We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).
Strict Trs:
{ not(true()) -> false()
, not(false()) -> true()
, odd(0()) -> false()
, odd(s(x)) -> not(odd(x))
, +(x, 0()) -> x
, +(x, s(y)) -> s(+(x, y))
, +(s(x), y) -> s(+(x, y)) }
Obligation:
innermost runtime complexity
Answer:
YES(?,O(n^1))
The input was oriented with the instance of 'Small Polynomial Path
Order (PS,1-bounded)' as induced by the safe mapping
safe(not) = {1}, safe(true) = {}, safe(false) = {}, safe(odd) = {},
safe(0) = {}, safe(s) = {1}, safe(+) = {}
and precedence
odd > not .
Following symbols are considered recursive:
{odd, +}
The recursion depth is 1.
For your convenience, here are the satisfied ordering constraints:
not(; true()) > false()
not(; false()) > true()
odd(0();) > false()
odd(s(; x);) > not(; odd(x;))
+(x, 0();) > x
+(x, s(; y);) > s(; +(x, y;))
+(s(; x), y;) > s(; +(x, y;))
Hurray, we answered YES(?,O(n^1))