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:
    {  plus(x, 0()) -> x
     , plus(x, s(y)) -> s(plus(x, y))
     , d(0()) -> 0()
     , d(s(x)) -> s(s(d(x)))
     , q(0()) -> 0()
     , q(s(x)) -> s(plus(q(x), d(x)))}

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