MAYBE Time: 0.007843 TRS: { app(app(app(curry(), g), x), y) -> app(app(g, x), y), app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)), app(app(plus(), 0()), y) -> y, app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)), app(app(map(), f), nil()) -> nil(), inc() -> app(map(), app(app(curry(), plus()), app(s(), 0())))} DP: DP: { app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), inc#() -> app#(app(curry(), plus()), app(s(), 0())), inc#() -> app#(s(), 0()), inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))), inc#() -> app#(curry(), plus())} TRS: { app(app(app(curry(), g), x), y) -> app(app(g, x), y), app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)), app(app(plus(), 0()), y) -> y, app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)), app(app(map(), f), nil()) -> nil(), inc() -> app(map(), app(app(curry(), plus()), app(s(), 0())))} UR: { app(app(app(curry(), g), x), y) -> app(app(g, x), y), app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)), app(app(plus(), 0()), y) -> y, app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)), app(app(map(), f), nil()) -> nil(), a(z, w) -> z, a(z, w) -> w} EDG: { (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(curry(), g), x), y) -> app#(g, x)) (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(app(curry(), g), x), y) -> app#(g, x)) (inc#() -> app#(s(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (inc#() -> app#(s(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (inc#() -> app#(s(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (inc#() -> app#(s(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (inc#() -> app#(s(), 0()), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (inc#() -> app#(s(), 0()), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (inc#() -> app#(s(), 0()), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (inc#() -> app#(s(), 0()), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (inc#() -> app#(s(), 0()), app#(app(app(curry(), g), x), y) -> app#(g, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(curry(), g), x), y) -> app#(g, x)) (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(app(curry(), g), x), y) -> app#(g, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(curry(), g), x), y) -> app#(g, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(curry(), g), x), y) -> app#(g, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(app(curry(), g), x), y) -> app#(g, x)) (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (inc#() -> app#(app(curry(), plus()), app(s(), 0())), app#(app(app(curry(), g), x), y) -> app#(g, x)) (inc#() -> app#(app(curry(), plus()), app(s(), 0())), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (inc#() -> app#(app(curry(), plus()), app(s(), 0())), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (inc#() -> app#(app(curry(), plus()), app(s(), 0())), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (inc#() -> app#(app(curry(), plus()), app(s(), 0())), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (inc#() -> app#(app(curry(), plus()), app(s(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (inc#() -> app#(app(curry(), plus()), app(s(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (inc#() -> app#(app(curry(), plus()), app(s(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (inc#() -> app#(app(curry(), plus()), app(s(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (inc#() -> app#(curry(), plus()), app#(app(app(curry(), g), x), y) -> app#(g, x)) (inc#() -> app#(curry(), plus()), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (inc#() -> app#(curry(), plus()), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (inc#() -> app#(curry(), plus()), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (inc#() -> app#(curry(), plus()), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (inc#() -> app#(curry(), plus()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (inc#() -> app#(curry(), plus()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (inc#() -> app#(curry(), plus()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (inc#() -> app#(curry(), plus()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))), app#(app(app(curry(), g), x), y) -> app#(g, x)) (inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(app(curry(), g), x), y) -> app#(g, x)) (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(app(curry(), g), x), y) -> app#(g, x)) (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y)) (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)) (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x)) (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y))) (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)) (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)) (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs))) (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))) } STATUS: arrows: 0.307692 SCCS (1): Scc: { app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))} SCC (9): Strict: { app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x))} Weak: { app(app(app(curry(), g), x), y) -> app(app(g, x), y), app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)), app(app(plus(), 0()), y) -> y, app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)), app(app(map(), f), nil()) -> nil(), inc() -> app(map(), app(app(curry(), plus()), app(s(), 0())))} Open