MAYBE

'Pop* with parameter subtitution (timeout of 60.0 seconds)'
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Answer:           MAYBE
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  p(s(x)) -> x
     , p(0()) -> 0()
     , le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , average(x, y) ->
       if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)
     , if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y)
     , if(false(), b1, b2, b3, x, y) -> average(p(x), s(y))
     , if2(true(), b2, b3, x, y) -> 0()
     , if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y)
     , if3(true(), b3, x, y) -> 0()
     , if3(false(), b3, x, y) -> if4(b3, x, y)
     , if4(true(), x, y) -> s(0())
     , if4(false(), x, y) -> average(s(x), p(p(y)))}

Proof Output:    
  The input cannot be shown compatible