YES(?,POLY)

'Pop* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,POLY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f(x, y) -> g1(x, x, y)
     , f(x, y) -> g1(y, x, x)
     , f(x, y) -> g2(x, y, y)
     , f(x, y) -> g2(y, y, x)
     , g1(x, x, y) -> h(x, y)
     , g1(y, x, x) -> h(x, y)
     , g2(x, y, y) -> h(x, y)
     , g2(y, y, x) -> h(x, y)
     , h(x, x) -> x}

Proof Output:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   f > g1, f > g2, f > h, g1 > g2, g1 > h, g2 ~ h
  
  and safe mapping
  
   safe(f) = {}, safe(g1) = {2, 3}, safe(g2) = {1, 3},
   safe(h) = {1, 2} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  f(x, y;) -> g1(x; x, y)
     , f(x, y;) -> g1(y; x, x)
     , f(x, y;) -> g2(y; x, y)
     , f(x, y;) -> g2(y; y, x)
     , g1(x; x, y) -> h(; x, y)
     , g1(y; x, x) -> h(; x, y)
     , g2(y; x, y) -> h(; x, y)
     , g2(y; y, x) -> h(; x, y)
     , h(; x, x) -> x}