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()) -> s(0()) , inc(s(x)) -> s(inc(x)) , logarithm(x) -> logIter(x, 0()) , logIter(x, y) -> if(le(s(0()), x), le(s(s(0())), x), half(x), inc(y)) , if(true(), true(), x, y) -> logIter(x, y) , if(true(), false(), x, s(y)) -> y , if(false(), b, x, y) -> logZeroError() , f() -> g() , f() -> h() } Obligation: innermost runtime complexity Answer: MAYBE The input cannot be shown compatible Arrrr..