YES(?,POLY)

'Pop* with parameter subtitution (timeout of 60.0 seconds)'
-----------------------------------------------------------
Answer:           YES(?,POLY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f(0()) -> 1()
     , f(s(x)) -> g(x, s(x))
     , g(0(), y) -> y
     , g(s(x), y) -> g(x, +(y, s(x)))
     , +(x, 0()) -> x
     , +(x, s(y)) -> s(+(x, y))
     , g(s(x), y) -> g(x, s(+(y, x)))}

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