MAYBE Time: 0.009135 TRS: { if(true(), x, y) -> averIter(y, x, y), if(false(), x, y) -> averIter(x, y, x), ge(x, 0()) -> true(), ge(s x, s y) -> ge(x, y), ge(0(), s y) -> false(), average(x, y) -> if(ge(x, y), x, y), averIter(x, y, z) -> ifIter(ge(x, y), x, y, z), ifIter(true(), x, y, z) -> z, ifIter(false(), x, y, z) -> averIter(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), plus(s x, y) -> s plus(x, y), plus(0(), y) -> y, append(nil(), y) -> y, append(cons(n, x), y) -> cons(n, app(x, y)), low(n, nil()) -> nil(), low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)), if_low(true(), n, cons(m, x)) -> low(n, x), if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)), high(n, nil()) -> nil(), high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)), if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)), if_high(false(), n, cons(m, x)) -> high(n, x), ifquick(true(), x) -> nil(), ifquick(false(), x) -> append(quicksort low(head x, tail x), cons(tail x, quicksort high(head x, tail x))), isempty nil() -> true(), isempty cons(n, x) -> false(), quicksort x -> ifquick(isempty x, x), head nil() -> error(), head cons(n, x) -> n, tail nil() -> nil(), tail cons(n, x) -> x, a() -> b(), a() -> c()} DP: DP: { if#(true(), x, y) -> averIter#(y, x, y), if#(false(), x, y) -> averIter#(x, y, x), ge#(s x, s y) -> ge#(x, y), average#(x, y) -> if#(ge(x, y), x, y), average#(x, y) -> ge#(x, y), averIter#(x, y, z) -> ge#(x, y), averIter#(x, y, z) -> ifIter#(ge(x, y), x, y, z), ifIter#(false(), x, y, z) -> averIter#(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), ifIter#(false(), x, y, z) -> plus#(x, s s s 0()), ifIter#(false(), x, y, z) -> plus#(y, s 0()), ifIter#(false(), x, y, z) -> plus#(z, s 0()), plus#(s x, y) -> plus#(x, y), low#(n, cons(m, x)) -> ge#(m, n), low#(n, cons(m, x)) -> if_low#(ge(m, n), n, cons(m, x)), if_low#(true(), n, cons(m, x)) -> low#(n, x), if_low#(false(), n, cons(m, x)) -> low#(n, x), high#(n, cons(m, x)) -> ge#(m, n), high#(n, cons(m, x)) -> if_high#(ge(m, n), n, cons(m, x)), if_high#(true(), n, cons(m, x)) -> average#(m, m), if_high#(true(), n, cons(m, x)) -> high#(n, x), if_high#(false(), n, cons(m, x)) -> high#(n, x), ifquick#(false(), x) -> append#(quicksort low(head x, tail x), cons(tail x, quicksort high(head x, tail x))), ifquick#(false(), x) -> low#(head x, tail x), ifquick#(false(), x) -> high#(head x, tail x), ifquick#(false(), x) -> quicksort# low(head x, tail x), ifquick#(false(), x) -> quicksort# high(head x, tail x), ifquick#(false(), x) -> head# x, ifquick#(false(), x) -> tail# x, quicksort# x -> ifquick#(isempty x, x), quicksort# x -> isempty# x} TRS: { if(true(), x, y) -> averIter(y, x, y), if(false(), x, y) -> averIter(x, y, x), ge(x, 0()) -> true(), ge(s x, s y) -> ge(x, y), ge(0(), s y) -> false(), average(x, y) -> if(ge(x, y), x, y), averIter(x, y, z) -> ifIter(ge(x, y), x, y, z), ifIter(true(), x, y, z) -> z, ifIter(false(), x, y, z) -> averIter(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), plus(s x, y) -> s plus(x, y), plus(0(), y) -> y, append(nil(), y) -> y, append(cons(n, x), y) -> cons(n, app(x, y)), low(n, nil()) -> nil(), low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)), if_low(true(), n, cons(m, x)) -> low(n, x), if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)), high(n, nil()) -> nil(), high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)), if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)), if_high(false(), n, cons(m, x)) -> high(n, x), ifquick(true(), x) -> nil(), ifquick(false(), x) -> append(quicksort low(head x, tail x), cons(tail x, quicksort high(head x, tail x))), isempty nil() -> true(), isempty cons(n, x) -> false(), quicksort x -> ifquick(isempty x, x), head nil() -> error(), head cons(n, x) -> n, tail nil() -> nil(), tail cons(n, x) -> x, a() -> b(), a() -> c()} EDG: {(ifIter#(false(), x, y, z) -> plus#(y, s 0()), plus#(s x, y) -> plus#(x, y)) (ifquick#(false(), x) -> low#(head x, tail x), low#(n, cons(m, x)) -> if_low#(ge(m, n), n, cons(m, x))) (ifquick#(false(), x) -> low#(head x, tail x), low#(n, cons(m, x)) -> ge#(m, n)) (if#(true(), x, y) -> averIter#(y, x, y), averIter#(x, y, z) -> ifIter#(ge(x, y), x, y, z)) (if#(true(), x, y) -> averIter#(y, x, y), averIter#(x, y, z) -> ge#(x, y)) (if#(false(), x, y) -> averIter#(x, y, x), averIter#(x, y, z) -> ifIter#(ge(x, y), x, y, z)) (if#(false(), x, y) -> averIter#(x, y, x), averIter#(x, y, z) -> ge#(x, y)) (if_high#(true(), n, cons(m, x)) -> average#(m, m), average#(x, y) -> ge#(x, y)) (if_high#(true(), n, cons(m, x)) -> average#(m, m), average#(x, y) -> if#(ge(x, y), x, y)) (high#(n, cons(m, x)) -> ge#(m, n), ge#(s x, s y) -> ge#(x, y)) (ge#(s x, s y) -> ge#(x, y), ge#(s x, s y) -> ge#(x, y)) (averIter#(x, y, z) -> ge#(x, y), ge#(s x, s y) -> ge#(x, y)) (plus#(s x, y) -> plus#(x, y), plus#(s x, y) -> plus#(x, y)) (if_low#(true(), n, cons(m, x)) -> low#(n, x), low#(n, cons(m, x)) -> if_low#(ge(m, n), n, cons(m, x))) (if_low#(true(), n, cons(m, x)) -> low#(n, x), low#(n, cons(m, x)) -> ge#(m, n)) (high#(n, cons(m, x)) -> if_high#(ge(m, n), n, cons(m, x)), if_high#(false(), n, cons(m, x)) -> high#(n, x)) (high#(n, cons(m, x)) -> if_high#(ge(m, n), n, cons(m, x)), if_high#(true(), n, cons(m, x)) -> high#(n, x)) (high#(n, cons(m, x)) -> if_high#(ge(m, n), n, cons(m, x)), if_high#(true(), n, cons(m, x)) -> average#(m, m)) (if_high#(false(), n, cons(m, x)) -> high#(n, x), high#(n, cons(m, x)) -> if_high#(ge(m, n), n, cons(m, x))) (if_high#(false(), n, cons(m, x)) -> high#(n, x), high#(n, cons(m, x)) -> ge#(m, n)) (ifquick#(false(), x) -> quicksort# high(head x, tail x), quicksort# x -> isempty# x) (ifquick#(false(), x) -> quicksort# high(head x, tail x), quicksort# x -> ifquick#(isempty x, x)) (ifquick#(false(), x) -> quicksort# low(head x, tail x), quicksort# x -> ifquick#(isempty x, x)) (ifquick#(false(), x) -> quicksort# low(head x, tail x), quicksort# x -> isempty# x) (if_high#(true(), n, cons(m, x)) -> high#(n, x), high#(n, cons(m, x)) -> ge#(m, n)) (if_high#(true(), n, cons(m, x)) -> high#(n, x), high#(n, cons(m, x)) -> if_high#(ge(m, n), n, cons(m, x))) (if_low#(false(), n, cons(m, x)) -> low#(n, x), low#(n, cons(m, x)) -> ge#(m, n)) (if_low#(false(), n, cons(m, x)) -> low#(n, x), low#(n, cons(m, x)) -> if_low#(ge(m, n), n, cons(m, x))) (low#(n, cons(m, x)) -> if_low#(ge(m, n), n, cons(m, x)), if_low#(true(), n, cons(m, x)) -> low#(n, x)) (low#(n, cons(m, x)) -> if_low#(ge(m, n), n, cons(m, x)), if_low#(false(), n, cons(m, x)) -> low#(n, x)) (ifIter#(false(), x, y, z) -> averIter#(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), averIter#(x, y, z) -> ge#(x, y)) (ifIter#(false(), x, y, z) -> averIter#(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), averIter#(x, y, z) -> ifIter#(ge(x, y), x, y, z)) (average#(x, y) -> ge#(x, y), ge#(s x, s y) -> ge#(x, y)) (averIter#(x, y, z) -> ifIter#(ge(x, y), x, y, z), ifIter#(false(), x, y, z) -> averIter#(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0()))) (averIter#(x, y, z) -> ifIter#(ge(x, y), x, y, z), ifIter#(false(), x, y, z) -> plus#(x, s s s 0())) (averIter#(x, y, z) -> ifIter#(ge(x, y), x, y, z), ifIter#(false(), x, y, z) -> plus#(y, s 0())) (averIter#(x, y, z) -> ifIter#(ge(x, y), x, y, z), ifIter#(false(), x, y, z) -> plus#(z, s 0())) (low#(n, cons(m, x)) -> ge#(m, n), ge#(s x, s y) -> ge#(x, y)) (quicksort# x -> ifquick#(isempty x, x), ifquick#(false(), x) -> append#(quicksort low(head x, tail x), cons(tail x, quicksort high(head x, tail x)))) (quicksort# x -> ifquick#(isempty x, x), ifquick#(false(), x) -> low#(head x, tail x)) (quicksort# x -> ifquick#(isempty x, x), ifquick#(false(), x) -> high#(head x, tail x)) (quicksort# x -> ifquick#(isempty x, x), ifquick#(false(), x) -> quicksort# low(head x, tail x)) (quicksort# x -> ifquick#(isempty x, x), ifquick#(false(), x) -> quicksort# high(head x, tail x)) (quicksort# x -> ifquick#(isempty x, x), ifquick#(false(), x) -> head# x) (quicksort# x -> ifquick#(isempty x, x), ifquick#(false(), x) -> tail# x) (average#(x, y) -> if#(ge(x, y), x, y), if#(true(), x, y) -> averIter#(y, x, y)) (average#(x, y) -> if#(ge(x, y), x, y), if#(false(), x, y) -> averIter#(x, y, x)) (ifquick#(false(), x) -> high#(head x, tail x), high#(n, cons(m, x)) -> ge#(m, n)) (ifquick#(false(), x) -> high#(head x, tail x), high#(n, cons(m, x)) -> if_high#(ge(m, n), n, cons(m, x))) (ifIter#(false(), x, y, z) -> plus#(z, s 0()), plus#(s x, y) -> plus#(x, y)) (ifIter#(false(), x, y, z) -> plus#(x, s s s 0()), plus#(s x, y) -> plus#(x, y))} STATUS: arrows: 0.943333 SCCS (6): Scc: {ifquick#(false(), x) -> quicksort# low(head x, tail x), ifquick#(false(), x) -> quicksort# high(head x, tail x), quicksort# x -> ifquick#(isempty x, x)} Scc: { high#(n, cons(m, x)) -> if_high#(ge(m, n), n, cons(m, x)), if_high#(true(), n, cons(m, x)) -> high#(n, x), if_high#(false(), n, cons(m, x)) -> high#(n, x)} Scc: { averIter#(x, y, z) -> ifIter#(ge(x, y), x, y, z), ifIter#(false(), x, y, z) -> averIter#(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0()))} Scc: { low#(n, cons(m, x)) -> if_low#(ge(m, n), n, cons(m, x)), if_low#(true(), n, cons(m, x)) -> low#(n, x), if_low#(false(), n, cons(m, x)) -> low#(n, x)} Scc: {ge#(s x, s y) -> ge#(x, y)} Scc: {plus#(s x, y) -> plus#(x, y)} SCC (3): Strict: {ifquick#(false(), x) -> quicksort# low(head x, tail x), ifquick#(false(), x) -> quicksort# high(head x, tail x), quicksort# x -> ifquick#(isempty x, x)} Weak: { if(true(), x, y) -> averIter(y, x, y), if(false(), x, y) -> averIter(x, y, x), ge(x, 0()) -> true(), ge(s x, s y) -> ge(x, y), ge(0(), s y) -> false(), average(x, y) -> if(ge(x, y), x, y), averIter(x, y, z) -> ifIter(ge(x, y), x, y, z), ifIter(true(), x, y, z) -> z, ifIter(false(), x, y, z) -> averIter(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), plus(s x, y) -> s plus(x, y), plus(0(), y) -> y, append(nil(), y) -> y, append(cons(n, x), y) -> cons(n, app(x, y)), low(n, nil()) -> nil(), low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)), if_low(true(), n, cons(m, x)) -> low(n, x), if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)), high(n, nil()) -> nil(), high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)), if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)), if_high(false(), n, cons(m, x)) -> high(n, x), ifquick(true(), x) -> nil(), ifquick(false(), x) -> append(quicksort low(head x, tail x), cons(tail x, quicksort high(head x, tail x))), isempty nil() -> true(), isempty cons(n, x) -> false(), quicksort x -> ifquick(isempty x, x), head nil() -> error(), head cons(n, x) -> n, tail nil() -> nil(), tail cons(n, x) -> x, a() -> b(), a() -> c()} Open SCC (3): Strict: { high#(n, cons(m, x)) -> if_high#(ge(m, n), n, cons(m, x)), if_high#(true(), n, cons(m, x)) -> high#(n, x), if_high#(false(), n, cons(m, x)) -> high#(n, x)} Weak: { if(true(), x, y) -> averIter(y, x, y), if(false(), x, y) -> averIter(x, y, x), ge(x, 0()) -> true(), ge(s x, s y) -> ge(x, y), ge(0(), s y) -> false(), average(x, y) -> if(ge(x, y), x, y), averIter(x, y, z) -> ifIter(ge(x, y), x, y, z), ifIter(true(), x, y, z) -> z, ifIter(false(), x, y, z) -> averIter(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), plus(s x, y) -> s plus(x, y), plus(0(), y) -> y, append(nil(), y) -> y, append(cons(n, x), y) -> cons(n, app(x, y)), low(n, nil()) -> nil(), low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)), if_low(true(), n, cons(m, x)) -> low(n, x), if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)), high(n, nil()) -> nil(), high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)), if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)), if_high(false(), n, cons(m, x)) -> high(n, x), ifquick(true(), x) -> nil(), ifquick(false(), x) -> append(quicksort low(head x, tail x), cons(tail x, quicksort high(head x, tail x))), isempty nil() -> true(), isempty cons(n, x) -> false(), quicksort x -> ifquick(isempty x, x), head nil() -> error(), head cons(n, x) -> n, tail nil() -> nil(), tail cons(n, x) -> x, a() -> b(), a() -> c()} Open SCC (2): Strict: { averIter#(x, y, z) -> ifIter#(ge(x, y), x, y, z), ifIter#(false(), x, y, z) -> averIter#(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0()))} Weak: { if(true(), x, y) -> averIter(y, x, y), if(false(), x, y) -> averIter(x, y, x), ge(x, 0()) -> true(), ge(s x, s y) -> ge(x, y), ge(0(), s y) -> false(), average(x, y) -> if(ge(x, y), x, y), averIter(x, y, z) -> ifIter(ge(x, y), x, y, z), ifIter(true(), x, y, z) -> z, ifIter(false(), x, y, z) -> averIter(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), plus(s x, y) -> s plus(x, y), plus(0(), y) -> y, append(nil(), y) -> y, append(cons(n, x), y) -> cons(n, app(x, y)), low(n, nil()) -> nil(), low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)), if_low(true(), n, cons(m, x)) -> low(n, x), if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)), high(n, nil()) -> nil(), high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)), if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)), if_high(false(), n, cons(m, x)) -> high(n, x), ifquick(true(), x) -> nil(), ifquick(false(), x) -> append(quicksort low(head x, tail x), cons(tail x, quicksort high(head x, tail x))), isempty nil() -> true(), isempty cons(n, x) -> false(), quicksort x -> ifquick(isempty x, x), head nil() -> error(), head cons(n, x) -> n, tail nil() -> nil(), tail cons(n, x) -> x, a() -> b(), a() -> c()} Open SCC (3): Strict: { low#(n, cons(m, x)) -> if_low#(ge(m, n), n, cons(m, x)), if_low#(true(), n, cons(m, x)) -> low#(n, x), if_low#(false(), n, cons(m, x)) -> low#(n, x)} Weak: { if(true(), x, y) -> averIter(y, x, y), if(false(), x, y) -> averIter(x, y, x), ge(x, 0()) -> true(), ge(s x, s y) -> ge(x, y), ge(0(), s y) -> false(), average(x, y) -> if(ge(x, y), x, y), averIter(x, y, z) -> ifIter(ge(x, y), x, y, z), ifIter(true(), x, y, z) -> z, ifIter(false(), x, y, z) -> averIter(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), plus(s x, y) -> s plus(x, y), plus(0(), y) -> y, append(nil(), y) -> y, append(cons(n, x), y) -> cons(n, app(x, y)), low(n, nil()) -> nil(), low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)), if_low(true(), n, cons(m, x)) -> low(n, x), if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)), high(n, nil()) -> nil(), high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)), if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)), if_high(false(), n, cons(m, x)) -> high(n, x), ifquick(true(), x) -> nil(), ifquick(false(), x) -> append(quicksort low(head x, tail x), cons(tail x, quicksort high(head x, tail x))), isempty nil() -> true(), isempty cons(n, x) -> false(), quicksort x -> ifquick(isempty x, x), head nil() -> error(), head cons(n, x) -> n, tail nil() -> nil(), tail cons(n, x) -> x, a() -> b(), a() -> c()} Open SCC (1): Strict: {ge#(s x, s y) -> ge#(x, y)} Weak: { if(true(), x, y) -> averIter(y, x, y), if(false(), x, y) -> averIter(x, y, x), ge(x, 0()) -> true(), ge(s x, s y) -> ge(x, y), ge(0(), s y) -> false(), average(x, y) -> if(ge(x, y), x, y), averIter(x, y, z) -> ifIter(ge(x, y), x, y, z), ifIter(true(), x, y, z) -> z, ifIter(false(), x, y, z) -> averIter(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), plus(s x, y) -> s plus(x, y), plus(0(), y) -> y, append(nil(), y) -> y, append(cons(n, x), y) -> cons(n, app(x, y)), low(n, nil()) -> nil(), low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)), if_low(true(), n, cons(m, x)) -> low(n, x), if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)), high(n, nil()) -> nil(), high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)), if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)), if_high(false(), n, cons(m, x)) -> high(n, x), ifquick(true(), x) -> nil(), ifquick(false(), x) -> append(quicksort low(head x, tail x), cons(tail x, quicksort high(head x, tail x))), isempty nil() -> true(), isempty cons(n, x) -> false(), quicksort x -> ifquick(isempty x, x), head nil() -> error(), head cons(n, x) -> n, tail nil() -> nil(), tail cons(n, x) -> x, a() -> b(), a() -> c()} Open SCC (1): Strict: {plus#(s x, y) -> plus#(x, y)} Weak: { if(true(), x, y) -> averIter(y, x, y), if(false(), x, y) -> averIter(x, y, x), ge(x, 0()) -> true(), ge(s x, s y) -> ge(x, y), ge(0(), s y) -> false(), average(x, y) -> if(ge(x, y), x, y), averIter(x, y, z) -> ifIter(ge(x, y), x, y, z), ifIter(true(), x, y, z) -> z, ifIter(false(), x, y, z) -> averIter(plus(x, s s s 0()), plus(y, s 0()), plus(z, s 0())), plus(s x, y) -> s plus(x, y), plus(0(), y) -> y, append(nil(), y) -> y, append(cons(n, x), y) -> cons(n, app(x, y)), low(n, nil()) -> nil(), low(n, cons(m, x)) -> if_low(ge(m, n), n, cons(m, x)), if_low(true(), n, cons(m, x)) -> low(n, x), if_low(false(), n, cons(m, x)) -> cons(m, low(n, x)), high(n, nil()) -> nil(), high(n, cons(m, x)) -> if_high(ge(m, n), n, cons(m, x)), if_high(true(), n, cons(m, x)) -> cons(average(m, m), high(n, x)), if_high(false(), n, cons(m, x)) -> high(n, x), ifquick(true(), x) -> nil(), ifquick(false(), x) -> append(quicksort low(head x, tail x), cons(tail x, quicksort high(head x, tail x))), isempty nil() -> true(), isempty cons(n, x) -> false(), quicksort x -> ifquick(isempty x, x), head nil() -> error(), head cons(n, x) -> n, tail nil() -> nil(), tail cons(n, x) -> x, a() -> b(), a() -> c()} Open