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