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:
    {  admit(x, nil()) -> nil()
     , admit(x, .(u, .(v, .(w(), z)))) ->
       cond(=(sum(x, u, v), w()),
            .(u, .(v, .(w(), admit(carry(x, u, v), z)))))
     , cond(true(), y) -> y}

Proof Output:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   admit > cond
  
  and safe mapping
  
   safe(admit) = {1}, safe(nil) = {}, safe(.) = {1, 2}, safe(w) = {},
   safe(cond) = {1, 2}, safe(=) = {1, 2}, safe(sum) = {1, 2, 3},
   safe(carry) = {1, 2, 3}, safe(true) = {} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  admit(nil(); x) -> nil()
     , admit(.(; u, .(; v, .(; w(), z))); x) ->
       cond(; =(; sum(; x, u, v), w()),
              .(; u, .(; v, .(; w(), admit(z; carry(; x, u, v))))))
     , cond(; true(), y) -> y}