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:
    {  exp(x, 0()) -> s(0())
     , exp(x, s(y)) -> *(x, exp(x, y))
     , *(0(), y) -> 0()
     , *(s(x), y) -> +(y, *(x, y))
     , -(0(), y) -> 0()
     , -(x, 0()) -> x
     , -(s(x), s(y)) -> -(x, y)}

Proof Output:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   exp > *, - > *, exp ~ -
  
  and safe mapping
  
   safe(exp) = {}, safe(0) = {}, safe(s) = {1}, safe(*) = {2},
   safe(+) = {1, 2}, safe(-) = {1} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  exp(x, 0();) -> s(; 0())
     , exp(x, s(; y);) -> *(x; exp(x, y;))
     , *(0(); y) -> 0()
     , *(s(; x); y) -> +(; y, *(x; y))
     , -(y; 0()) -> 0()
     , -(0(); x) -> x
     , -(s(; y); s(; x)) -> -(y; x)}