MAYBE

Problem:
 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:
 DP Processor:
  DPs:
   gt#(s(x),s(y)) -> gt#(x,y)
   plus#(s(x),y) -> plus#(x,y)
   double#(s(x)) -> double#(x)
   average#(x,y) -> plus#(x,y)
   average#(x,y) -> aver#(plus(x,y),0())
   aver#(sum,z) -> double#(z)
   aver#(sum,z) -> gt#(sum,double(z))
   aver#(sum,z) -> if#(gt(sum,double(z)),sum,z)
   if#(true(),sum,z) -> aver#(sum,s(z))
  TRS:
   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
  Open