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(diff(p(X),Y)))
 0() -> n__0()
 s(X) -> n__s(X)
 activate(n__0()) -> 0()
 activate(n__s(X)) -> s(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) -> p#(X)
   diff#(X,Y) -> diff#(p(X),Y)
   diff#(X,Y) -> leq#(X,Y)
   diff#(X,Y) -> if#(leq(X,Y),n__0(),n__s(diff(p(X),Y)))
   activate#(n__0()) -> 0#()
   activate#(n__s(X)) -> s#(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(diff(p(X),Y)))
   0() -> n__0()
   s(X) -> n__s(X)
   activate(n__0()) -> 0()
   activate(n__s(X)) -> s(X)
   activate(X) -> X
  ADG 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) -> p#(X)
    diff#(X,Y) -> diff#(p(X),Y)
    diff#(X,Y) -> leq#(X,Y)
    diff#(X,Y) -> if#(leq(X,Y),n__0(),n__s(diff(p(X),Y)))
    activate#(n__0()) -> 0#()
    activate#(n__s(X)) -> s#(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(diff(p(X),Y)))
    0() -> n__0()
    s(X) -> n__s(X)
    activate(n__0()) -> 0()
    activate(n__s(X)) -> s(X)
    activate(X) -> X
   graph:
    diff#(X,Y) -> diff#(p(X),Y) -> diff#(X,Y) -> p#(X)
    diff#(X,Y) -> diff#(p(X),Y) -> diff#(X,Y) -> diff#(p(X),Y)
    diff#(X,Y) -> diff#(p(X),Y) -> diff#(X,Y) -> leq#(X,Y)
    diff#(X,Y) -> diff#(p(X),Y) ->
    diff#(X,Y) -> if#(leq(X,Y),n__0(),n__s(diff(p(X),Y)))
    diff#(X,Y) -> if#(leq(X,Y),n__0(),n__s(diff(p(X),Y))) ->
    if#(true(),X,Y) -> activate#(X)
    diff#(X,Y) -> if#(leq(X,Y),n__0(),n__s(diff(p(X),Y))) ->
    if#(false(),X,Y) -> activate#(Y)
    diff#(X,Y) -> leq#(X,Y) -> leq#(s(X),s(Y)) -> leq#(X,Y)
    if#(false(),X,Y) -> activate#(Y) -> activate#(n__0()) -> 0#()
    if#(false(),X,Y) -> activate#(Y) -> activate#(n__s(X)) -> s#(X)
    if#(true(),X,Y) -> activate#(X) -> activate#(n__0()) -> 0#()
    if#(true(),X,Y) -> activate#(X) -> activate#(n__s(X)) -> s#(X)
    leq#(s(X),s(Y)) -> leq#(X,Y) -> leq#(s(X),s(Y)) -> leq#(X,Y)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 12/81
    DPs:
     diff#(X,Y) -> diff#(p(X),Y)
    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(diff(p(X),Y)))
     0() -> n__0()
     s(X) -> n__s(X)
     activate(n__0()) -> 0()
     activate(n__s(X)) -> s(X)
     activate(X) -> X
    Open
    
    DPs:
     leq#(s(X),s(Y)) -> leq#(X,Y)
    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(diff(p(X),Y)))
     0() -> n__0()
     s(X) -> n__s(X)
     activate(n__0()) -> 0()
     activate(n__s(X)) -> s(X)
     activate(X) -> X
    Open