i (0) => 0.
i (i (X)) => f (0,X).
i (f (X,Y)) => f (i (Y),i (X)).
f (X,0) => X.
f (i (X),X) => 0.
f (f (X,Y),Z) => f (X,f (Y,Z)).
f (0,i (X)) => i (X).
f (X,f (0,Y)) => f (X,Y).
f (i (X),f (X,Y)) => f (0,Y).
f (X,f (Y,i (Y))) => X.
f (0,f (i (X),Y)) => f (i (X),Y).
f (X,f (Y,f (i (Y),Z))) => f (X,Z).
.

0=0.
0=0.
0=X1.
f(0,X1)=f(0,f(X3,f(X2,f(i(X3),f(i(X2),f(i(X1),f(i(X2),i(X2)))))))).
f(i(X2),f(i(X1),i(X1)))=f(0,X2).
f(i(X3),f(i(X2),i(X1)))=f(i(X3),i(X2)).
0=X1.
f(i(X1),f(X2,f(i(X1),i(X1))))=f(i(X2),f(X3,f(X3,f(X3,f(X3,X1))))).
f(0,X1)=0.
0=f(0,f(X1,f(i(X2),f(i(X2),f(i(X3),X2))))).
f(i(X1),f(i(X1),f(i(X2),i(X1))))=X3.
f(X1,i(X2))=f(X1,f(i(X3),f(i(X1),i(X2)))).
f(0,X1)=f(i(X2),f(i(X2),f(X1,X3))).
i(X1)=0.
f(X1,i(X1))=i(X3).
f(0,f(X1,f(X1,X1)))=f(X1,X2).
f(0,f(X1,f(X2,X1)))=0.
f(0,f(X1,X2))=f(X3,f(X1,f(X2,f(X2,f(X2,f(i(X3),f(X1,X2))))))).
f(i(X1),f(i(X2),X1))=i(X2).
X1=f(0,f(X2,f(i(X3),f(i(X1),f(i(X3),f(i(X1),i(X3))))))).
f(0,X1)=f(i(X1),X2).
0=f(0,f(X1,X2)).
f(0,f(X2,X2))=X1.
X1=i(X2).
f(0,X1)=f(i(X2),f(X1,i(X3))).
f(X1,f(i(X2),X1))=X3.
X1=f(i(X1),f(0,f(i(X3),f(i(X3),f(i(X2),f(X1,f(X1,f(X3,f(X3,X1))))))))).
X1=f(i(X2),f(0,f(X2,f(X2,f(X3,X2))))).
X1=0.
f(i(X1),f(0,f(i(X2),f(X1,f(i(X3),f(i(X1),f(i(X1),i(X1))))))))=f(X3,f(X3,f(i(X2),f(i(X1),f(i(X1),f(X3,f(X3,X1))))))).
f(0,f(X1,i(X2)))=X2.
X1=X2.
f(0,X1)=f(i(X2),f(i(X2),f(i(X3),f(i(X1),f(X3,f(X1,X1)))))).
f(0,X1)=f(i(X2),f(i(X1),i(X2))).
f(X1,f(i(X2),f(i(X3),f(i(X3),f(i(X2),f(X1,f(X1,f(i(X3),i(X2)))))))))=f(0,f(X1,f(X2,f(i(X3),i(X1))))).
f(i(X3),f(X2,f(X1,f(i(X2),f(X1,i(X3))))))=X3.
i(X1)=f(i(X3),f(i(X2),i(X2))).
f(0,X1)=f(0,X2).
f(X1,f(X1,f(X2,X3)))=f(i(X3),X2).
X1=X1.
X1=f(i(X2),X1).
f(X1,f(X1,f(X1,f(X2,f(X1,f(X3,X2))))))=f(i(X2),f(i(X3),f(i(X1),f(i(X1),f(X3,X1))))).
0=0.
f(0,X1)=0.
f(0,f(X1,f(X2,i(X3))))=f(i(X3),f(X1,f(i(X3),i(X3)))).
f(0,X1)=X2.
X1=0.
f(0,f(X1,f(X2,i(X3))))=X3.
f(i(X1),f(i(X2),X3))=i(X1).
f(0,f(X1,i(X2)))=i(X1).
f(i(X1),i(X2))=f(0,X1).
f(0,X1)=0.
0=f(i(X1),i(X2)).
i(X1)=X1.
X1=i(X3).
X1=f(0,f(X1,f(X1,X1))).
f(i(X1),f(X2,f(X3,X1)))=f(0,f(X2,X1)).
0=0.
X1=X2.
X1=f(0,f(X3,f(X3,f(i(X2),f(X1,X1))))).
f(0,f(X2,f(i(X1),f(i(X1),f(i(X2),i(X3))))))=0.
f(i(X2),f(X1,f(X3,X1)))=f(i(X2),X3).
f(X1,X1)=f(0,f(X3,X2)).
f(X1,f(i(X2),f(X3,f(i(X2),f(X1,X2)))))=f(X3,f(X2,f(X3,f(X1,X2)))).
f(0,X1)=i(X1).
f(0,f(X3,f(X1,X2)))=f(i(X1),f(i(X3),f(X1,f(i(X3),f(0,f(X1,f(X2,f(X2,X3)))))))).
f(X1,f(i(X3),f(X1,f(X3,X2))))=f(0,X3).
f(i(X3),f(X1,f(X2,i(X1))))=f(0,f(X2,f(X2,X1))).
X1=f(i(X2),f(i(X1),f(i(X1),i(X2)))).
X1=f(0,f(X3,f(i(X2),f(i(X2),f(i(X2),i(X2)))))).
f(0,X1)=X1.
f(i(X1),f(i(X1),f(i(X1),i(X1))))=f(i(X2),f(i(X2),f(0,f(i(X2),X3)))).
f(X1,f(i(X2),f(i(X3),X2)))=f(i(X1),f(X3,f(X1,f(i(X3),f(0,f(X3,f(X1,i(X2)))))))).
f(i(X2),f(i(X2),i(X1)))=X1.
X1=f(0,X2).
f(0,f(X2,i(X1)))=f(X3,f(X3,f(X3,f(i(X1),X2)))).
X1=f(0,f(X2,X1)).
0=f(0,f(X1,f(X2,f(X2,f(i(X3),i(X3)))))).
f(X1,f(X2,X2))=f(0,f(X3,f(X2,f(X2,f(X2,X3))))).
0=f(X1,f(X1,f(X1,f(X1,f(X3,f(X1,X2)))))).
f(0,X1)=i(X2).
f(i(X2),i(X1))=0.
X1=f(i(X2),f(i(X1),f(i(X2),f(i(X1),f(X3,f(X1,i(X2))))))).
f(0,f(X1,f(i(X2),i(X2))))=f(X3,f(X2,f(X2,f(X3,f(i(X1),X2))))).
f(X1,f(X2,f(i(X3),f(i(X1),f(i(X3),f(i(X2),f(X3,X3)))))))=f(i(X1),X3).
i(X3)=i(X3).
f(0,f(X1,f(X2,f(X2,f(X3,X3)))))=f(0,f(X3,X1)).
f(i(X2),i(X1))=f(i(X2),i(X1)).
f(X1,i(X1))=0.
f(i(X2),i(X1))=f(0,X2).
f(i(X1),i(X1))=f(i(X3),f(X2,f(X1,X2))).
0=f(X1,X2).
0=i(X2).
f(X1,f(X1,f(X1,f(X1,f(X2,X3)))))=f(0,f(X3,f(X3,X2))).
f(i(X1),f(X2,f(X3,X3)))=f(i(X1),X3).
X1=i(X2).
0=f(i(X2),f(X1,X2)).
f(0,f(X1,f(X2,f(i(X1),f(i(X2),X3)))))=f(0,X1).
f(i(X1),i(X2))=X3.
f(i(X3),f(i(X2),X1))=0.
X1=f(i(X2),f(X1,f(X1,X1))).
X1=X2.
f(i(X1),i(X1))=f(i(X2),f(X3,f(X2,X1))).
X1=i(X2).
X1=0.
f(i(X3),f(i(X1),f(i(X2),f(i(X1),i(X1)))))=f(0,f(X1,f(X1,X1))).
f(i(X1),f(i(X2),f(i(X1),f(X3,f(X1,f(i(X3),f(i(X3),f(i(X2),f(i(X2),f(X1,X2))))))))))=f(i(X3),X2).
f(0,X1)=i(X2).
0=f(0,X1).
i(X1)=f(0,X2).
f(i(X2),f(i(X2),i(X1)))=f(0,X3).
X1=f(i(X2),f(i(X1),f(i(X1),X2))).
X1=f(0,X2).
X1=f(0,f(X1,f(X3,f(i(X2),f(i(X2),f(i(X3),f(i(X2),f(i(X2),f(i(X3),f(i(X2),f(i(X3),i(X1)))))))))))).
i(X1)=X1.
X1=f(i(X2),f(X3,f(i(X2),X3))).
X1=0.
f(X1,f(X2,f(i(X1),i(X1))))=0.
0=f(0,f(X1,i(X2))).
X1=0.
f(i(X1),f(X2,X1))=f(i(X3),i(X1)).
f(i(X1),X2)=i(X3).
0=f(i(X2),f(i(X1),f(X3,X3))).
f(i(X1),f(i(X2),i(X1)))=i(X3).
0=f(0,f(X1,X2)).
f(i(X1),f(X2,f(X2,f(i(X3),f(i(X2),i(X3))))))=f(0,X1).
X1=f(0,f(X3,f(X2,f(X3,f(i(X2),X3))))).
f(i(X2),f(i(X2),i(X1)))=X2.
X1=f(X2,i(X3)).
f(i(X1),X2)=f(X1,i(X2)).
f(0,X1)=X1.
X1=f(0,f(X2,f(X2,f(X2,f(X3,f(X3,i(X1))))))).
f(i(X1),f(X2,X1))=f(0,f(X3,X3)).
X1=i(X3).
f(X1,X2)=f(i(X2),f(X1,f(X1,i(X3)))).
i(X1)=f(i(X2),X1).
f(X1,i(X2))=f(0,X2).
f(i(X1),f(i(X1),f(i(X1),f(i(X2),f(X1,f(X1,f(X2,f(X1,X3))))))))=X2.
0=f(0,f(X2,i(X1))).
f(i(X1),i(X1))=f(i(X1),f(i(X2),i(X2))).
X1=f(i(X2),X3).
f(0,f(X1,f(X2,X1)))=f(i(X1),f(X2,f(X1,i(X2)))).
i(X1)=0.
i(X1)=X1.
f(X1,f(i(X1),f(i(X1),f(X2,f(X2,f(X3,f(X2,X1)))))))=0.
f(i(X1),X2)=i(X3).
f(0,f(X2,f(i(X1),f(X2,i(X1)))))=i(X2).
0=f(i(X2),X3).
f(0,f(X1,f(X2,f(i(X1),f(i(X1),i(X3))))))=f(X3,X2).
f(0,X1)=X2.
f(0,X1)=X1.
f(0,X1)=f(i(X1),f(X2,X1)).
X1=X1.
X1=f(0,X1).
f(0,f(X1,X2))=f(X2,f(i(X2),f(i(X1),f(i(X3),i(X3))))).
f(i(X2),i(X1))=X2.
X1=f(0,X2).
f(0,f(X1,f(X2,f(i(X1),f(i(X3),i(X2))))))=f(0,X2).
f(0,f(X2,f(X3,f(X3,X1))))=f(i(X2),f(i(X3),i(X2))).
f(0,f(X1,f(i(X2),f(i(X2),f(X1,f(X1,f(X1,f(i(X3),f(i(X2),X1)))))))))=f(i(X3),i(X1)).
X1=f(X2,f(i(X3),f(i(X1),i(X3)))).
X1=f(i(X2),i(X2)).
0=f(0,f(X1,f(X2,f(X3,f(i(X1),f(X3,f(i(X2),i(X1)))))))).
f(0,f(X1,f(X2,X2)))=i(X1).
f(i(X1),f(X2,f(X1,f(X3,f(X1,X3)))))=f(i(X3),i(X2)).
f(i(X1),f(i(X2),X3))=f(i(X1),X2).
f(i(X1),f(X3,f(X1,f(i(X2),i(X1)))))=f(0,f(X2,f(i(X3),X2))).
f(0,f(X1,X2))=X3.
f(i(X2),f(X1,f(X2,f(X1,X2))))=f(i(X1),f(i(X2),f(i(X2),f(i(X2),i(X3))))).
f(i(X1),i(X2))=f(0,f(X2,f(X2,f(X3,f(X2,X2))))).
f(0,f(X1,f(i(X2),f(X1,f(X2,X2)))))=f(X2,f(i(X1),i(X1))).
f(i(X1),f(X2,f(X3,i(X1))))=f(i(X1),f(X3,f(X3,f(X1,f(i(X2),i(X3)))))).
0=f(X1,f(X1,i(X2))).
f(i(X2),f(i(X1),f(i(X2),f(X1,f(X1,X1)))))=i(X3).
f(i(X3),X2)=i(X1).
f(i(X1),f(i(X1),i(X3)))=i(X3).
f(X1,f(X2,f(X1,X2)))=f(0,f(X2,i(X1))).
f(i(X1),f(X2,X1))=f(X3,f(i(X2),i(X3))).
f(i(X2),f(i(X2),f(X1,f(X3,X2))))=X3.
i(X1)=X2.
X1=f(i(X2),f(X3,f(X2,f(X3,f(X1,f(X1,X1)))))).
f(i(X1),f(i(X2),X3))=f(0,f(X3,f(X3,X1))).
f(i(X2),f(X1,f(X1,X1)))=f(i(X1),f(i(X3),f(i(X3),f(i(X1),i(X3))))).
0=f(0,f(X3,f(i(X1),f(i(X3),f(X2,i(X1)))))).
f(0,f(X1,f(X2,i(X3))))=f(0,f(X1,f(X2,i(X3)))).
f(0,f(X2,f(i(X1),X2)))=f(0,f(X3,f(X2,f(X2,f(X3,f(i(X1),i(X3))))))).
f(i(X2),X1)=f(i(X1),f(X3,f(X1,f(X1,f(i(X3),f(X2,X2)))))).
f(i(X1),f(i(X2),i(X1)))=X1.
f(0,f(X2,X1))=X1.
f(i(X1),f(i(X2),f(i(X2),f(i(X1),f(i(X3),X1)))))=f(X1,f(X1,X3)).
i(X1)=f(0,X2).
i(X1)=f(i(X2),f(X1,f(X1,X1))).
f(0,f(X1,X2))=i(X1).
X1=f(0,X2).
0=X1.
0=X1.
f(0,X1)=X2.
X1=f(i(X2),f(i(X3),f(X2,f(X3,f(X3,f(X3,X1)))))).
f(i(X1),f(i(X3),f(i(X3),f(i(X2),X3))))=f(0,f(X2,X1)).
i(X1)=0.
f(0,f(X1,f(X1,X2)))=f(0,f(X1,f(X3,f(X2,f(X1,f(X2,f(i(X3),i(X2)))))))).
0=i(X1).
f(0,f(X2,f(X2,f(X1,f(X1,f(X2,f(X3,f(X2,f(i(X3),i(X2))))))))))=i(X1).
i(X1)=f(X2,f(X1,i(X3))).
f(i(X1),f(i(X1),f(i(X1),f(i(X2),i(X1)))))=f(X2,f(X1,f(X3,f(i(X2),X3)))).
f(i(X3),f(i(X1),f(i(X2),f(i(X1),f(i(X1),X3)))))=f(i(X2),f(X1,i(X2))).
f(0,f(X1,f(i(X3),f(i(X2),i(X2)))))=f(i(X1),f(i(X1),f(i(X2),X1))).
f(0,X1)=f(0,f(X2,f(i(X3),f(i(X3),X1)))).
0=0.
X1=f(X2,X2).
f(i(X1),f(X2,f(i(X1),f(i(X3),X2))))=0.
f(X1,f(i(X2),i(X1)))=i(X1).
X1=f(0,f(X2,X3)).
0=f(0,f(X1,f(X2,f(X1,i(X3))))).
f(0,X1)=i(X2).
X1=f(i(X2),f(i(X3),i(X3))).
f(i(X1),f(X3,f(i(X2),f(i(X2),X3))))=X3.
f(0,f(X1,f(X2,X3)))=f(i(X1),f(i(X1),f(X2,f(X3,f(i(X1),f(X2,X2)))))).
f(0,f(X3,f(X2,f(X3,f(X2,X1)))))=f(0,f(X3,f(X3,f(X3,i(X2))))).
X1=f(0,f(X2,f(i(X3),f(i(X1),i(X2))))).
f(0,f(X1,f(i(X2),i(X2))))=0.
i(X1)=X1.
f(0,X1)=i(X2).
f(0,f(X1,X1))=f(i(X1),f(i(X2),i(X1))).
f(X1,f(i(X2),f(i(X1),f(i(X2),f(i(X2),f(i(X2),f(i(X2),i(X2))))))))=f(0,f(X3,f(X1,X1))).
