YES(?,O(n^1))
409.76/241.39	YES(?,O(n^1))
409.76/241.39	
409.76/241.39	We are left with following problem, upon which TcT provides the
409.76/241.39	certificate YES(?,O(n^1)).
409.76/241.39	
409.76/241.39	Strict Trs:
409.76/241.39	  { double(0()) -> 0()
409.76/241.39	  , double(s(x)) -> s(s(double(x)))
409.76/241.39	  , half(double(x)) -> x
409.76/241.39	  , half(0()) -> 0()
409.76/241.39	  , half(s(0())) -> 0()
409.76/241.39	  , half(s(s(x))) -> s(half(x))
409.76/241.39	  , -(x, 0()) -> x
409.76/241.39	  , -(s(x), s(y)) -> -(x, y)
409.76/241.39	  , if(0(), y, z) -> y
409.76/241.39	  , if(s(x), y, z) -> z }
409.76/241.39	Obligation:
409.76/241.39	  runtime complexity
409.76/241.39	Answer:
409.76/241.39	  YES(?,O(n^1))
409.76/241.39	
409.76/241.39	The problem is match-bounded by 1. The enriched problem is
409.76/241.39	compatible with the following automaton.
409.76/241.39	{ double_0(2) -> 1
409.76/241.39	, double_1(2) -> 4
409.76/241.39	, 0_0() -> 1
409.76/241.39	, 0_0() -> 2
409.76/241.39	, 0_1() -> 1
409.76/241.39	, 0_1() -> 3
409.76/241.39	, 0_1() -> 4
409.76/241.39	, s_0(2) -> 1
409.76/241.39	, s_0(2) -> 2
409.76/241.39	, s_1(3) -> 1
409.76/241.39	, s_1(3) -> 3
409.76/241.39	, s_1(3) -> 4
409.76/241.39	, s_1(4) -> 3
409.76/241.39	, half_0(2) -> 1
409.76/241.39	, half_1(2) -> 3
409.76/241.39	, -_0(2, 2) -> 1
409.76/241.39	, -_1(2, 2) -> 1
409.76/241.39	, if_0(2, 2, 2) -> 1 }
409.76/241.39	
409.76/241.39	Hurray, we answered YES(?,O(n^1))
410.22/241.73	EOF