MAYBE

Problem:
 double(x) -> permute(x,x,a())
 permute(x,y,a()) -> permute(isZero(x),x,b())
 permute(false(),x,b()) -> permute(ack(x,x),p(x),c())
 permute(true(),x,b()) -> 0()
 permute(y,x,c()) -> s(s(permute(x,y,a())))
 p(0()) -> 0()
 p(s(x)) -> x
 ack(0(),x) -> plus(x,s(0()))
 ack(s(x),0()) -> ack(x,s(0()))
 ack(s(x),s(y)) -> ack(x,ack(s(x),y))
 plus(0(),y) -> y
 plus(s(x),y) -> plus(x,s(y))
 plus(x,s(s(y))) -> s(plus(s(x),y))
 plus(x,s(0())) -> s(x)
 plus(x,0()) -> x
 isZero(0()) -> true()
 isZero(s(x)) -> false()

Proof:
 DP Processor:
  DPs:
   double#(x) -> permute#(x,x,a())
   permute#(x,y,a()) -> isZero#(x)
   permute#(x,y,a()) -> permute#(isZero(x),x,b())
   permute#(false(),x,b()) -> p#(x)
   permute#(false(),x,b()) -> ack#(x,x)
   permute#(false(),x,b()) -> permute#(ack(x,x),p(x),c())
   permute#(y,x,c()) -> permute#(x,y,a())
   ack#(0(),x) -> plus#(x,s(0()))
   ack#(s(x),0()) -> ack#(x,s(0()))
   ack#(s(x),s(y)) -> ack#(s(x),y)
   ack#(s(x),s(y)) -> ack#(x,ack(s(x),y))
   plus#(s(x),y) -> plus#(x,s(y))
   plus#(x,s(s(y))) -> plus#(s(x),y)
  TRS:
   double(x) -> permute(x,x,a())
   permute(x,y,a()) -> permute(isZero(x),x,b())
   permute(false(),x,b()) -> permute(ack(x,x),p(x),c())
   permute(true(),x,b()) -> 0()
   permute(y,x,c()) -> s(s(permute(x,y,a())))
   p(0()) -> 0()
   p(s(x)) -> x
   ack(0(),x) -> plus(x,s(0()))
   ack(s(x),0()) -> ack(x,s(0()))
   ack(s(x),s(y)) -> ack(x,ack(s(x),y))
   plus(0(),y) -> y
   plus(s(x),y) -> plus(x,s(y))
   plus(x,s(s(y))) -> s(plus(s(x),y))
   plus(x,s(0())) -> s(x)
   plus(x,0()) -> x
   isZero(0()) -> true()
   isZero(s(x)) -> false()
  Open