MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { plus(x, y) -> plusIter(x, y, 0()) , plusIter(x, y, z) -> ifPlus(le(x, z), x, y, z) , ifPlus(true(), x, y, z) -> y , ifPlus(false(), x, y, z) -> plusIter(x, s(y), s(z)) , le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , sum(xs) -> sumIter(xs, 0()) , sumIter(xs, x) -> ifSum(isempty(xs), xs, x, plus(x, head(xs))) , ifSum(true(), xs, x, y) -> x , ifSum(false(), xs, x, y) -> sumIter(tail(xs), y) , isempty(nil()) -> true() , isempty(cons(x, xs)) -> false() , head(nil()) -> error() , head(cons(x, xs)) -> x , tail(nil()) -> nil() , tail(cons(x, xs)) -> xs , a() -> b() , a() -> c() } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..