MAYBE MAYBE TRS: { app(app(app(comp(), f), g), x) -> app(f, app(g, x)), app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)), app(app(plus(), 0()), y) -> y, app(app(times(), app(s(), x)), y) -> app(app(plus(), app(app(times(), x), y)), y), app(app(times(), 0()), y) -> 0(), app(twice(), f) -> app(app(comp(), f), f) } DUP: We consider a duplicating system. Trs: { app(app(app(comp(), f), g), x) -> app(f, app(g, x)), app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)), app(app(plus(), 0()), y) -> y, app(app(times(), app(s(), x)), y) -> app(app(plus(), app(app(times(), x), y)), y), app(app(times(), 0()), y) -> 0(), app(twice(), f) -> app(app(comp(), f), f) } Fail