MAYBE

Problem:
 p(0()) -> 0()
 p(s(X)) -> X
 leq(0(),Y) -> true()
 leq(s(X),0()) -> false()
 leq(s(X),s(Y)) -> leq(X,Y)
 if(true(),X,Y) -> activate(X)
 if(false(),X,Y) -> activate(Y)
 diff(X,Y) -> if(leq(X,Y),n__0(),n__s(n__diff(n__p(X),Y)))
 0() -> n__0()
 s(X) -> n__s(X)
 diff(X1,X2) -> n__diff(X1,X2)
 p(X) -> n__p(X)
 activate(n__0()) -> 0()
 activate(n__s(X)) -> s(activate(X))
 activate(n__diff(X1,X2)) -> diff(activate(X1),activate(X2))
 activate(n__p(X)) -> p(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   leq#(s(X),s(Y)) -> leq#(X,Y)
   if#(true(),X,Y) -> activate#(X)
   if#(false(),X,Y) -> activate#(Y)
   diff#(X,Y) -> leq#(X,Y)
   diff#(X,Y) -> if#(leq(X,Y),n__0(),n__s(n__diff(n__p(X),Y)))
   activate#(n__0()) -> 0#()
   activate#(n__s(X)) -> activate#(X)
   activate#(n__s(X)) -> s#(activate(X))
   activate#(n__diff(X1,X2)) -> activate#(X2)
   activate#(n__diff(X1,X2)) -> activate#(X1)
   activate#(n__diff(X1,X2)) -> diff#(activate(X1),activate(X2))
   activate#(n__p(X)) -> activate#(X)
   activate#(n__p(X)) -> p#(activate(X))
  TRS:
   p(0()) -> 0()
   p(s(X)) -> X
   leq(0(),Y) -> true()
   leq(s(X),0()) -> false()
   leq(s(X),s(Y)) -> leq(X,Y)
   if(true(),X,Y) -> activate(X)
   if(false(),X,Y) -> activate(Y)
   diff(X,Y) -> if(leq(X,Y),n__0(),n__s(n__diff(n__p(X),Y)))
   0() -> n__0()
   s(X) -> n__s(X)
   diff(X1,X2) -> n__diff(X1,X2)
   p(X) -> n__p(X)
   activate(n__0()) -> 0()
   activate(n__s(X)) -> s(activate(X))
   activate(n__diff(X1,X2)) -> diff(activate(X1),activate(X2))
   activate(n__p(X)) -> p(activate(X))
   activate(X) -> X
  Open