YES(?,O(n^1)) 19.91/5.93 YES(?,O(n^1)) 19.91/5.93 19.91/5.93 We are left with following problem, upon which TcT provides the 19.91/5.93 certificate YES(?,O(n^1)). 19.91/5.93 19.91/5.93 Strict Trs: 19.91/5.93 { f(nil()) -> nil() 19.91/5.93 , f(.(nil(), y)) -> .(nil(), f(y)) 19.91/5.93 , f(.(.(x, y), z)) -> f(.(x, .(y, z))) 19.91/5.93 , g(nil()) -> nil() 19.91/5.93 , g(.(x, nil())) -> .(g(x), nil()) 19.91/5.93 , g(.(x, .(y, z))) -> g(.(.(x, y), z)) } 19.91/5.93 Obligation: 19.91/5.93 runtime complexity 19.91/5.93 Answer: 19.91/5.93 YES(?,O(n^1)) 19.91/5.93 19.91/5.93 The input is overlay and right-linear. Switching to innermost 19.91/5.93 rewriting. 19.91/5.93 19.91/5.93 We are left with following problem, upon which TcT provides the 19.91/5.93 certificate YES(?,O(n^1)). 19.91/5.93 19.91/5.93 Strict Trs: 19.91/5.93 { f(nil()) -> nil() 19.91/5.93 , f(.(nil(), y)) -> .(nil(), f(y)) 19.91/5.93 , f(.(.(x, y), z)) -> f(.(x, .(y, z))) 19.91/5.93 , g(nil()) -> nil() 19.91/5.93 , g(.(x, nil())) -> .(g(x), nil()) 19.91/5.93 , g(.(x, .(y, z))) -> g(.(.(x, y), z)) } 19.91/5.93 Obligation: 19.91/5.93 innermost runtime complexity 19.91/5.93 Answer: 19.91/5.93 YES(?,O(n^1)) 19.91/5.93 19.91/5.93 The problem is match-bounded by 1. The enriched problem is 19.91/5.93 compatible with the following automaton. 19.91/5.93 { f_0(2) -> 1 19.91/5.93 , f_0(3) -> 1 19.91/5.93 , f_1(2) -> 5 19.91/5.93 , f_1(3) -> 5 19.91/5.93 , f_1(6) -> 1 19.91/5.93 , f_1(6) -> 5 19.91/5.93 , f_1(7) -> 5 19.91/5.93 , nil_0() -> 2 19.91/5.93 , nil_1() -> 1 19.91/5.93 , nil_1() -> 4 19.91/5.93 , nil_1() -> 5 19.91/5.93 , nil_1() -> 8 19.91/5.93 , ._0(2, 2) -> 3 19.91/5.93 , ._0(2, 3) -> 3 19.91/5.93 , ._0(3, 2) -> 3 19.91/5.93 , ._0(3, 3) -> 3 19.91/5.93 , ._1(1, 5) -> 1 19.91/5.93 , ._1(2, 2) -> 7 19.91/5.93 , ._1(2, 3) -> 7 19.91/5.93 , ._1(2, 6) -> 6 19.91/5.93 , ._1(2, 7) -> 6 19.91/5.93 , ._1(3, 2) -> 7 19.91/5.93 , ._1(3, 3) -> 7 19.91/5.93 , ._1(3, 6) -> 6 19.91/5.93 , ._1(3, 7) -> 6 19.91/5.93 , ._1(5, 5) -> 5 19.91/5.93 , ._1(7, 2) -> 9 19.91/5.93 , ._1(7, 3) -> 9 19.91/5.93 , ._1(8, 4) -> 4 19.91/5.93 , ._1(8, 8) -> 8 19.91/5.93 , ._1(9, 2) -> 9 19.91/5.93 , ._1(9, 3) -> 9 19.91/5.93 , g_0(2) -> 4 19.91/5.93 , g_0(3) -> 4 19.91/5.93 , g_1(2) -> 8 19.91/5.93 , g_1(3) -> 8 19.91/5.93 , g_1(7) -> 8 19.91/5.93 , g_1(9) -> 4 19.91/5.93 , g_1(9) -> 8 } 19.91/5.93 19.91/5.93 Hurray, we answered YES(?,O(n^1)) 19.91/5.94 EOF