YES(?,POLY)

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

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