YES(?,O(n^1))
0.00/0.81	YES(?,O(n^1))
0.00/0.81	
0.00/0.81	We are left with following problem, upon which TcT provides the
0.00/0.81	certificate YES(?,O(n^1)).
0.00/0.81	
0.00/0.81	Strict Trs:
0.00/0.81	  { g(x, s(y)) -> g(f(x, y), 0())
0.00/0.81	  , g(0(), f(x, x)) -> x
0.00/0.81	  , g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0()))
0.00/0.81	  , g(s(x), y) -> g(f(x, y), 0()) }
0.00/0.81	Obligation:
0.00/0.81	  runtime complexity
0.00/0.81	Answer:
0.00/0.81	  YES(?,O(n^1))
0.00/0.81	
0.00/0.81	The input is overlay and right-linear. Switching to innermost
0.00/0.81	rewriting.
0.00/0.81	
0.00/0.81	We are left with following problem, upon which TcT provides the
0.00/0.81	certificate YES(?,O(n^1)).
0.00/0.81	
0.00/0.81	Strict Trs:
0.00/0.81	  { g(x, s(y)) -> g(f(x, y), 0())
0.00/0.81	  , g(0(), f(x, x)) -> x
0.00/0.81	  , g(f(x, y), 0()) -> f(g(x, 0()), g(y, 0()))
0.00/0.81	  , g(s(x), y) -> g(f(x, y), 0()) }
0.00/0.81	Obligation:
0.00/0.81	  innermost runtime complexity
0.00/0.81	Answer:
0.00/0.81	  YES(?,O(n^1))
0.00/0.81	
0.00/0.81	The problem is match-bounded by 2. The enriched problem is
0.00/0.81	compatible with the following automaton.
0.00/0.81	{ g_0(2, 2) -> 1
0.00/0.81	, g_1(2, 4) -> 5
0.00/0.81	, g_1(2, 4) -> 6
0.00/0.81	, g_1(3, 4) -> 1
0.00/0.81	, g_1(4, 4) -> 6
0.00/0.81	, g_1(11, 4) -> 7
0.00/0.81	, g_1(12, 4) -> 8
0.00/0.81	, g_2(2, 9) -> 7
0.00/0.81	, g_2(2, 10) -> 8
0.00/0.81	, g_2(4, 10) -> 13
0.00/0.81	, g_2(9, 10) -> 13
0.00/0.81	, g_2(10, 10) -> 13
0.00/0.81	, 0_0() -> 1
0.00/0.81	, 0_0() -> 2
0.00/0.81	, 0_1() -> 4
0.00/0.81	, 0_2() -> 9
0.00/0.81	, 0_2() -> 10
0.00/0.81	, f_0(2, 2) -> 1
0.00/0.81	, f_0(2, 2) -> 2
0.00/0.81	, f_1(2, 2) -> 3
0.00/0.81	, f_1(2, 4) -> 1
0.00/0.81	, f_1(2, 4) -> 2
0.00/0.81	, f_1(2, 9) -> 11
0.00/0.81	, f_1(2, 10) -> 12
0.00/0.81	, f_1(5, 6) -> 1
0.00/0.81	, f_1(6, 6) -> 5
0.00/0.81	, f_1(6, 6) -> 6
0.00/0.81	, f_1(6, 6) -> 7
0.00/0.81	, f_1(6, 6) -> 8
0.00/0.81	, f_2(7, 8) -> 1
0.00/0.81	, f_2(8, 13) -> 5
0.00/0.81	, f_2(8, 13) -> 6
0.00/0.81	, f_2(8, 13) -> 7
0.00/0.81	, f_2(8, 13) -> 8
0.00/0.81	, s_0(2) -> 1
0.00/0.81	, s_0(2) -> 2 }
0.00/0.81	
0.00/0.81	Hurray, we answered YES(?,O(n^1))
0.00/0.81	EOF