We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ +(0(), y) -> y
, +(s(x), y) -> s(+(x, y))
, -(x, 0()) -> x
, -(0(), y) -> 0()
, -(s(x), s(y)) -> -(x, y) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The input was oriented with the instance of 'Small Polynomial Path
Order (PS)' as induced by the safe mapping
safe(+) = {2}, safe(0) = {}, safe(s) = {1}, safe(-) = {}
and precedence
empty .
Following symbols are considered recursive:
{+, -}
The recursion depth is 1.
For your convenience, here are the satisfied ordering constraints:
+(0(); y) > y
+(s(; x); y) > s(; +(x; y))
-(x, 0();) > x
-(0(), y;) > 0()
-(s(; x), s(; y);) > -(x, y;)
Hurray, we answered YES(?,O(n^1))