YES(?,O(n^1)) We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { rec[foldl_0][3](x6, Nil()) -> x6 , rec[foldl_0][3](x24, Cons(x40, x14)) -> rec[foldl_0][3](Cons(x40, x24), x14) , main(x3) -> rec[foldl_0][3](Nil(), x3) } 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(Nil) = {}, safe(rec[foldl_0][3]) = {1}, safe(Cons) = {1, 2}, safe(main) = {} and precedence main > rec[foldl_0][3] . Following symbols are considered recursive: {rec[foldl_0][3]} The recursion depth is 1. For your convenience, here are the satisfied ordering constraints: rec[foldl_0][3](Nil(); x6) > x6 rec[foldl_0][3](Cons(; x40, x14); x24) > rec[foldl_0][3](x14; Cons(; x40, x24)) main(x3;) > rec[foldl_0][3](x3; Nil()) Hurray, we answered YES(?,O(n^1))