MAYBE

Problem:
 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:
 DP Processor:
  DPs:
   le#(s(x),s(y)) -> le#(x,y)
   average#(x,y) -> le#(y,s(s(0())))
   average#(x,y) -> le#(y,s(0()))
   average#(x,y) -> le#(y,0())
   average#(x,y) -> le#(x,0())
   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) -> p#(x)
   if#(false(),b1,b2,b3,x,y) -> average#(p(x),s(y))
   if2#(false(),b2,b3,x,y) -> if3#(b2,b3,x,y)
   if3#(false(),b3,x,y) -> if4#(b3,x,y)
   if4#(false(),x,y) -> p#(y)
   if4#(false(),x,y) -> p#(p(y))
   if4#(false(),x,y) -> average#(s(x),p(p(y)))
  TRS:
   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)))
  Open