YES(?,PRIMREC) We are left with following problem, upon which TcT provides the certificate YES(?,PRIMREC). Strict Trs: { D(t()) -> 1() , D(constant()) -> 0() , D(+(x, y)) -> +(D(x), D(y)) , D(*(x, y)) -> +(*(y, D(x)), *(x, D(y))) , D(-(x, y)) -> -(D(x), D(y)) } Obligation: innermost runtime complexity Answer: YES(?,PRIMREC) The input was oriented with the instance of'multiset path order' as induced by the precedence D > 1, D > +, D > *, D > -, t > 1, t > +, t > *, t > -, constant > 1, constant > +, constant > *, constant > -, 0 > 1, 0 > +, 0 > *, 0 > -, D ~ t, D ~ constant, D ~ 0, t ~ constant, t ~ 0, 1 ~ +, 1 ~ *, 1 ~ -, constant ~ 0, + ~ *, + ~ -, * ~ - . Hurray, we answered YES(?,PRIMREC)