MAYBE

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

Proof:
 DP Processor:
  DPs:
   g#(tt(),x,y) -> f#(x,y)
   g#(tt(),x,y) -> g#(f(x,y),s(x),s(y))
   f#(s(x),y) -> f#(x,y)
   f#(x,s(y)) -> f#(x,y)
  TRS:
   g(tt(),x,y) -> g(f(x,y),s(x),s(y))
   f(s(x),y) -> f(x,y)
   f(x,s(y)) -> f(x,y)
   f(0(),0()) -> tt()
  TDG Processor:
   DPs:
    g#(tt(),x,y) -> f#(x,y)
    g#(tt(),x,y) -> g#(f(x,y),s(x),s(y))
    f#(s(x),y) -> f#(x,y)
    f#(x,s(y)) -> f#(x,y)
   TRS:
    g(tt(),x,y) -> g(f(x,y),s(x),s(y))
    f(s(x),y) -> f(x,y)
    f(x,s(y)) -> f(x,y)
    f(0(),0()) -> tt()
   graph:
    f#(s(x),y) -> f#(x,y) -> f#(x,s(y)) -> f#(x,y)
    f#(s(x),y) -> f#(x,y) -> f#(s(x),y) -> f#(x,y)
    f#(x,s(y)) -> f#(x,y) -> f#(x,s(y)) -> f#(x,y)
    f#(x,s(y)) -> f#(x,y) -> f#(s(x),y) -> f#(x,y)
    g#(tt(),x,y) -> f#(x,y) -> f#(x,s(y)) -> f#(x,y)
    g#(tt(),x,y) -> f#(x,y) -> f#(s(x),y) -> f#(x,y)
    g#(tt(),x,y) -> g#(f(x,y),s(x),s(y)) ->
    g#(tt(),x,y) -> g#(f(x,y),s(x),s(y))
    g#(tt(),x,y) -> g#(f(x,y),s(x),s(y)) -> g#(tt(),x,y) -> f#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 8/16
    DPs:
     g#(tt(),x,y) -> g#(f(x,y),s(x),s(y))
    TRS:
     g(tt(),x,y) -> g(f(x,y),s(x),s(y))
     f(s(x),y) -> f(x,y)
     f(x,s(y)) -> f(x,y)
     f(0(),0()) -> tt()
    Open
    
    DPs:
     f#(s(x),y) -> f#(x,y)
     f#(x,s(y)) -> f#(x,y)
    TRS:
     g(tt(),x,y) -> g(f(x,y),s(x),s(y))
     f(s(x),y) -> f(x,y)
     f(x,s(y)) -> f(x,y)
     f(0(),0()) -> tt()
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [f#](x0, x1) = 5x0 + 5x1,
      
      [0] = 5,
      
      [s](x0) = x0 + 5,
      
      [f](x0, x1) = x1 + 7,
      
      [g](x0, x1, x2) = 0,
      
      [tt] = 0
     orientation:
      f#(s(x),y) = 5x + 5y + 25 >= 5x + 5y = f#(x,y)
      
      f#(x,s(y)) = 5x + 5y + 25 >= 5x + 5y = f#(x,y)
      
      g(tt(),x,y) = 0 >= 0 = g(f(x,y),s(x),s(y))
      
      f(s(x),y) = y + 7 >= y + 7 = f(x,y)
      
      f(x,s(y)) = y + 12 >= y + 7 = f(x,y)
      
      f(0(),0()) = 12 >= 0 = tt()
     problem:
      DPs:
       
      TRS:
       g(tt(),x,y) -> g(f(x,y),s(x),s(y))
       f(s(x),y) -> f(x,y)
       f(x,s(y)) -> f(x,y)
       f(0(),0()) -> tt()
     Qed