MAYBE

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

Proof:
 DP Processor:
  DPs:
   g#(x,s(y)) -> g#(f(x,y),0())
   g#(s(x),y) -> g#(f(x,y),0())
   g#(f(x,y),0()) -> g#(y,0())
   g#(f(x,y),0()) -> g#(x,0())
  TRS:
   g(0(),f(x,x)) -> x
   g(x,s(y)) -> g(f(x,y),0())
   g(s(x),y) -> g(f(x,y),0())
   g(f(x,y),0()) -> f(g(x,0()),g(y,0()))
  Usable Rule Processor:
   DPs:
    g#(x,s(y)) -> g#(f(x,y),0())
    g#(s(x),y) -> g#(f(x,y),0())
    g#(f(x,y),0()) -> g#(y,0())
    g#(f(x,y),0()) -> g#(x,0())
   TRS:
    
   CDG Processor:
    DPs:
     g#(x,s(y)) -> g#(f(x,y),0())
     g#(s(x),y) -> g#(f(x,y),0())
     g#(f(x,y),0()) -> g#(y,0())
     g#(f(x,y),0()) -> g#(x,0())
    TRS:
     
    graph:
     g#(s(x),y) -> g#(f(x,y),0()) -> g#(f(x,y),0()) -> g#(y,0())
     g#(s(x),y) -> g#(f(x,y),0()) -> g#(f(x,y),0()) -> g#(x,0())
     g#(f(x,y),0()) -> g#(y,0()) -> g#(f(x,y),0()) -> g#(y,0())
     g#(f(x,y),0()) -> g#(y,0()) -> g#(f(x,y),0()) -> g#(x,0())
     g#(f(x,y),0()) -> g#(x,0()) -> g#(f(x,y),0()) -> g#(y,0())
     g#(f(x,y),0()) -> g#(x,0()) -> g#(f(x,y),0()) -> g#(x,0())
     g#(x,s(y)) -> g#(f(x,y),0()) -> g#(f(x,y),0()) -> g#(y,0())
     g#(x,s(y)) -> g#(f(x,y),0()) -> g#(f(x,y),0()) -> g#(x,0())
    Restore Modifier:
     DPs:
      g#(x,s(y)) -> g#(f(x,y),0())
      g#(s(x),y) -> g#(f(x,y),0())
      g#(f(x,y),0()) -> g#(y,0())
      g#(f(x,y),0()) -> g#(x,0())
     TRS:
      g(0(),f(x,x)) -> x
      g(x,s(y)) -> g(f(x,y),0())
      g(s(x),y) -> g(f(x,y),0())
      g(f(x,y),0()) -> f(g(x,0()),g(y,0()))
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 8/16
      DPs:
       g#(f(x,y),0()) -> g#(x,0())
       g#(f(x,y),0()) -> g#(y,0())
      TRS:
       g(0(),f(x,x)) -> x
       g(x,s(y)) -> g(f(x,y),0())
       g(s(x),y) -> g(f(x,y),0())
       g(f(x,y),0()) -> f(g(x,0()),g(y,0()))
      Open