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