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