YES(?,PRIMREC) We are left with following problem, upon which TcT provides the certificate YES(?,PRIMREC). Strict Trs: { half(0()) -> 0() , half(s(s(x))) -> s(half(x)) , log(s(0())) -> 0() , log(s(s(x))) -> s(log(s(half(x)))) } Obligation: innermost runtime complexity Answer: YES(?,PRIMREC) The input was oriented with the instance of'multiset path order' as induced by the precedence 0 > half, 0 > s, 0 > log, s > half, log > half, log > s . Hurray, we answered YES(?,PRIMREC)