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:
    {  not(x) -> xor(x, true())
     , implies(x, y) -> xor(and(x, y), xor(x, true()))
     , or(x, y) -> xor(and(x, y), xor(x, y))
     , =(x, y) -> xor(x, xor(y, true()))}

Proof Output:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   not ~ implies, not ~ or, not ~ =, implies ~ or, implies ~ =, or ~ =
  
  and safe mapping
  
   safe(not) = {}, safe(xor) = {1, 2}, safe(true) = {},
   safe(implies) = {}, safe(and) = {1, 2}, safe(or) = {},
   safe(=) = {} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  not(x;) -> xor(; x, true())
     , implies(x, y;) -> xor(; and(; x, y), xor(; x, true()))
     , or(x, y;) -> xor(; and(; x, y), xor(; x, y))
     , =(x, y;) -> xor(; x, xor(; y, true()))}