MAYBE

Problem:
 ack(0(),y) -> s(y)
 ack(s(x),0()) -> ack(x,s(0()))
 ack(s(x),s(y)) -> ack(x,ack(s(x),y))
 f(s(x),y) -> f(x,s(x))
 f(x,s(y)) -> f(y,x)
 f(x,y) -> ack(x,y)
 ack(s(x),y) -> f(x,x)

Proof:
 DP Processor:
  DPs:
   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))
   f#(s(x),y) -> f#(x,s(x))
   f#(x,s(y)) -> f#(y,x)
   f#(x,y) -> ack#(x,y)
   ack#(s(x),y) -> f#(x,x)
  TRS:
   ack(0(),y) -> s(y)
   ack(s(x),0()) -> ack(x,s(0()))
   ack(s(x),s(y)) -> ack(x,ack(s(x),y))
   f(s(x),y) -> f(x,s(x))
   f(x,s(y)) -> f(y,x)
   f(x,y) -> ack(x,y)
   ack(s(x),y) -> f(x,x)
  Open