YES(?,O(n^1)) 20.37/6.04 YES(?,O(n^1)) 20.37/6.04 20.37/6.04 We are left with following problem, upon which TcT provides the 20.37/6.04 certificate YES(?,O(n^1)). 20.37/6.04 20.37/6.04 Strict Trs: 20.37/6.04 { f(nil()) -> nil() 20.37/6.04 , f(.(nil(), y)) -> .(nil(), f(y)) 20.37/6.04 , f(.(.(x, y), z)) -> f(.(x, .(y, z))) 20.37/6.04 , g(nil()) -> nil() 20.37/6.04 , g(.(x, nil())) -> .(g(x), nil()) 20.37/6.04 , g(.(x, .(y, z))) -> g(.(.(x, y), z)) } 20.37/6.04 Obligation: 20.37/6.04 innermost runtime complexity 20.37/6.04 Answer: 20.37/6.04 YES(?,O(n^1)) 20.37/6.04 20.37/6.04 The problem is match-bounded by 1. The enriched problem is 20.37/6.04 compatible with the following automaton. 20.37/6.04 { f_0(2) -> 1 20.37/6.04 , f_0(3) -> 1 20.37/6.04 , f_1(2) -> 5 20.37/6.04 , f_1(3) -> 5 20.37/6.04 , f_1(6) -> 1 20.37/6.04 , f_1(6) -> 5 20.37/6.04 , f_1(7) -> 5 20.37/6.04 , nil_0() -> 2 20.37/6.04 , nil_1() -> 1 20.37/6.04 , nil_1() -> 4 20.37/6.04 , nil_1() -> 5 20.37/6.04 , nil_1() -> 8 20.37/6.04 , ._0(2, 2) -> 3 20.37/6.04 , ._0(2, 3) -> 3 20.37/6.04 , ._0(3, 2) -> 3 20.37/6.04 , ._0(3, 3) -> 3 20.37/6.04 , ._1(1, 5) -> 1 20.37/6.04 , ._1(2, 2) -> 7 20.37/6.04 , ._1(2, 3) -> 7 20.37/6.04 , ._1(2, 6) -> 6 20.37/6.04 , ._1(2, 7) -> 6 20.37/6.04 , ._1(3, 2) -> 7 20.37/6.04 , ._1(3, 3) -> 7 20.37/6.04 , ._1(3, 6) -> 6 20.37/6.04 , ._1(3, 7) -> 6 20.37/6.04 , ._1(5, 5) -> 5 20.37/6.04 , ._1(7, 2) -> 9 20.37/6.04 , ._1(7, 3) -> 9 20.37/6.04 , ._1(8, 4) -> 4 20.37/6.04 , ._1(8, 8) -> 8 20.37/6.04 , ._1(9, 2) -> 9 20.37/6.04 , ._1(9, 3) -> 9 20.37/6.04 , g_0(2) -> 4 20.37/6.04 , g_0(3) -> 4 20.37/6.04 , g_1(2) -> 8 20.37/6.04 , g_1(3) -> 8 20.37/6.04 , g_1(7) -> 8 20.37/6.04 , g_1(9) -> 4 20.37/6.04 , g_1(9) -> 8 } 20.37/6.04 20.37/6.04 Hurray, we answered YES(?,O(n^1)) 20.37/6.05 EOF