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:
    {  a__f(f(a())) -> c(f(g(f(a()))))
     , mark(f(X)) -> a__f(mark(X))
     , mark(a()) -> a()
     , mark(c(X)) -> c(X)
     , mark(g(X)) -> g(mark(X))
     , a__f(X) -> f(X)}

Proof Output:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   mark > a__f
  
  and safe mapping
  
   safe(a__f) = {1}, safe(f) = {1}, safe(a) = {}, safe(c) = {1},
   safe(g) = {1}, safe(mark) = {} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  a__f(; f(; a())) -> c(; f(; g(; f(; a()))))
     , mark(f(; X);) -> a__f(; mark(X;))
     , mark(a();) -> a()
     , mark(c(; X);) -> c(; X)
     , mark(g(; X);) -> g(; mark(X;))
     , a__f(; X) -> f(; X)}