We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).

Strict Trs:
  { p(m, n, s(r)) -> p(m, r, n)
  , p(m, s(n), 0()) -> p(0(), n, m)
  , p(m, 0(), 0()) -> m }
Obligation:
  runtime complexity
Answer:
  YES(?,O(n^1))

The input is overlay and right-linear. Switching to innermost
rewriting.

We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^1)).

Strict Trs:
  { p(m, n, s(r)) -> p(m, r, n)
  , p(m, s(n), 0()) -> p(0(), n, m)
  , p(m, 0(), 0()) -> m }
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(p) = {}, safe(s) = {1}, safe(0) = {}

and precedence

 empty .

Following symbols are considered recursive:

 {p}

The recursion depth is 1.

For your convenience, here are the satisfied ordering constraints:

    p(m,  n,  s(; r);) > p(m,  r,  n;)  
                                        
  p(m,  s(; n),  0();) > p(0(),  n,  m;)
                                        
     p(m,  0(),  0();) > m              
                                        

Hurray, we answered YES(?,O(n^1))