YES(?,O(n^1)) 894.60/297.15 YES(?,O(n^1)) 894.60/297.15 894.60/297.15 We are left with following problem, upon which TcT provides the 894.60/297.15 certificate YES(?,O(n^1)). 894.60/297.15 894.60/297.15 Strict Trs: 894.60/297.15 { +(+(x, y), z) -> +(x, +(y, z)) 894.60/297.15 , +(*(x, y), +(*(x, z), u())) -> +(*(x, +(y, z)), u()) 894.60/297.15 , +(*(x, y), *(x, z)) -> *(x, +(y, z)) } 894.60/297.15 Obligation: 894.60/297.15 runtime complexity 894.60/297.15 Answer: 894.60/297.15 YES(?,O(n^1)) 894.60/297.15 894.60/297.15 The problem is match-bounded by 1. The enriched problem is 894.60/297.15 compatible with the following automaton. 894.60/297.15 { +_0(2, 2) -> 1 894.60/297.15 , +_0(2, 3) -> 1 894.60/297.15 , +_0(3, 2) -> 1 894.60/297.15 , +_0(3, 3) -> 1 894.60/297.15 , +_1(2, 2) -> 4 894.60/297.15 , +_1(2, 3) -> 4 894.60/297.15 , +_1(3, 2) -> 4 894.60/297.15 , +_1(3, 3) -> 4 894.60/297.15 , *_0(2, 2) -> 2 894.60/297.15 , *_0(2, 3) -> 2 894.60/297.15 , *_0(3, 2) -> 2 894.60/297.15 , *_0(3, 3) -> 2 894.60/297.15 , *_1(2, 4) -> 1 894.60/297.15 , *_1(2, 4) -> 4 894.60/297.15 , *_1(3, 4) -> 1 894.60/297.15 , *_1(3, 4) -> 4 894.60/297.15 , u_0() -> 3 } 894.60/297.15 894.60/297.15 Hurray, we answered YES(?,O(n^1)) 895.07/297.49 EOF