(x,G(x)))),G(x)),f(f(f(x,f(x,f(x,G(x)))),G(x)),f(x,x)))) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(G(x),f(f(f(x,G(x)),G(x)),f(f(f(x,f(x,f(x,G(x)))),G(x)),f(x,x)))) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(G(x),f(x,f(f(f(x,f(x,f(x,G(x)))),G(x)),f(x,x)))) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(G(x),f(x,f(f(f(x,G(x)),G(x)),f(x,x)))) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(G(x),f(x,f(x,f(x,x)))) = f(f(x,f(x,f(x,G(x)))),G(x)).
f(f(x,f(x,f(x,G(x)))),G(x)) = f(G(x),f(x,f(x,f(x,x)))).
f(f(x,f(x,f(x,G(x)))),G(x)) = f(G(x),f(x,G(x))).
f(f(x,G(x)),G(x)) = f(G(x),f(x,G(x))).
f(G(x),f(x,G(x))) = x.
f(f(G(x),x),f(G(x),f(G(x),x))) = G(x).
f(f(x,f(x,f(G(x),G(x)))),x) = G(x).
f(f(f(x,f(x,f(G(y),f(G(y),y)))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),y)))),f(f(x,G(G(y))),f(f(x,f(x,f(G(y),f(G(y),y)))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(x,y),f(y,f(G(f(x,y)),x))) = y.
f(f(x,f(x,f(f(G(f(y,x)),y),f(y,x)))),x) = f(y,x).
f(f(x,G(x)),f(G(x),f(G(x),x))) = G(x).
f(f(x,G(x)),f(G(x),f(x,G(x)))) = G(x).
f(f(x,G(x)),x) = G(x).
G(x) = G(f(x,x)).
G(f(x,x)) = G(x).
f(f(x,x),G(x)) = x.
f(f(x,x),x) = G(x).
f(G(x),f(f(x,x),G(f(x,x)))) = f(x,x).
f(f(f(x,x),x),f(f(G(x),f(y,z)),f(f(x,x),f(y,f(y,f(z,G(x))))))) = f(G(x),f(y,z)).
f(f(f(x,x),f(f(x,x),G(x))),f(f(G(x),G(x)),x)) = f(G(x),G(x)).
f(f(f(f(x,y),f(x,y)),G(f(x,y))),f(y,f(f(f(x,y),f(x,y)),x))) = y.
f(f(x,f(x,f(y,f(f(x,y),f(x,y))))),G(f(x,y))) = f(f(x,y),f(x,y)).
f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))) = f(f(x,x),x).
f(x,G(x)) = f(x,x).
f(f(x,f(x,f(y,y))),f(G(y),f(x,y))) = G(y).
f(G(x),f(f(G(x),G(x)),f(x,x))) = f(G(x),G(x)).
f(G(x),x) = f(x,x).
f(f(x,f(x,f(y,y))),f(y,f(x,G(y)))) = y.
f(f(x,f(x,f(f(y,y),f(G(y),f(G(y),f(y,x)))))),x) = f(G(y),f(G(y),f(y,x))).
f(f(G(x),f(G(x),f(f(x,x),y))),f(y,x)) = y.
f(G(x),f(f(f(G(x),G(x)),f(x,x)),G(x))) = f(f(G(x),G(x)),f(x,G(x))).
f(f(x,x),f(x,x)) = x.
f(G(x),f(x,x)) = x.
f(f(x,f(x,f(y,G(f(x,y))))),f(f(x,y),f(x,y))) = G(f(x,y)).
f(f(f(f(x,f(x,y)),f(y,y)),f(f(f(x,f(x,f(G(y),f(y,y)))),f(y,y)),f(f(f(x,G(y)),f(f(x,f(x,f(G(y),f(y,y)))),f(y,y))),z))),f(z,f(x,G(y)))) = z.
f(f(x,f(x,y)),f(f(y,y),f(x,f(y,y)))) = f(y,y).
f(f(f(x,x),f(f(x,x),f(f(x,x),y))),f(y,x)) = y.
f(G(x),f(f(x,G(x)),G(x))) = f(x,x).
f(G(x),f(G(x),f(x,G(x)))) = f(x,x).
f(f(x,x),f(x,f(G(x),G(x)))) = x.
f(f(f(f(x,x),x),f(f(x,f(G(x),G(x))),f(x,f(G(x),f(G(x),f(G(x),x)))))),f(f(f(x,x),G(x)),f(f(f(x,x),f(f(x,x),f(x,f(G(x),G(x))))),f(f(x,f(G(x),G(x))),f(x,f(G(x),f(G(x),f(G(x),x)))))))) = f(f(x,x),G(x)).
f(f(f(x,f(x,f(y,f(x,y)))),f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(x,y)))) = G(f(x,y)).
f(f(f(G(x),f(G(x),G(x))),f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(x,f(x,f(x,f(G(x),G(x)))))))),f(f(G(x),G(f(G(x),G(x)))),f(f(G(x),f(G(x),f(f(G(x),G(x)),f(x,x)))),f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(x,f(x,f(x,f(G(x),G(x)))))))))) = f(G(x),G(f(G(x),G(x)))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,f(y,y)),f(f(x,f(x,y)),f(y,y)))) = f(x,f(y,y)).
f(f(G(x),f(G(x),f(f(x,x),f(x,f(x,f(f(G(f(y,x)),y),f(y,x))))))),f(y,x)) = f(x,f(x,f(f(G(f(y,x)),y),f(y,x)))).
f(f(f(x,x),x),f(f(G(x),G(x)),x)) = f(G(x),G(x)).
f(G(x),f(f(G(x),G(x)),x)) = f(G(x),G(x)).
f(G(f(G(x),G(x))),f(f(f(G(x),G(x)),x),f(f(G(x),f(f(G(x),G(x)),x)),G(x)))) = f(f(G(x),G(x)),x).
f(f(x,y),f(y,f(f(f(x,y),f(x,y)),x))) = y.
f(x,f(f(x,y),f(f(f(f(G(f(z,y)),f(G(f(z,y)),f(f(y,f(f(z,y),z)),x))),f(x,y)),f(f(G(f(z,y)),f(G(f(z,y)),f(f(y,f(f(z,y),z)),x))),f(x,y))),f(G(f(z,y)),f(G(f(z,y)),f(f(y,f(f(z,y),z)),x)))))) = f(x,y).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(f(x,y),f(x,y)))))))),f(f(x,y),f(x,y))) = f(x,f(x,f(y,f(f(x,y),f(x,y))))).
f(G(x),f(f(f(G(x),G(x)),f(x,x)),G(x))) = f(f(G(x),G(x)),f(x,x)).
f(f(f(x,x),f(f(x,x),f(f(x,x),f(x,f(x,f(f(y,y),f(G(y),f(G(y),f(y,x))))))))),f(G(y),f(G(y),f(y,x)))) = f(x,f(x,f(f(y,y),f(G(y),f(G(y),f(y,x)))))).
f(G(x),f(f(G(x),f(y,z)),f(f(x,x),f(y,f(y,f(z,G(x))))))) = f(G(x),f(y,z)).
f(G(x),f(f(G(x),f(y,f(x,x))),f(f(x,x),f(y,f(y,x))))) = f(G(x),f(y,f(x,x))).
f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))) = G(x).
f(G(x),f(f(f(G(x),G(x)),x),f(f(G(x),f(f(G(x),G(x)),x)),G(x)))) = f(f(G(x),G(x)),x).
f(G(x),f(f(f(G(x),G(x)),x),f(f(G(x),G(x)),G(x)))) = f(f(G(x),G(x)),x).
f(G(x),f(f(f(G(x),G(x)),x),G(x))) = f(f(G(x),G(x)),x).
f(f(f(f(G(x),f(f(G(x),G(x)),x)),G(x)),f(f(f(G(x),f(G(x),f(f(f(G(x),G(x)),x),G(x)))),G(x)),f(f(f(G(x),f(f(G(x),G(x)),x)),f(f(G(x),f(G(x),f(f(f(G(x),G(x)),x),G(x)))),G(x))),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(f(f(x,y),f(f(x,y),f(x,y))),f(f(x,y),f(f(x,f(x,f(y,z))),z))),f(G(f(f(x,y),f(f(x,f(x,f(y,z))),z))),f(f(f(x,y),f(f(x,y),f(f(f(x,f(x,f(y,z))),z),f(f(x,y),f(f(x,f(x,f(y,z))),z))))),f(f(x,y),f(f(x,f(x,f(y,z))),z))))) = G(f(f(x,y),f(f(x,f(x,f(y,z))),z))).
f(f(f(f(x,f(x,y)),f(y,y)),f(f(f(x,f(x,y)),f(y,y)),f(f(f(x,G(y)),f(f(x,f(x,f(G(y),f(y,y)))),f(y,y))),z))),f(z,f(x,G(y)))) = z.
f(f(f(f(x,f(x,y)),f(y,y)),f(f(f(x,f(x,y)),f(y,y)),f(f(f(x,G(y)),f(f(x,f(x,y)),f(y,y))),z))),f(z,f(x,G(y)))) = z.
f(f(f(x,f(x,f(G(y),f(y,G(y))))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),y)))),f(f(x,G(G(y))),f(f(x,f(x,f(G(y),f(G(y),y)))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),y)))),f(f(x,G(G(y))),f(f(x,f(x,f(G(y),f(G(y),y)))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(f(G(y),f(y,G(y))),f(G(y),f(G(y),y)))),f(f(x,G(G(y))),f(f(x,f(x,f(G(y),f(G(y),y)))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,f(G(y),f(G(y),y)))),f(f(x,G(G(y))),f(f(x,f(x,f(G(y),f(G(y),y)))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,f(G(y),f(y,G(y))))),f(f(x,G(G(y))),f(f(x,f(x,f(G(y),f(G(y),y)))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,G(G(y))),f(f(x,f(x,f(G(y),f(G(y),y)))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,G(y)),f(f(x,f(x,f(G(y),f(G(y),y)))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,G(y)),f(f(x,f(x,f(G(y),f(y,G(y))))),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,G(y)),f(f(x,f(x,y)),f(f(G(y),f(G(y),y)),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,G(y)),f(f(x,f(x,y)),f(f(G(y),f(y,G(y))),f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,G(y)),f(f(x,f(x,y)),f(y,f(G(y),f(G(y),f(G(y),f(y,G(y))))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,G(y)),f(f(x,f(x,y)),f(y,f(G(y),f(G(y),y)))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,G(y)),f(f(x,f(x,y)),f(y,f(G(y),f(y,G(y))))))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,G(y)),f(f(x,f(x,y)),f(y,y)))) = f(x,G(G(y))).
f(f(f(x,f(x,y)),f(y,y)),f(f(x,G(y)),f(f(x,f(x,y)),f(y,y)))) = f(x,G(y)).
f(f(G(x),f(f(x,f(G(x),G(x))),f(x,f(G(x),f(G(x),f(G(x),x)))))),f(f(f(x,x),G(x)),f(f(f(x,x),f(f(x,x),f(x,f(G(x),G(x))))),f(f(x,f(G(x),G(x))),f(x,f(G(x),f(G(x),f(G(x),x)))))))) = f(f(x,x),G(x)).
f(f(x,f(G(x),G(x))),f(f(f(x,x),G(x)),f(f(f(x,x),f(f(x,x),f(x,f(G(x),G(x))))),f(f(x,f(G(x),G(x))),f(x,f(G(x),f(G(x),f(G(x),x)))))))) = f(f(x,x),G(x)).
f(f(x,f(G(x),G(x))),f(x,f(f(f(x,x),f(f(x,x),f(x,f(G(x),G(x))))),f(f(x,f(G(x),G(x))),f(x,f(G(x),f(G(x),f(G(x),x)))))))) = f(f(x,x),G(x)).
f(f(x,f(G(x),G(x))),f(x,f(f(f(x,x),x),f(f(x,f(G(x),G(x))),f(x,f(G(x),f(G(x),f(G(x),x)))))))) = f(f(x,x),G(x)).
f(f(x,f(G(x),G(x))),f(x,f(G(x),f(f(x,f(G(x),G(x))),f(x,f(G(x),f(G(x),f(G(x),x)))))))) = f(f(x,x),G(x)).
f(f(x,f(G(x),G(x))),f(x,f(x,f(G(x),G(x))))) = f(f(x,x),G(x)).
f(f(x,f(G(x),G(x))),f(x,f(x,f(G(x),G(x))))) = x.
f(f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(x,f(G(x),G(x)))))),x) = f(x,f(G(x),G(x))).
f(x,f(f(x,f(x,f(G(x),G(x)))),f(f(f(f(x,f(G(x),G(x))),f(x,f(x,f(G(x),G(x))))),f(f(x,f(G(x),G(x))),f(x,f(x,f(G(x),G(x)))))),f(x,f(G(x),G(x)))))) = f(x,f(x,f(G(x),G(x)))).
f(x,f(f(x,f(x,f(G(x),G(x)))),f(f(x,f(f(x,f(G(x),G(x))),f(x,f(x,f(G(x),G(x)))))),f(x,f(G(x),G(x)))))) = f(x,f(x,f(G(x),G(x)))).
f(x,f(f(x,f(x,f(G(x),G(x)))),f(f(x,x),f(x,f(G(x),G(x)))))) = f(x,f(x,f(G(x),G(x)))).
f(x,f(f(x,f(x,f(G(x),G(x)))),x)) = f(x,f(x,f(G(x),G(x)))).
f(x,G(x)) = f(x,f(x,f(G(x),G(x)))).
f(x,f(x,f(G(x),G(x)))) = f(x,G(x)).
f(x,f(x,f(G(x),G(x)))) = f(x,x).
f(x,f(f(x,y),f(f(x,f(f(G(f(z,y)),f(G(f(z,y)),f(f(y,f(f(z,y),z)),x))),f(x,y))),f(G(f(z,y)),f(G(f(z,y)),f(f(y,f(f(z,y),z)),x)))))) = f(x,y).
f(x,f(f(x,y),f(f(x,x),f(G(f(z,y)),f(G(f(z,y)),f(f(y,f(f(z,y),z)),x)))))) = f(x,y).
f(f(f(f(x,x),f(x,f(x,f(G(x),G(x))))),f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(x,f(G(x),G(x)))))),x) = f(x,f(G(x),G(x))).
f(f(f(f(x,x),f(x,x)),f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(x,f(G(x),G(x)))))),x) = f(x,f(G(x),G(x))).
f(f(x,f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(x,f(G(x),G(x)))))),x) = f(x,f(G(x),G(x))).
f(f(x,f(f(f(x,x),f(x,f(x,f(G(x),G(x))))),f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(x,f(G(x),G(x)))))),x) = f(x,f(G(x),G(x))).
f(f(x,f(f(f(x,x),f(x,x)),f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(x,f(G(x),G(x)))))),x) = f(x,f(G(x),G(x))).
f(f(x,f(x,f(f(f(x,f(x,f(G(x),G(x)))),f(x,f(x,f(G(x),G(x))))),f(x,f(G(x),G(x)))))),x) = f(x,f(G(x),G(x))).
f(f(x,f(x,f(f(f(x,x),f(x,f(x,f(G(x),G(x))))),f(x,f(G(x),G(x)))))),x) = f(x,f(G(x),G(x))).
f(f(x,f(x,f(f(f(x,x),f(x,x)),f(x,f(G(x),G(x)))))),x) = f(x,f(G(x),G(x))).
f(f(x,f(x,f(x,f(x,f(G(x),G(x)))))),x) = f(x,f(G(x),G(x))).
f(f(x,f(x,f(x,x))),x) = f(x,f(G(x),G(x))).
f(f(x,G(x)),x) = f(x,f(G(x),G(x))).
f(x,f(G(x),G(x))) = f(f(x,G(x)),x).
f(x,f(G(x),G(x))) = G(x).
f(f(x,x),f(G(f(x,x)),G(f(x,x)))) = G(x).
f(f(x,x),f(G(x),G(f(x,x)))) = G(x).
f(f(x,x),f(G(x),G(x))) = G(x).
f(G(x),f(f(G(x),G(x)),f(f(f(f(x,x),f(G(x),G(x))),f(f(x,x),f(G(x),G(x)))),f(x,x)))) = f(G(x),G(x)).
f(G(x),f(f(G(x),G(x)),f(f(G(x),f(f(x,x),f(G(x),G(x)))),f(x,x)))) = f(G(x),G(x)).
f(G(x),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,x)))) = f(G(x),G(x)).
f(f(G(x),f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(x,f(x,f(x,f(G(x),G(x)))))))),f(f(G(x),G(f(G(x),G(x)))),f(f(G(x),f(G(x),f(f(G(x),G(x)),f(x,x)))),f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(x,f(x,f(x,f(G(x),G(x)))))))))) = f(G(x),G(f(G(x),G(x)))).
f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(f(G(x),G(x)))),f(f(G(x),f(G(x),f(f(G(x),G(x)),f(x,x)))),f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(x,f(x,f(x,f(G(x),G(x)))))))))) = f(G(x),G(f(G(x),G(x)))).
f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(f(G(x),f(G(x),f(f(G(x),G(x)),f(x,x)))),f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(x,f(x,f(x,f(G(x),G(x)))))))))) = f(G(x),G(f(G(x),G(x)))).
f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(f(G(x),f(G(x),G(x))),f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(x,f(x,f(x,f(G(x),G(x)))))))))) = f(G(x),G(f(G(x),G(x)))).
f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(G(x),f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(x,f(x,f(x,f(G(x),G(x)))))))))) = f(G(x),G(f(G(x),G(x)))).
f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,x)))) = f(G(x),G(f(G(x),G(x)))).
f(f(f(G(x),G(x)),f(x,x)),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,x)))) = f(G(x),G(x)).
f(f(f(f(G(x),G(x)),G(x)),f(f(f(G(x),f(G(x),f(f(f(G(x),G(x)),x),G(x)))),G(x)),f(f(f(G(x),f(f(G(x),G(x)),x)),f(f(G(x),f(G(x),f(f(f(G(x),G(x)),x),G(x)))),G(x))),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(f(f(G(x),f(G(x),f(f(f(G(x),G(x)),x),G(x)))),G(x)),f(f(f(G(x),f(f(G(x),G(x)),x)),f(f(G(x),f(G(x),f(f(f(G(x),G(x)),x),G(x)))),G(x))),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(f(f(G(x),f(f(G(x),G(x)),x)),G(x)),f(f(f(G(x),f(f(G(x),G(x)),x)),f(f(G(x),f(G(x),f(f(f(G(x),G(x)),x),G(x)))),G(x))),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(f(f(G(x),G(x)),G(x)),f(f(f(G(x),f(f(G(x),G(x)),x)),f(f(G(x),f(G(x),f(f(f(G(x),G(x)),x),G(x)))),G(x))),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(G(x),f(f(f(G(x),f(f(G(x),G(x)),x)),f(f(G(x),f(G(x),f(f(f(G(x),G(x)),x),G(x)))),G(x))),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(G(x),f(f(f(G(x),G(x)),f(f(G(x),f(G(x),f(f(f(G(x),G(x)),x),G(x)))),G(x))),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(G(x),f(f(f(G(x),G(x)),f(f(G(x),f(f(G(x),G(x)),x)),G(x))),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(G(x),f(f(f(G(x),G(x)),f(f(G(x),G(x)),G(x))),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(G(x),f(f(f(G(x),G(x)),G(x)),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(G(x),f(G(x),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x))))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(G(x),f(G(x),f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,x)))))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),f(G(x),f(G(x),G(x)))),G(x)) = f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))).
f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))) = f(f(G(x),f(G(x),f(G(x),G(x)))),G(x)).
f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))) = f(f(G(x),G(x)),G(x)).
f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,G(x)))) = G(x).
f(f(G(x),G(x)),f(f(G(x),G(x)),f(x,x))) = G(x).
f(f(f(G(x),G(x)),f(x,x)),G(x)) = f(G(x),G(x)).
f(G(x),f(G(x),G(x))) = f(f(G(x),G(x)),f(x,x)).
f(f(G(x),G(x)),f(x,x)) = f(G(x),f(G(x),G(x))).
f(f(G(x),G(x)),f(x,x)) = G(x).
f(f(G(f(x,x)),G(f(x,x))),f(f(x,x),f(x,x))) = G(x).
f(f(G(x),G(f(x,x))),f(f(x,x),f(x,x))) = G(x).
f(f(G(x),G(x)),f(f(x,x),f(x,x))) = G(x).
f(f(G(x),G(x)),x) = G(x).
f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),f(y,f(f(G(f(x,y)),G(f(x,y))),x))) = y.
f(f(x,f(x,f(y,f(G(f(x,y)),G(f(x,y)))))),G(f(x,y))) = f(G(f(x,y)),G(f(x,y))).
f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(G(f(x,y)),G(f(x,y))))))))) = f(f(G(f(x,y)),G(f(x,y))),f(x,y)).
f(G(f(x,y)),f(y,f(f(G(f(x,y)),G(f(x,y))),x))) = y.
f(f(x,f(x,f(f(f(G(f(y,x)),G(f(y,x))),y),G(f(y,x))))),x) = G(f(y,x)).
f(G(f(f(x,y),f(x,y))),f(G(f(x,y)),f(f(G(f(f(x,f(x,f(y,f(f(x,y),f(x,y))))),G(f(x,y)))),G(f(f(x,f(x,f(y,f(f(x,y),f(x,y))))),G(f(x,y))))),f(x,f(x,f(y,f(f(x,y),f(x,y)))))))) = G(f(x,y)).
f(G(x),f(f(x,f(f(G(f(y,x)),G(f(y,x))),y)),f(f(G(f(G(f(y,x)),f(x,f(f(G(f(y,x)),G(f(y,x))),y)))),G(f(G(f(y,x)),f(x,f(f(G(f(y,x)),G(f(y,x))),y))))),G(f(y,x))))) = f(x,f(f(G(f(y,x)),G(f(y,x))),y)).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(G(f(x,y)),G(f(x,y))))))))),f(G(f(x,y)),G(f(x,y)))) = f(x,f(x,f(y,f(G(f(x,y)),G(f(x,y)))))).
f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(G(f(x,y)),G(f(x,y))))))))) = G(f(x,y)).
f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))) = f(x,f(x,f(y,f(G(f(x,y)),G(f(x,y)))))).
f(x,f(x,f(y,f(G(f(x,y)),G(f(x,y)))))) = f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))).
f(x,f(x,f(y,f(G(f(x,y)),G(f(x,y)))))) = G(f(x,y)).
f(f(x,f(x,f(y,z))),f(f(x,f(x,f(y,z))),f(f(z,f(x,y)),f(G(z),G(f(f(x,f(x,f(y,z))),f(z,f(x,y)))))))) = G(f(f(x,f(x,f(y,z))),f(z,f(x,y)))).
f(f(x,y),f(f(x,y),f(f(y,f(G(f(x,y)),x)),f(G(y),G(f(f(x,y),f(y,f(G(f(x,y)),x)))))))) = G(f(f(x,y),f(y,f(G(f(x,y)),x)))).
f(f(x,y),f(f(x,y),f(f(y,f(G(f(x,y)),x)),f(G(y),G(y))))) = G(f(f(x,y),f(y,f(G(f(x,y)),x)))).
f(f(x,y),f(f(x,y),f(f(y,f(G(f(x,y)),x)),f(G(y),G(y))))) = G(y).
f(G(x),f(f(f(f(x,f(x,f(f(x,x),y))),y),f(G(x),f(f(x,f(x,f(f(x,x),y))),y))),f(f(f(G(x),f(f(x,f(x,f(f(x,x),y))),y)),f(G(f(f(f(x,f(x,f(f(x,x),y))),y),f(G(x),f(f(x,f(x,f(f(x,x),y))),y)))),f(f(x,f(x,f(f(x,x),y))),y))),f(G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))),G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))))))) = G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))).
f(f(x,f(x,f(y,z))),f(f(x,f(x,f(y,z))),f(f(z,f(x,y)),f(G(z),G(z))))) = G(f(f(x,f(x,f(y,z))),f(z,f(x,y)))).
f(f(x,f(x,f(y,z))),f(f(x,f(x,f(y,z))),f(f(z,f(x,y)),f(G(z),G(z))))) = G(z).
f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))) = G(f(x,y)).
f(f(G(f(x,y)),f(f(x,y),f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(x,y),f(x,y))))) = f(f(x,f(x,f(y,f(x,y)))),f(x,y)).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))),G(f(x,y))) = f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = G(f(x,y)).
f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))) = f(G(f(x,y)),G(f(x,y))).
f(f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))))) = f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
f(G(G(f(x,y))),f(f(G(G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))))) = f(G(G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))).
f(f(f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y))),f(f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y))),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y)))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y))) = f(x,f(x,f(y,f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))),G(f(x,y))) = G(f(x,y)).
f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = G(f(x,y)).
f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(f(x,f(x,f(y,f(f(x,y),f(x,y))))),G(f(x,y)))),G(f(f(x,f(x,f(y,f(f(x,y),f(x,y))))),G(f(x,y))))),f(x,f(x,f(y,f(f(x,y),f(x,y)))))))) = G(f(x,y)).
f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(f(x,y),f(x,y))),G(f(f(x,f(x,f(y,f(f(x,y),f(x,y))))),G(f(x,y))))),f(x,f(x,f(y,f(f(x,y),f(x,y)))))))) = G(f(x,y)).
f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(f(x,y),f(x,y))))),G(f(x,y))))),f(x,f(x,f(y,f(f(x,y),f(x,y)))))))) = G(f(x,y)).
f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(f(x,y),f(x,y)))),f(x,f(x,f(y,f(f(x,y),f(x,y)))))))) = G(f(x,y)).
f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(f(x,y),f(x,y)))))))) = G(f(x,y)).
f(G(f(x,y)),f(f(x,y),f(x,y))) = f(x,f(x,f(y,f(f(x,y),f(x,y))))).
f(x,f(x,f(y,f(f(x,y),f(x,y))))) = f(G(f(x,y)),f(f(x,y),f(x,y))).
f(x,f(x,f(y,f(f(x,y),f(x,y))))) = f(x,y).
f(f(x,f(x,f(f(y,f(f(x,y),f(x,y))),x))),f(x,y)) = x.
f(f(x,f(x,f(y,z))),f(f(x,f(x,f(y,z))),f(f(z,f(x,y)),f(f(f(x,f(x,f(y,z))),f(z,f(x,y))),f(f(x,f(x,f(y,z))),f(z,f(x,y))))))) = z.
f(G(f(x,y)),f(G(f(x,y)),f(f(y,f(f(x,y),x)),f(f(G(f(x,y)),f(y,f(f(x,y),x))),f(G(f(x,y)),f(y,f(f(x,y),x))))))) = y.
f(G(x),f(G(x),f(f(f(x,f(y,z)),f(x,f(y,f(y,f(z,x))))),f(f(G(x),f(f(x,f(y,z)),f(x,f(y,f(y,f(z,x)))))),f(G(x),f(f(x,f(y,z)),f(x,f(y,f(y,f(z,x)))))))))) = f(x,f(y,z)).
f(G(f(x,y)),f(G(f(x,y)),f(f(y,f(G(f(x,y)),f(y,f(y,f(f(f(x,y),x),G(f(x,y))))))),f(f(G(f(x,y)),f(y,f(G(f(x,y)),f(y,f(y,f(f(f(x,y),x),G(f(x,y)))))))),f(G(f(x,y)),f(y,f(G(f(x,y)),f(y,f(y,f(f(f(x,y),x),G(f(x,y)))))))))))) = y.
f(f(f(x,y),f(f(x,y),f(f(f(y,f(G(f(x,y)),x)),f(y,f(f(x,y),f(y,f(G(f(x,y)),x))))),f(x,y)))),f(f(x,y),f(y,f(G(f(x,y)),x)))) = f(x,y).
f(G(f(x,y)),f(G(f(x,y)),f(f(y,f(f(x,y),x)),f(y,f(G(f(x,y)),f(y,f(f(x,y),x))))))) = y.
f(G(f(x,y)),f(G(f(x,y)),f(f(y,f(f(x,y),x)),f(y,y)))) = y.
f(G(G(x)),f(G(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))),f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))) = f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)).
f(f(x,f(x,f(y,z))),f(f(x,f(x,f(y,z))),f(f(z,f(x,y)),f(z,f(f(x,f(x,f(y,z))),f(z,f(x,y))))))) = z.
f(f(x,f(x,f(y,z))),f(f(x,f(x,f(y,z))),f(f(z,f(x,y)),f(z,z)))) = z.
f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))) = f(x,y).
f(f(x,y),f(f(f(x,y),f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(f(x,y),f(x,y)))))) = f(f(x,y),f(x,y)).
f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y))))) = f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))).
f(f(x,y),f(f(f(x,y),f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(x,y),f(x,y)).
f(f(f(x,y),f(f(x,y),f(f(f(y,f(G(f(x,y)),x)),f(y,y)),f(x,y)))),f(f(x,y),f(y,f(G(f(x,y)),x)))) = f(x,y).
f(f(f(x,y),f(f(x,y),f(f(f(y,f(G(f(x,y)),x)),f(y,y)),f(x,y)))),y) = f(x,y).
f(G(x),f(G(x),f(f(f(x,f(y,z)),f(x,f(y,f(y,f(z,x))))),f(f(x,f(y,z)),f(G(x),f(f(x,f(y,z)),f(x,f(y,f(y,f(z,x)))))))))) = f(x,f(y,z)).
f(G(x),f(G(x),f(f(f(x,f(y,z)),f(x,f(y,f(y,f(z,x))))),f(f(x,f(y,z)),f(x,f(y,z)))))) = f(x,f(y,z)).
f(G(x),f(G(x),f(f(f(x,f(f(f(x,x),f(f(x,x),f(f(x,x),y))),y)),f(x,f(f(f(x,x),f(f(x,x),f(f(x,x),y))),y))),f(f(x,f(f(f(x,x),f(f(x,x),f(f(x,x),y))),y)),f(x,f(f(f(x,x),f(f(x,x),f(f(x,x),y))),y)))))) = f(x,f(f(f(x,x),f(f(x,x),f(f(x,x),y))),y)).
f(G(f(x,y)),f(f(G(G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))))) = f(G(G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))))) = f(G(G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(x,y)))) = f(G(G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(x,y)))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))).
f(f(x,y),f(f(f(x,f(x,f(y,f(x,y)))),f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(x,y),f(x,y))))) = f(f(x,f(x,f(y,f(x,y)))),f(x,y)).
f(f(x,y),f(f(f(x,f(x,f(y,f(x,y)))),f(x,y)),f(G(f(x,y)),f(f(x,y),f(x,y))))) = f(f(x,f(x,f(y,f(x,y)))),f(x,y)).
f(f(x,y),f(f(f(x,f(x,f(y,f(x,y)))),f(x,y)),f(x,y))) = f(f(x,f(x,f(y,f(x,y)))),f(x,y)).
f(f(f(x,y),f(f(x,f(x,f(y,z))),z)),f(f(f(f(x,y),f(f(x,y),f(x,y))),f(f(x,y),f(f(x,f(x,f(y,z))),z))),f(f(x,y),f(f(x,f(x,f(y,z))),z)))) = f(f(f(x,y),f(f(x,y),f(f(f(x,f(x,f(y,z))),z),f(f(x,y),f(f(x,f(x,f(y,z))),z))))),f(f(x,y),f(f(x,f(x,f(y,z))),z))).
f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y))))) = f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))).
f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,y),f(f(x,y),f(x,y))))) = f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))).
f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),G(f(x,y)))) = f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))).
f(f(f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),G(f(x,y))))))))) = f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(G(x),f(f(x,f(f(G(f(y,x)),G(f(y,x))),y)),f(f(G(x),G(f(G(f(y,x)),f(x,f(f(G(f(y,x)),G(f(y,x))),y))))),G(f(y,x))))) = f(x,f(f(G(f(y,x)),G(f(y,x))),y)).
f(G(x),f(f(x,f(f(G(f(y,x)),G(f(y,x))),y)),f(f(G(x),G(x)),G(f(y,x))))) = f(x,f(f(G(f(y,x)),G(f(y,x))),y)).
f(G(f(x,y)),f(G(f(x,y)),f(f(y,f(G(f(x,y)),f(y,f(y,f(f(f(x,y),x),G(f(x,y))))))),f(y,f(G(f(x,y)),f(y,f(G(f(x,y)),f(y,f(y,f(f(f(x,y),x),G(f(x,y)))))))))))) = y.
f(G(f(x,y)),f(G(f(x,y)),f(f(y,f(G(f(x,y)),f(y,f(y,f(f(f(x,y),x),G(f(x,y))))))),f(y,y)))) = y.
f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))))) = f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))))) = f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))) = f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(x,y))) = G(f(x,y)).
f(G(f(x,y)),G(f(x,y))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))).
f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))) = f(G(f(x,y)),G(f(x,y))).
f(G(x),f(G(x),f(x,f(f(f(x,x),f(f(x,x),f(f(x,x),y))),y)))) = f(x,f(f(f(x,x),f(f(x,x),f(f(x,x),y))),y)).
f(G(x),f(G(f(x,x)),f(f(x,x),f(f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),y))),y)))) = f(f(x,x),f(f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),y))),y)).
f(G(x),f(G(x),f(f(x,x),f(f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),y))),y)))) = f(f(x,x),f(f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),y))),y)).
f(G(x),f(G(x),f(f(x,x),f(f(x,f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),y))),y)))) = f(f(x,x),f(f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),y))),y)).
f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(f(f(x,x),f(x,x)),y))),y)))) = f(f(x,x),f(f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),y))),y)).
f(f(x,x),f(f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),y))),y)) = f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(f(f(x,x),f(x,x)),y))),y)))).
f(f(x,x),f(f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),y))),y)) = f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))).
f(f(x,x),f(f(x,f(f(f(x,x),f(x,x)),f(f(f(x,x),f(x,x)),y))),y)) = f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))).
f(f(x,x),f(f(x,f(x,f(f(f(x,x),f(x,x)),y))),y)) = f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))).
f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))) = f(f(x,x),f(f(x,f(x,f(f(f(x,x),f(x,x)),y))),y)).
f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))) = f(f(x,x),f(f(x,f(x,f(x,y))),y)).
f(f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(x,x),f(f(x,f(x,f(x,y))),f(f(x,f(x,f(x,y))),f(y,f(x,x))))))),f(f(G(x),G(f(x,x))),f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(x,x),f(f(x,f(x,f(x,y))),f(f(x,f(x,f(x,y))),f(y,f(x,x))))))))) = f(G(x),G(f(x,x))).
f(G(G(f(x,y))),f(G(G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))).
f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(f(f(x,x),x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y)))) = f(f(f(x,x),f(f(x,x),f(f(f(x,f(x,f(x,y))),y),f(f(x,x),f(f(x,f(x,f(x,y))),y))))),f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y)))) = f(f(f(x,x),f(f(x,x),f(f(f(x,f(x,f(x,y))),y),f(f(x,x),f(f(x,f(x,f(x,y))),y))))),f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(f(x,x),f(f(x,x),f(f(f(x,f(x,f(x,y))),y),f(f(x,x),f(f(x,f(x,f(x,y))),y))))),f(f(x,x),f(f(x,f(x,f(x,y))),y))) = f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y)))).
f(f(f(x,x),f(f(x,x),f(x,x))),f(f(x,x),f(f(x,f(x,f(x,y))),y))) = f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y)))).
f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y)))) = f(f(f(x,x),f(f(x,x),f(x,x))),f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y)))) = f(f(f(x,x),x),f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y)))) = f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(f(f(x,x),x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(f(x,x),f(f(x,x),f(f(f(x,f(x,f(x,y))),y),f(f(x,x),f(f(x,f(x,f(x,y))),y))))),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(f(x,x),f(f(x,x),f(f(f(x,f(x,f(x,y))),y),f(f(x,x),f(f(x,f(x,f(x,y))),y))))),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(f(x,x),f(f(x,x),f(x,x))),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(f(x,x),x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),f(f(G(x),G(f(x,x))),f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(x,x),f(f(x,f(x,f(x,y))),f(f(x,f(x,f(x,y))),f(y,f(x,x))))))))) = f(G(x),G(f(x,x))).
f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(G(x),G(f(x,x))),f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(x,x),f(f(x,f(x,f(x,y))),f(f(x,f(x,f(x,y))),f(y,f(x,x))))))))) = f(G(x),G(f(x,x))).
f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(G(x),G(x)),f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(x,x),f(f(x,f(x,f(x,y))),f(f(x,f(x,f(x,y))),f(y,f(x,x))))))))) = f(G(x),G(f(x,x))).
f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(G(x),G(x)),f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(x,x),f(f(x,f(x,f(x,y))),f(f(x,f(x,f(x,y))),f(y,f(x,x))))))))) = f(G(x),G(f(x,x))).
f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(G(x),G(x)),f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),f(f(x,x),f(f(x,f(x,f(x,y))),y)))))) = f(G(x),G(f(x,x))).
f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(G(x),G(x)),G(f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = f(G(x),G(f(x,x))).
f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(G(x),G(x)),G(f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = f(G(x),G(x)).
f(G(x),f(G(x),f(f(f(G(x),f(f(x,f(x,f(f(x,x),y))),y)),f(G(f(f(f(x,f(x,f(f(x,x),y))),y),f(G(x),f(f(x,f(x,f(f(x,x),y))),y)))),f(f(x,f(x,f(f(x,x),y))),y))),f(G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))),G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))))))) = G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))).
f(G(x),f(G(x),f(f(f(G(x),f(f(x,f(x,f(f(x,x),y))),y)),f(G(G(x)),f(f(x,f(x,f(f(x,x),y))),y))),f(G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))),G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))))))) = G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))).
f(G(x),f(G(x),f(f(f(G(x),f(f(x,f(x,f(f(x,x),y))),y)),f(G(x),f(f(x,f(x,f(f(x,x),y))),y))),f(G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))),G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))))))) = G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))).
f(G(x),f(G(x),G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))))) = G(f(G(x),f(f(x,f(x,f(f(x,x),y))),y))).
f(G(f(x,y)),f(G(f(x,y)),G(f(G(f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = G(f(G(f(x,y)),f(f(f(x,y),f(f(x,y),f(f(f(x,y),f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
G(f(G(f(x,y)),f(f(f(x,y),f(f(x,y),f(f(f(x,y),f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(x,y)),f(G(f(x,y)),G(f(G(f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))).
G(f(G(f(x,y)),f(f(f(x,y),f(f(x,y),f(f(f(x,y),f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(x,y)),f(G(f(x,y)),G(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))).
G(f(G(f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(x,y)),f(G(f(x,y)),G(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))).
f(G(f(x,y)),f(G(f(x,y)),G(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = G(f(G(f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(G(f(x,y)),f(G(f(x,y)),G(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = G(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y))),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y)))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y))) = f(x,f(x,f(y,f(x,y)))).
f(f(G(f(x,y)),f(f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y))),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y)))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y))) = f(x,f(x,f(y,f(x,y)))).
f(f(G(f(x,y)),f(f(f(x,y),f(f(x,y),f(x,y))),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y)))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y))) = f(x,f(x,f(y,f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,y))),f(f(x,y),f(x,y)))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y))) = f(x,f(x,f(y,f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,y),f(f(x,y),f(x,y)))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y))) = f(x,f(x,f(y,f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),G(f(x,y))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y))) = f(x,f(x,f(y,f(x,y)))).
f(G(x),f(G(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))),f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))) = f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)).
f(G(x),f(G(G(x)),f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))) = f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)).
f(G(x),f(G(x),f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))) = f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)).
f(G(x),f(G(x),f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))) = f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)).
f(G(x),f(G(x),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))) = f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)).
f(G(f(x,y)),f(G(G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))).
f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))) = f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))) = f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))) = f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))) = f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))) = f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))) = G(f(x,y)).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))) = G(f(x,y)).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))) = G(f(x,y)).
f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))),G(f(x,y))))) = G(f(x,y)).
f(f(G(f(x,y)),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))) = G(f(x,y)).
f(f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))),f(G(f(x,y)),G(f(x,y)))))) = f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))).
f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))) = f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))),f(G(f(x,y)),G(f(x,y)))))) = f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))).
f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))),f(G(f(x,y)),G(f(x,y)))))) = f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))).
f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))),f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))))) = f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))).
f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))),f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))))) = f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))).
f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))),G(f(x,y)))) = f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))).
f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y))))))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))) = f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))) = f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))) = f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))) = f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))) = f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))).
f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))) = G(f(x,y)).
f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = G(f(x,y)).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))).
f(G(G(f(x,y))),f(G(G(f(x,y))),f(f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))).
f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),G(f(x,y)))))) = f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))).
f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))) = f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(G(f(x,y)),f(G(G(f(x,y))),f(f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(G(f(x,y)),f(G(f(x,y)),f(f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),G(f(x,y))))))))) = f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),G(f(x,y))))))))) = f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),G(f(x,y))))))))) = f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = f(G(G(f(x,y))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))) = f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y)))) = f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y)))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = G(f(x,y)).
f(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))))) = f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))).
f(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(G(f(x,y)))))),f(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = G(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))).
f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))))) = f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))).
f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))).
f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))) = f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))).
f(f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))).
f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))).
f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))) = f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))).
f(G(f(x,y)),f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = G(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),G(f(x,y))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y))) = f(x,f(x,f(y,f(x,y)))).
f(G(f(x,y)),f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(G(f(x,y)))))),f(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = G(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(G(f(x,y)))))),f(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = G(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))))),f(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = G(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = G(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = G(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = G(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))) = G(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
G(f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
G(G(f(x,y))) = f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))) = G(G(f(x,y))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))) = G(f(x,y)).
f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(x,y))) = G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(G(f(x,y)),G(f(x,y))).
f(f(G(f(G(f(x,y)),G(f(x,y)))),f(G(f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))))))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))) = f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))).
f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))) = G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(x,y)),G(f(x,y))).
f(f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(x,y)),G(f(x,y))).
f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(G(f(x,y)),G(f(x,y))).
f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(G(f(x,y)),G(f(x,y))).
f(f(G(f(x,y)),f(G(f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))))))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))) = f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))))))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))) = f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))))))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))) = f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y)))))))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))) = f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))).
f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y)))))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))) = f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))) = f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y)))))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))) = f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))) = f(f(G(f(x,y)),f(G(f(x,y)),f(G(f(x,y)),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))) = G(f(x,y)).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))) = G(f(x,y)).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(G(f(x,y)),G(f(x,y))))))) = G(f(x,y)).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))))) = G(f(x,y)).
f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = G(f(x,y)).
f(f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))).
f(f(f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y))))),f(f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y))))))) = f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),f(f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))),G(f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))).
f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))).
f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))).
f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(G(f(x,y)),f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))).
f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))).
f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = G(f(x,y)).
f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(x,y)),G(f(x,y))).
f(G(f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),f(f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))),G(f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(G(f(x,y)),f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),f(f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))),G(f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))),G(f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))),G(f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(G(f(x,y)),G(f(x,y))))),G(f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y)))),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(G(f(x,y)),f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(G(f(x,y)),G(f(x,y)))),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(x,y)),G(f(G(f(x,y)),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(G(f(x,y)),G(f(x,y))).
f(G(f(G(f(x,y)),G(f(x,y)))),f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),f(f(f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(x,y)),f(G(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),f(f(f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(x,y)),f(G(f(G(f(x,y)),G(f(x,y)))),f(f(f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(x,y)),f(G(f(x,y)),f(f(f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(x,y)),f(G(f(x,y)),f(f(f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))))) = f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))) = f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))).
f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = G(f(x,y)).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))) = f(G(f(x,y)),G(f(x,y))).
f(f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y))))),f(f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y))))))) = f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))),f(f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y))))))) = f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y))))))) = f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y))))))) = f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y))))))) = f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y))))))) = f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(x,y))),f(G(f(x,y)),G(f(x,y))))))) = f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))))) = f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))).
f(f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))).
f(f(f(G(f(x,y)),G(f(x,y))),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))).
f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))).
f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(x,y))) = f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))).
f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))) = f(G(f(x,y)),G(f(x,y))).
f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))) = G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))) = f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))).
G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))) = G(f(x,y)).
G(f(f(x,f(x,f(y,f(f(z,f(z,f(u,f(z,u)))),G(f(z,u)))))),f(f(f(z,f(z,f(u,f(z,u)))),G(f(z,u))),f(x,y)))) = G(f(z,u)).
f(f(f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y)))),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(x,f(x,f(y,f(x,y)))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(x,y))) = G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(G(G(f(x,y))),f(f(G(f(x,y)),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))),f(f(G(G(f(x,y))),G(G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(G(f(x,y)),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))).
G(f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = G(f(x,y)).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))),G(f(x,y))) = G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))),G(f(x,y))))),G(f(x,y))) = G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y)))))),G(f(x,y))) = G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y)))))),G(f(x,y))) = G(f(x,y)).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))),f(f(G(G(f(x,y))),G(G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(G(f(x,y)),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y)))))),f(f(G(G(f(x,y))),G(G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(G(f(x,y)),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y)))))),f(f(G(f(x,y)),G(G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(G(f(x,y)),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y)))))),f(f(G(f(x,y)),G(f(x,y))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))))) = f(G(f(x,y)),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y)))))),G(f(x,y)))) = f(G(f(x,y)),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))).
f(G(f(x,y)),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))) = f(G(f(x,y)),f(f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y)))))),G(f(x,y)))).
f(G(f(x,y)),f(f(G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))) = f(G(f(x,y)),G(f(x,y))).
f(G(f(x,y)),f(f(G(f(x,y)),G(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),f(x,f(x,f(y,f(x,y)))))) = f(G(f(x,y)),G(f(x,y))).
f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y)))))) = f(G(f(x,y)),G(f(x,y))).
f(f(f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))),f(f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y)))),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(x,f(x,f(y,f(x,y)))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(f(G(f(x,y)),f(G(f(x,y)),f(f(G(f(x,y)),G(f(x,y))),f(x,f(x,f(y,f(x,y))))))),G(f(x,y)))),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(x,f(x,f(y,f(x,y)))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))),G(f(x,y)))),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(x,f(x,f(y,f(x,y)))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),G(f(x,y)))),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(x,f(x,f(y,f(x,y)))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(G(f(x,y)),f(f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(x,f(x,f(y,f(x,y)))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(x,f(x,f(y,f(x,y)))))) = f(f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(G(f(x,y)),f(f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))),f(x,f(x,f(y,f(x,y)))))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(f(G(f(x,y)),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y))))),G(f(x,y))) = f(x,f(x,f(y,f(x,y)))).
f(x,f(x,f(y,f(x,y)))) = f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))).
f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))) = f(x,f(x,f(y,f(x,y)))).
G(f(f(f(x,f(x,f(y,f(x,y)))),f(f(x,f(x,f(y,f(x,y)))),f(x,f(x,f(y,f(x,y)))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = G(f(x,y)).
G(f(G(f(x,f(x,f(y,f(x,y))))),f(G(f(x,y)),f(f(x,f(x,f(y,f(x,y)))),G(f(x,y)))))) = G(f(x,y)).
G(f(G(f(x,f(x,f(y,f(x,y))))),f(x,f(x,f(y,f(x,y)))))) = G(f(x,y)).
G(f(G(f(f(x,y),f(f(x,y),f(x,y)))),f(f(x,y),f(f(x,y),f(f(f(x,f(x,f(y,z))),z),f(f(x,y),f(f(x,f(x,f(y,z))),z))))))) = G(f(f(x,y),f(f(x,f(x,f(y,z))),z))).
G(f(G(f(G(x),f(G(x),G(x)))),f(G(x),f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))))))) = G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))).
G(f(G(G(f(x,y))),f(f(x,y),f(f(x,y),f(f(f(x,f(x,f(y,z))),z),f(f(x,y),f(f(x,f(x,f(y,z))),z))))))) = G(f(f(x,y),f(f(x,f(x,f(y,z))),z))).
G(f(G(f(x,y)),f(f(x,y),f(f(x,y),f(f(f(x,f(x,f(y,z))),z),f(f(x,y),f(f(x,f(x,f(y,z))),z))))))) = G(f(f(x,y),f(f(x,f(x,f(y,z))),z))).
G(f(G(f(x,y)),f(f(x,y),f(f(x,y),f(x,y))))) = G(f(f(x,y),f(f(x,f(x,f(y,z))),z))).
G(f(G(f(x,y)),G(f(x,y)))) = G(f(f(x,y),f(f(x,f(x,f(y,z))),z))).
G(f(f(x,y),f(f(x,f(x,f(y,z))),z))) = G(f(G(f(x,y)),G(f(x,y)))).
G(f(f(x,y),f(f(x,f(x,f(y,z))),z))) = G(f(x,y)).
G(f(f(f(x,y),x),f(G(f(x,y)),y))) = G(f(f(x,y),x)).
f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(f(x,x)),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(f(f(x,x),f(f(x,f(x,f(x,y))),y))).
G(f(f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),G(x)),f(G(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))))) = G(f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),G(x))).
f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y))) = G(f(f(x,x),f(f(x,f(x,f(x,y))),y))).
f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y))) = G(f(x,x)).
f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y))) = G(x).
f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),G(x)) = f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))).
G(f(G(G(x)),f(G(x),f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))))))) = G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))).
G(f(G(x),f(G(x),f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))))))) = G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))).
G(f(G(x),f(G(x),f(G(x),G(x))))) = G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))).
G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))) = G(f(G(x),f(G(x),f(G(x),G(x))))).
G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))) = G(f(G(x),G(x))).
G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))) = G(x).
f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))),G(x)) = f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)).
f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),G(x)) = f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))).
f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))) = f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),G(x)).
f(f(G(x),G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))) = G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))).
f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))),G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))),G(x)))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
f(G(x),f(G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),G(x)),G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))))),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(x,x),f(f(x,x),f(x,y))),y))))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
G(f(G(G(x)),f(f(f(G(x),G(x)),f(f(G(x),G(x)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))),f(G(x),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))) = G(G(x)).
f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),G(x)),G(x)) = f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)).
f(f(G(x),G(x)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))) = G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))).
f(f(G(x),G(x)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))) = G(x).
G(f(G(x),f(f(f(G(x),G(x)),f(f(G(x),G(x)),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))),f(G(x),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))) = G(G(x)).
G(f(G(x),f(f(f(G(x),G(x)),G(x)),f(G(x),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))) = G(G(x)).
G(f(G(x),f(G(x),f(G(x),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))) = G(G(x)).
G(f(G(x),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))) = G(G(x)).
G(f(G(x),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))) = G(x).
f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(G(x),G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))),G(x)))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(G(x),G(x)),G(x)))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),G(x))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
G(f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))))) = G(f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),G(x))).
G(f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))))) = G(f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),G(x))).
G(f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(f(x,x)),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))))) = G(f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),G(x))).
G(f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))))) = G(f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),G(x))).
G(f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(f(x,x),f(f(x,f(x,f(x,y))),y)))) = G(f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),G(x))).
G(G(x)) = G(f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),G(x))).
G(f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),G(x))) = G(G(x)).
G(f(f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),G(x))) = G(x).
G(f(f(f(x,x),f(f(x,f(x,f(x,y))),y)),G(x))) = G(x).
G(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))) = G(x).
f(f(G(x),G(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))).
f(f(G(x),G(x)),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))).
f(f(G(x),G(x)),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(x).
f(f(G(x),G(x)),f(G(f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))),f(f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))))) = G(x).
f(f(G(x),G(x)),f(G(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),f(f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))))) = G(x).
f(f(G(x),G(x)),f(G(x),f(f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y)))),f(f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))))) = G(x).
f(f(G(x),G(x)),f(G(x),f(G(x),f(f(x,x),f(f(x,f(x,f(x,y))),y))))) = G(x).
f(f(G(x),G(x)),f(f(x,x),f(f(x,f(x,f(x,y))),y))) = G(x).
f(f(f(G(x),G(x)),G(x)),f(f(f(x,f(x,f(x,y))),y),f(f(G(x),G(x)),f(x,x)))) = f(f(x,f(x,f(x,y))),y).
f(f(G(G(x)),G(G(x))),f(f(G(x),G(x)),f(f(G(x),f(G(x),f(G(x),y))),y))) = G(x).
f(f(G(x),G(G(x))),f(f(G(x),G(x)),f(f(G(x),f(G(x),f(G(x),y))),y))) = G(x).
f(f(G(x),G(x)),f(f(G(x),G(x)),f(f(G(x),f(G(x),f(G(x),y))),y))) = G(x).
f(G(x),f(f(f(x,f(x,f(x,y))),y),f(f(G(x),G(x)),f(x,x)))) = f(f(x,f(x,f(x,y))),y).
f(G(x),f(f(f(x,f(x,f(x,y))),y),G(x))) = f(f(x,f(x,f(x,y))),y).
f(G(x),f(f(f(G(x),f(G(x),f(G(x),y))),y),G(G(x)))) = f(f(G(x),f(G(x),f(G(x),y))),y).
f(G(x),f(f(f(G(x),f(G(x),f(G(x),y))),y),G(x))) = f(f(G(x),f(G(x),f(G(x),y))),y).
f(G(x),f(G(x),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),G(x)),G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))))),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(x,x),f(f(x,x),f(x,y))),y))))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
f(G(x),f(G(x),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),G(x)),G(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))))),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(x,x),f(f(x,x),f(x,y))),y))))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
f(G(x),f(G(x),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)),G(x)),G(x)))))),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(x,x),f(f(x,x),f(x,y))),y))))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
f(G(x),f(G(x),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y)))))),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(x,x),f(f(x,x),f(x,y))),y))))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
f(G(x),f(G(x),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(G(x),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),G(x)))),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(x,x),f(f(x,x),f(x,y))),y))))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
f(G(x),f(G(x),f(f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(x,x),f(f(x,x),f(x,y))),y)),f(f(f(f(x,x),f(f(x,x),f(x,y))),y),f(f(f(x,x),f(f(x,x),f(x,y))),y))))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
f(G(x),f(G(x),f(f(f(x,x),f(f(x,x),f(x,y))),y))) = f(f(f(x,x),f(f(x,x),f(x,y))),y).
G(f(f(f(x,x),f(f(x,x),f(x,y))),y)) = G(x).
G(f(f(f(G(x),G(x)),f(f(G(x),G(x)),f(f(G(x),f(G(x),f(G(x),y))),y))),f(f(f(G(x),f(G(x),f(G(x),y))),y),G(x)))) = G(G(x)).
G(f(G(x),f(f(f(G(x),f(G(x),f(G(x),y))),y),G(x)))) = G(G(x)).
G(f(f(G(x),f(G(x),f(G(x),y))),y)) = G(G(x)).
G(f(f(G(x),f(G(x),f(G(x),y))),y)) = G(x).
f(f(G(x),f(G(x),f(G(x),y))),f(f(G(x),f(G(x),f(G(x),y))),f(y,f(G(x),G(f(f(G(x),f(G(x),f(G(x),y))),y)))))) = G(f(f(G(x),f(G(x),f(G(x),y))),y)).
G(f(f(f(f(G(x),f(G(x),f(G(x),y))),y),f(G(x),f(G(x),f(G(x),y)))),f(G(x),y))) = G(f(f(f(G(x),f(G(x),f(G(x),y))),y),f(G(x),f(G(x),f(G(x),y))))).
f(f(G(x),f(G(x),f(G(x),y))),f(f(G(x),f(G(x),f(G(x),y))),f(y,f(G(x),G(x))))) = G(f(f(G(x),f(G(x),f(G(x),y))),y)).
f(f(G(x),f(G(x),f(G(x),y))),y) = G(f(f(G(x),f(G(x),f(G(x),y))),y)).
G(f(f(G(x),f(G(x),f(G(x),y))),y)) = f(f(G(x),f(G(x),f(G(x),y))),y).
f(f(G(x),f(G(x),f(G(x),y))),y) = G(x).
G(f(f(G(x),f(G(x),f(G(x),f(G(x),y)))),f(G(x),y))) = G(f(f(f(G(x),f(G(x),f(G(x),y))),y),f(G(x),f(G(x),f(G(x),y))))).
G(f(f(f(G(x),f(G(x),f(G(x),y))),y),f(G(x),f(G(x),f(G(x),y))))) = G(f(f(G(x),f(G(x),f(G(x),f(G(x),y)))),f(G(x),y))).
G(f(f(f(G(x),f(G(x),f(G(x),y))),y),f(G(x),f(G(x),f(G(x),y))))) = G(x).
G(f(G(x),f(G(x),f(G(x),f(G(x),y))))) = G(x).
G(f(G(x),f(G(x),f(G(x),y)))) = G(x).
G(f(G(x),f(G(x),y))) = G(x).
G(x) = G(f(y,x)).
G(f(x,y)) = G(y).
G(x) = G(y).
f(f(x,f(x,G(y))),f(f(z,z),f(x,z))) = f(z,z).
f(f(f(x,f(x,G(y))),f(y,y)),f(f(x,y),f(f(x,f(x,G(z))),f(y,y)))) = f(x,y).
f(x,f(x,G(y))) = G(x).
f(G(x),y) = f(y,y).
f(G(x),f(y,y)) = y.
f(f(f(x,x),f(f(x,x),f(f(x,x),f(x,f(x,f(f(y,y),f(G(z),f(G(y),f(y,x))))))))),f(G(y),f(G(y),f(y,x)))) = f(x,f(x,f(f(y,y),f(G(y),f(G(y),f(y,x)))))).
f(x,f(f(x,y),f(f(x,x),f(G(z),f(G(f(u,y)),f(f(y,f(f(u,y),u)),x)))))) = f(x,y).
f(G(x),f(G(y),z)) = z.
f(x,f(x,G(y))) = G(z).
G(x) = f(y,f(y,G(z))).
f(G(x),f(f(y,f(y,G(z))),u)) = u.
f(G(x),f(y,y)) = f(f(y,y),f(z,y)).
f(f(x,x),f(y,x)) = x.
f(f(x,x),f(y,f(y,f(z,x)))) = x.
f(f(f(x,y),f(x,y)),x) = f(x,y).
f(f(x,x),f(x,y)) = x.
f(f(G(x),f(y,y)),f(f(z,y),f(f(z,f(z,G(u))),f(y,y)))) = f(z,y).
f(x,f(f(y,x),f(f(y,f(y,G(z))),f(x,x)))) = f(y,x).
f(x,f(f(y,x),f(G(z),f(x,x)))) = f(y,x).
f(x,f(f(y,x),x)) = f(y,x).
f(x,f(f(x,y),x)) = f(x,y).
f(f(f(x,x),f(f(x,x),f(f(x,x),f(x,f(x,f(f(y,y),f(y,x))))))),f(G(y),f(G(y),f(y,x)))) = f(x,f(x,f(f(y,y),f(G(y),f(G(y),f(y,x)))))).
f(f(f(x,x),f(f(x,x),f(f(x,x),f(x,f(x,f(f(y,y),f(y,x))))))),f(y,x)) = f(x,f(x,f(f(y,y),f(G(y),f(G(y),f(y,x)))))).
f(f(f(x,x),f(f(x,x),f(f(x,x),f(x,f(x,f(f(y,y),f(y,x))))))),f(y,x)) = f(x,f(x,f(f(y,y),f(y,x)))).
f(f(f(x,x),f(f(x,x),x)),f(y,x)) = f(x,f(x,f(f(y,y),f(y,x)))).
f(x,f(y,x)) = f(x,f(x,f(f(y,y),f(y,x)))).
f(x,f(x,f(f(y,y),f(y,x)))) = f(x,f(y,x)).
f(x,f(x,y)) = f(x,f(y,x)).
f(x,f(y,x)) = f(x,f(x,y)).
f(x,f(x,f(y,x))) = f(y,x).
f(x,f(x,f(x,y))) = f(x,y).
f(x,f(x,f(x,y))) = f(y,x).
f(f(x,y),f(x,f(y,z))) = x.
f(f(c3,c4),f(c3,f(c4,c5))) != c3.
f(x,G(y)) = f(x,x).
f(f(x,f(x,f(f(y,y),f(y,f(y,f(G(z),x)))))),x) = f(y,f(y,f(G(z),x))).
f(x,G(y)) = f(G(z),x).
f(G(x),y) = f(y,G(z)).
f(f(x,f(x,f(f(y,y),f(y,f(y,f(x,G(z))))))),x) = f(y,f(y,f(G(u),x))).
f(f(x,f(x,f(f(y,y),f(y,f(y,f(x,G(z))))))),x) = f(y,f(y,f(x,G(u)))).
f(f(x,f(x,y)),x) = f(y,f(y,f(x,G(z)))).
f(f(x,f(x,y)),x) = f(y,f(y,f(x,x))).
f(f(x,f(x,f(y,z))),f(y,f(x,z))) = y.
f(f(x,f(y,z)),f(y,f(y,f(z,x)))) = x.
f(f(x,f(x,f(y,z))),f(z,z)) = z.
f(f(x,y),f(x,x)) = x.
f(x,f(x,f(x,y))) = f(y,f(y,f(x,x))).
f(x,f(x,f(y,y))) = f(y,f(y,f(y,x))).
x = f(f(x,f(y,z)),f(y,f(y,f(x,z)))).
f(f(x,f(y,z)),f(y,f(y,f(x,z)))) = x.
f(f(x,y),f(f(y,z),f(f(y,z),f(f(y,y),x)))) = x.
f(x,f(x,f(y,y))) = f(y,x).
f(x,f(x,y)) = f(f(y,y),x).
f(f(x,x),y) = f(y,f(y,x)).
f(x,f(y,x)) = f(x,f(y,y)).
f(x,f(y,y)) = f(x,f(y,x)).
f(f(x,f(x,f(y,z))),f(f(z,f(x,y)),f(z,f(x,y)))) = f(f(x,f(x,f(y,z))),z).
f(f(x,f(y,z)),f(z,f(z,f(x,y)))) = x.
f(f(f(x,f(y,z)),x),f(f(z,f(x,y)),f(z,f(x,y)))) = f(z,f(x,y)).
f(f(x,y),f(f(y,z),f(f(y,z),f(x,f(x,y))))) = x.
f(f(x,f(x,f(y,z))),f(f(z,f(x,y)),f(z,f(x,y)))) = f(z,f(x,y)).
f(f(x,f(x,f(y,z))),f(G(u),f(z,f(x,y)))) = f(z,f(x,y)).
f(f(x,f(x,f(y,z))),f(G(u),f(z,f(x,y)))) = f(f(x,f(x,f(y,z))),z).
f(f(x,f(x,f(y,z))),f(G(u),f(z,f(x,y)))) = f(z,f(x,f(x,f(y,z)))).
f(x,f(y,f(y,f(z,x)))) = f(x,f(y,z)).
f(f(x,y),f(f(y,z),x)) = x.

end_of_list.
