YES(?,POLY)

'Pop* with parameter subtitution (timeout of 60.0 seconds)'
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Answer:           YES(?,POLY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  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)}

Proof Output:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   and > plus, x > plus, and ~ x
  
  and safe mapping
  
   safe(and) = {}, safe(tt) = {}, safe(plus) = {1}, safe(0) = {},
   safe(s) = {1}, safe(x) = {} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  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;))}