MAYBE MAYBE TRS: { app(l, nil()) -> l, app(nil(), k) -> k, app(cons(x, l), k) -> cons(x, app(l, k)), sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))), sum(cons(x, nil())) -> cons(x, nil()), sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)), sum(plus(cons(0(), x), cons(y, l))) -> pred(sum(cons(s(x), cons(y, l)))), plus(0(), y) -> y, plus(s(x), y) -> s(plus(x, y)), pred(cons(s(x), nil())) -> cons(x, nil()) } DUP: We consider a non-duplicating system. Trs: { app(l, nil()) -> l, app(nil(), k) -> k, app(cons(x, l), k) -> cons(x, app(l, k)), sum(app(l, cons(x, cons(y, k)))) -> sum(app(l, sum(cons(x, cons(y, k))))), sum(cons(x, nil())) -> cons(x, nil()), sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l)), sum(plus(cons(0(), x), cons(y, l))) -> pred(sum(cons(s(x), cons(y, l)))), plus(0(), y) -> y, plus(s(x), y) -> s(plus(x, y)), pred(cons(s(x), nil())) -> cons(x, nil()) } Fail