MAYBE

Problem:
 f(X,g(X)) -> f(1(),g(X))
 g(1()) -> g(0())

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