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