MAYBE MAYBE TRS: { mark(f(X1, X2, X3)) -> active(f(X1, mark(X2), X3)), mark(b()) -> active(b()), mark(a()) -> active(a()), f(X1, X2, mark(X3)) -> f(X1, X2, X3), f(X1, X2, active(X3)) -> f(X1, X2, X3), f(X1, mark(X2), X3) -> f(X1, X2, X3), f(X1, active(X2), X3) -> f(X1, X2, X3), f(mark(X1), X2, X3) -> f(X1, X2, X3), f(active(X1), X2, X3) -> f(X1, X2, X3), active(f(a(), X, X)) -> mark(f(X, b(), b())), active(b()) -> mark(a()) } DUP: We consider a non-duplicating system. Trs: { mark(f(X1, X2, X3)) -> active(f(X1, mark(X2), X3)), mark(b()) -> active(b()), mark(a()) -> active(a()), f(X1, X2, mark(X3)) -> f(X1, X2, X3), f(X1, X2, active(X3)) -> f(X1, X2, X3), f(X1, mark(X2), X3) -> f(X1, X2, X3), f(X1, active(X2), X3) -> f(X1, X2, X3), f(mark(X1), X2, X3) -> f(X1, X2, X3), f(active(X1), X2, X3) -> f(X1, X2, X3), active(f(a(), X, X)) -> mark(f(X, b(), b())), active(b()) -> mark(a()) } Fail