MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { lcm(x, y) -> lcmIter(x, y, 0(), times(x, y)) , lcmIter(x, y, z, u) -> if(or(ge(0(), x), ge(z, u)), x, y, z, u) , times(x, y) -> ifTimes(ge(0(), x), x, y) , if(true(), x, y, z, u) -> z , if(false(), x, y, z, u) -> if2(divisible(z, y), x, y, z, u) , or(true(), y) -> true() , or(false(), y) -> y , ge(x, 0()) -> true() , ge(0(), s(y)) -> false() , ge(s(x), s(y)) -> ge(x, y) , if2(true(), x, y, z, u) -> z , if2(false(), x, y, z, u) -> lcmIter(x, y, plus(x, z), u) , divisible(0(), s(y)) -> true() , divisible(s(x), s(y)) -> div(s(x), s(y), s(y)) , plus(0(), y) -> y , plus(s(x), y) -> s(plus(x, y)) , ifTimes(true(), x, y) -> 0() , ifTimes(false(), x, y) -> plus(y, times(y, p(x))) , p(0()) -> s(s(0())) , p(s(x)) -> x , div(x, y, 0()) -> divisible(x, y) , div(0(), y, s(z)) -> false() , div(s(x), y, s(z)) -> div(x, y, z) , a() -> b() , a() -> c() } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..