YES(?,O(n^1)) 0.00/0.76 YES(?,O(n^1)) 0.00/0.76 0.00/0.76 We are left with following problem, upon which TcT provides the 0.00/0.76 certificate YES(?,O(n^1)). 0.00/0.76 0.00/0.76 Strict Trs: 0.00/0.76 { ++(x, nil()) -> x 0.00/0.76 , ++(++(x, y), z) -> ++(x, ++(y, z)) 0.00/0.76 , ++(nil(), y) -> y 0.00/0.76 , ++(.(x, y), z) -> .(x, ++(y, z)) } 0.00/0.76 Obligation: 0.00/0.76 runtime complexity 0.00/0.76 Answer: 0.00/0.76 YES(?,O(n^1)) 0.00/0.76 0.00/0.76 The problem is match-bounded by 1. The enriched problem is 0.00/0.76 compatible with the following automaton. 0.00/0.76 { ++_0(2, 2) -> 1 0.00/0.76 , ++_0(2, 3) -> 1 0.00/0.76 , ++_0(3, 2) -> 1 0.00/0.76 , ++_0(3, 3) -> 1 0.00/0.76 , ++_1(2, 2) -> 4 0.00/0.76 , ++_1(2, 3) -> 4 0.00/0.76 , ++_1(3, 2) -> 4 0.00/0.76 , ++_1(3, 3) -> 4 0.00/0.76 , nil_0() -> 1 0.00/0.76 , nil_0() -> 2 0.00/0.76 , nil_0() -> 4 0.00/0.76 , ._0(2, 2) -> 1 0.00/0.76 , ._0(2, 2) -> 3 0.00/0.76 , ._0(2, 2) -> 4 0.00/0.76 , ._0(2, 3) -> 1 0.00/0.76 , ._0(2, 3) -> 3 0.00/0.76 , ._0(2, 3) -> 4 0.00/0.76 , ._0(3, 2) -> 1 0.00/0.76 , ._0(3, 2) -> 3 0.00/0.76 , ._0(3, 2) -> 4 0.00/0.76 , ._0(3, 3) -> 1 0.00/0.76 , ._0(3, 3) -> 3 0.00/0.76 , ._0(3, 3) -> 4 0.00/0.76 , ._1(2, 4) -> 1 0.00/0.76 , ._1(2, 4) -> 4 0.00/0.76 , ._1(3, 4) -> 1 0.00/0.76 , ._1(3, 4) -> 4 } 0.00/0.76 0.00/0.76 Hurray, we answered YES(?,O(n^1)) 0.00/0.76 EOF