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