YES(?,O(n^2))

We are left with following problem, upon which TcT provides the
certificate YES(?,O(n^2)).

Strict Trs:
  { and(tt(), X) -> X
  , plus(N, 0()) -> N
  , plus(N, s(M)) -> s(plus(N, M))
  , x(N, 0()) -> 0()
  , x(N, s(M)) -> plus(x(N, M), N) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(n^2))

The input was oriented with the instance of 'Small Polynomial Path
Order (PS)' as induced by the safe mapping

 safe(and) = {}, safe(tt) = {}, safe(plus) = {1}, safe(0) = {},
 safe(s) = {1}, safe(x) = {}

and precedence

 and > plus, x > plus, and ~ x .

Following symbols are considered recursive:

 {plus, x}

The recursion depth is 2.

For your convenience, here are the satisfied ordering constraints:

   and(tt(),  X;) > X                 
                                      
     plus(0(); N) > N                 
                                      
  plus(s(; M); N) > s(; plus(M; N))   
                                      
      x(N,  0();) > 0()               
                                      
   x(N,  s(; M);) > plus(N; x(N,  M;))
                                      

Hurray, we answered YES(?,O(n^2))