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:
    {  gt(0(), y) -> false()
     , gt(s(x), 0()) -> true()
     , gt(s(x), s(y)) -> gt(x, y)
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , double(0()) -> 0()
     , double(s(x)) -> s(s(double(x)))
     , average(x, y) -> aver(plus(x, y), 0())
     , aver(sum, z) -> if(gt(sum, double(z)), sum, z)
     , if(true(), sum, z) -> aver(sum, s(z))
     , if(false(), sum, z) -> z}

Proof Output:    
  The input cannot be shown compatible