MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { half(0()) -> 0() , half(s(0())) -> 0() , half(s(s(x))) -> s(half(x)) , le(0(), y) -> true() , le(s(x), 0()) -> false() , le(s(x), s(y)) -> le(x, y) , inc(0()) -> 0() , inc(s(x)) -> s(inc(x)) , log(x) -> log2(x, 0()) , log2(x, y) -> if(le(x, s(0())), x, inc(y)) , if(true(), x, s(y)) -> y , if(false(), x, y) -> log2(half(x), y) } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..