MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(t(),x,y) -> g#(x,y)
   f#(t(),x,y) -> f#(g(x,y),x,s(y))
   g#(s(x),s(y)) -> g#(x,y)
  TRS:
   f(t(),x,y) -> f(g(x,y),x,s(y))
   g(s(x),0()) -> t()
   g(s(x),s(y)) -> g(x,y)
  Usable Rule Processor:
   DPs:
    f#(t(),x,y) -> g#(x,y)
    f#(t(),x,y) -> f#(g(x,y),x,s(y))
    g#(s(x),s(y)) -> g#(x,y)
   TRS:
    f7(x,y) -> x
    f7(x,y) -> y
    g(s(x),0()) -> t()
    g(s(x),s(y)) -> g(x,y)
   TDG Processor:
    DPs:
     f#(t(),x,y) -> g#(x,y)
     f#(t(),x,y) -> f#(g(x,y),x,s(y))
     g#(s(x),s(y)) -> g#(x,y)
    TRS:
     f7(x,y) -> x
     f7(x,y) -> y
     g(s(x),0()) -> t()
     g(s(x),s(y)) -> g(x,y)
    graph:
     g#(s(x),s(y)) -> g#(x,y) -> g#(s(x),s(y)) -> g#(x,y)
     f#(t(),x,y) -> g#(x,y) -> g#(s(x),s(y)) -> g#(x,y)
     f#(t(),x,y) -> f#(g(x,y),x,s(y)) ->
     f#(t(),x,y) -> f#(g(x,y),x,s(y))
     f#(t(),x,y) -> f#(g(x,y),x,s(y)) -> f#(t(),x,y) -> g#(x,y)
    Restore Modifier:
     DPs:
      f#(t(),x,y) -> g#(x,y)
      f#(t(),x,y) -> f#(g(x,y),x,s(y))
      g#(s(x),s(y)) -> g#(x,y)
     TRS:
      f(t(),x,y) -> f(g(x,y),x,s(y))
      g(s(x),0()) -> t()
      g(s(x),s(y)) -> g(x,y)
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 4/9
      DPs:
       f#(t(),x,y) -> f#(g(x,y),x,s(y))
      TRS:
       f(t(),x,y) -> f(g(x,y),x,s(y))
       g(s(x),0()) -> t()
       g(s(x),s(y)) -> g(x,y)
      Open
      
      DPs:
       g#(s(x),s(y)) -> g#(x,y)
      TRS:
       f(t(),x,y) -> f(g(x,y),x,s(y))
       g(s(x),0()) -> t()
       g(s(x),s(y)) -> g(x,y)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [g#](x0, x1) = x1 + 1,
        
        [0] = 0,
        
        [s](x0) = x0 + 1,
        
        [g](x0, x1) = 0,
        
        [f](x0, x1, x2) = 0,
        
        [t] = 0
       orientation:
        g#(s(x),s(y)) = y + 2 >= y + 1 = g#(x,y)
        
        f(t(),x,y) = 0 >= 0 = f(g(x,y),x,s(y))
        
        g(s(x),0()) = 0 >= 0 = t()
        
        g(s(x),s(y)) = 0 >= 0 = g(x,y)
       problem:
        DPs:
         
        TRS:
         f(t(),x,y) -> f(g(x,y),x,s(y))
         g(s(x),0()) -> t()
         g(s(x),s(y)) -> g(x,y)
       Qed