We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { odd(Cons(x, xs)) -> even(xs) , odd(Nil()) -> False() , even(Cons(x, xs)) -> odd(xs) , even(Nil()) -> True() , notEmpty(Cons(x, xs)) -> True() , notEmpty(Nil()) -> False() , evenodd(x) -> even(x) } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The input was oriented with the instance of 'Small Polynomial Path Order (PS,1-bounded)' as induced by the safe mapping safe(odd) = {}, safe(Cons) = {1, 2}, safe(even) = {}, safe(Nil) = {}, safe(False) = {}, safe(notEmpty) = {}, safe(True) = {}, safe(evenodd) = {} and precedence evenodd > even, odd ~ even . Following symbols are considered recursive: {odd, even} The recursion depth is 1. For your convenience, here are the satisfied ordering constraints: odd(Cons(; x, xs);) > even(xs;) odd(Nil();) > False() even(Cons(; x, xs);) > odd(xs;) even(Nil();) > True() notEmpty(Cons(; x, xs);) > True() notEmpty(Nil();) > False() evenodd(x;) > even(x;) Hurray, we answered YES(?,O(n^1))