MAYBE MAYBE TRS: { active(app(X1, X2)) -> app(X1, active(X2)), active(app(X1, X2)) -> app(active(X1), X2), active(app(nil(), YS)) -> mark(YS), active(app(cons(X, XS), YS)) -> mark(cons(X, app(XS, YS))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(zWadr(XS, nil())) -> mark(nil()), active(zWadr(X1, X2)) -> zWadr(X1, active(X2)), active(zWadr(X1, X2)) -> zWadr(active(X1), X2), active(zWadr(nil(), YS)) -> mark(nil()), active(zWadr(cons(X, XS), cons(Y, YS))) -> mark(cons(app(Y, cons(X, nil())), zWadr(XS, YS))), active(prefix(X)) -> prefix(active(X)), active(prefix(L)) -> mark(cons(nil(), zWadr(L, prefix(L)))), app(X1, mark(X2)) -> mark(app(X1, X2)), app(mark(X1), X2) -> mark(app(X1, X2)), app(ok(X1), ok(X2)) -> ok(app(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), zWadr(X1, mark(X2)) -> mark(zWadr(X1, X2)), zWadr(mark(X1), X2) -> mark(zWadr(X1, X2)), zWadr(ok(X1), ok(X2)) -> ok(zWadr(X1, X2)), prefix(mark(X)) -> mark(prefix(X)), prefix(ok(X)) -> ok(prefix(X)), proper(app(X1, X2)) -> app(proper(X1), proper(X2)), proper(nil()) -> ok(nil()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(zWadr(X1, X2)) -> zWadr(proper(X1), proper(X2)), proper(prefix(X)) -> prefix(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X)) } DUP: We consider a duplicating system. Trs: { active(app(X1, X2)) -> app(X1, active(X2)), active(app(X1, X2)) -> app(active(X1), X2), active(app(nil(), YS)) -> mark(YS), active(app(cons(X, XS), YS)) -> mark(cons(X, app(XS, YS))), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(zWadr(XS, nil())) -> mark(nil()), active(zWadr(X1, X2)) -> zWadr(X1, active(X2)), active(zWadr(X1, X2)) -> zWadr(active(X1), X2), active(zWadr(nil(), YS)) -> mark(nil()), active(zWadr(cons(X, XS), cons(Y, YS))) -> mark(cons(app(Y, cons(X, nil())), zWadr(XS, YS))), active(prefix(X)) -> prefix(active(X)), active(prefix(L)) -> mark(cons(nil(), zWadr(L, prefix(L)))), app(X1, mark(X2)) -> mark(app(X1, X2)), app(mark(X1), X2) -> mark(app(X1, X2)), app(ok(X1), ok(X2)) -> ok(app(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), zWadr(X1, mark(X2)) -> mark(zWadr(X1, X2)), zWadr(mark(X1), X2) -> mark(zWadr(X1, X2)), zWadr(ok(X1), ok(X2)) -> ok(zWadr(X1, X2)), prefix(mark(X)) -> mark(prefix(X)), prefix(ok(X)) -> ok(prefix(X)), proper(app(X1, X2)) -> app(proper(X1), proper(X2)), proper(nil()) -> ok(nil()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(zWadr(X1, X2)) -> zWadr(proper(X1), proper(X2)), proper(prefix(X)) -> prefix(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X)) } Fail