MAYBE

Problem:
 +(X,0()) -> X
 +(X,s(Y)) -> s(+(X,Y))
 f(0(),s(0()),X) -> f(X,+(X,X),X)
 g(X,Y) -> X
 g(X,Y) -> Y

Proof:
 DP Processor:
  DPs:
   +#(X,s(Y)) -> +#(X,Y)
   f#(0(),s(0()),X) -> +#(X,X)
   f#(0(),s(0()),X) -> f#(X,+(X,X),X)
  TRS:
   +(X,0()) -> X
   +(X,s(Y)) -> s(+(X,Y))
   f(0(),s(0()),X) -> f(X,+(X,X),X)
   g(X,Y) -> X
   g(X,Y) -> Y
  Usable Rule Processor:
   DPs:
    +#(X,s(Y)) -> +#(X,Y)
    f#(0(),s(0()),X) -> +#(X,X)
    f#(0(),s(0()),X) -> f#(X,+(X,X),X)
   TRS:
    f8(x,y) -> x
    f8(x,y) -> y
    +(X,0()) -> X
    +(X,s(Y)) -> s(+(X,Y))
   CDG Processor:
    DPs:
     +#(X,s(Y)) -> +#(X,Y)
     f#(0(),s(0()),X) -> +#(X,X)
     f#(0(),s(0()),X) -> f#(X,+(X,X),X)
    TRS:
     f8(x,y) -> x
     f8(x,y) -> y
     +(X,0()) -> X
     +(X,s(Y)) -> s(+(X,Y))
    graph:
     f#(0(),s(0()),X) -> f#(X,+(X,X),X) ->
     f#(0(),s(0()),X) -> +#(X,X)
     f#(0(),s(0()),X) -> f#(X,+(X,X),X) ->
     f#(0(),s(0()),X) -> f#(X,+(X,X),X)
     f#(0(),s(0()),X) -> +#(X,X) -> +#(X,s(Y)) -> +#(X,Y)
     +#(X,s(Y)) -> +#(X,Y) -> +#(X,s(Y)) -> +#(X,Y)
    Restore Modifier:
     DPs:
      +#(X,s(Y)) -> +#(X,Y)
      f#(0(),s(0()),X) -> +#(X,X)
      f#(0(),s(0()),X) -> f#(X,+(X,X),X)
     TRS:
      +(X,0()) -> X
      +(X,s(Y)) -> s(+(X,Y))
      f(0(),s(0()),X) -> f(X,+(X,X),X)
      g(X,Y) -> X
      g(X,Y) -> Y
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 4/9
      DPs:
       f#(0(),s(0()),X) -> f#(X,+(X,X),X)
      TRS:
       +(X,0()) -> X
       +(X,s(Y)) -> s(+(X,Y))
       f(0(),s(0()),X) -> f(X,+(X,X),X)
       g(X,Y) -> X
       g(X,Y) -> Y
      Open
      
      DPs:
       +#(X,s(Y)) -> +#(X,Y)
      TRS:
       +(X,0()) -> X
       +(X,s(Y)) -> s(+(X,Y))
       f(0(),s(0()),X) -> f(X,+(X,X),X)
       g(X,Y) -> X
       g(X,Y) -> Y
      Open