MAYBE

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

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