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) -> X
 if(false(),X,Y) -> Y
 diff(X,Y) -> if(leq(X,Y),0(),s(diff(p(X),Y)))

Proof:
 DP Processor:
  DPs:
   leq#(s(X),s(Y)) -> leq#(X,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),0(),s(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) -> X
   if(false(),X,Y) -> Y
   diff(X,Y) -> if(leq(X,Y),0(),s(diff(p(X),Y)))
  TDG Processor:
   DPs:
    leq#(s(X),s(Y)) -> leq#(X,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),0(),s(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) -> X
    if(false(),X,Y) -> Y
    diff(X,Y) -> if(leq(X,Y),0(),s(diff(p(X),Y)))
   graph:
    diff#(X,Y) -> diff#(p(X),Y) ->
    diff#(X,Y) -> if#(leq(X,Y),0(),s(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) -> diff#(p(X),Y)
    diff#(X,Y) -> diff#(p(X),Y) -> diff#(X,Y) -> p#(X)
    diff#(X,Y) -> leq#(X,Y) -> leq#(s(X),s(Y)) -> leq#(X,Y)
    leq#(s(X),s(Y)) -> leq#(X,Y) -> leq#(s(X),s(Y)) -> leq#(X,Y)
   Restore Modifier:
    DPs:
     leq#(s(X),s(Y)) -> leq#(X,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),0(),s(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) -> X
     if(false(),X,Y) -> Y
     diff(X,Y) -> if(leq(X,Y),0(),s(diff(p(X),Y)))
    SCC Processor:
     #sccs: 2
     #rules: 2
     #arcs: 6/25
     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) -> X
      if(false(),X,Y) -> Y
      diff(X,Y) -> if(leq(X,Y),0(),s(diff(p(X),Y)))
     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) -> X
      if(false(),X,Y) -> Y
      diff(X,Y) -> if(leq(X,Y),0(),s(diff(p(X),Y)))
     Open