MAYBE

Problem:
 f(0(),1(),g(x,y),z) -> f(g(x,y),g(x,y),g(x,y),h(x))
 g(0(),1()) -> 0()
 g(0(),1()) -> 1()
 h(g(x,y)) -> h(x)

Proof:
 DP Processor:
  DPs:
   f#(0(),1(),g(x,y),z) -> h#(x)
   f#(0(),1(),g(x,y),z) -> f#(g(x,y),g(x,y),g(x,y),h(x))
   h#(g(x,y)) -> h#(x)
  TRS:
   f(0(),1(),g(x,y),z) -> f(g(x,y),g(x,y),g(x,y),h(x))
   g(0(),1()) -> 0()
   g(0(),1()) -> 1()
   h(g(x,y)) -> h(x)
  Usable Rule Processor:
   DPs:
    f#(0(),1(),g(x,y),z) -> h#(x)
    f#(0(),1(),g(x,y),z) -> f#(g(x,y),g(x,y),g(x,y),h(x))
    h#(g(x,y)) -> h#(x)
   TRS:
    h(g(x,y)) -> h(x)
    g(0(),1()) -> 0()
    g(0(),1()) -> 1()
   EDG Processor:
    DPs:
     f#(0(),1(),g(x,y),z) -> h#(x)
     f#(0(),1(),g(x,y),z) -> f#(g(x,y),g(x,y),g(x,y),h(x))
     h#(g(x,y)) -> h#(x)
    TRS:
     h(g(x,y)) -> h(x)
     g(0(),1()) -> 0()
     g(0(),1()) -> 1()
    graph:
     h#(g(x,y)) -> h#(x) -> h#(g(x,y)) -> h#(x)
     f#(0(),1(),g(x,y),z) -> h#(x) ->
     h#(g(x,y)) -> h#(x)
     f#(0(),1(),g(x,y),z) -> f#(g(x,y),g(x,y),g(x,y),h(x)) ->
     f#(0(),1(),g(x,y),z) -> h#(x)
     f#(0(),1(),g(x,y),z) -> f#(g(x,y),g(x,y),g(x,y),h(x)) ->
     f#(0(),1(),g(x,y),z) -> f#(g(x,y),g(x,y),g(x,y),h(x))
    Restore Modifier:
     DPs:
      f#(0(),1(),g(x,y),z) -> h#(x)
      f#(0(),1(),g(x,y),z) -> f#(g(x,y),g(x,y),g(x,y),h(x))
      h#(g(x,y)) -> h#(x)
     TRS:
      f(0(),1(),g(x,y),z) -> f(g(x,y),g(x,y),g(x,y),h(x))
      g(0(),1()) -> 0()
      g(0(),1()) -> 1()
      h(g(x,y)) -> h(x)
     SCC Processor:
      #sccs: 2
      #rules: 2
      #arcs: 4/9
      DPs:
       f#(0(),1(),g(x,y),z) -> f#(g(x,y),g(x,y),g(x,y),h(x))
      TRS:
       f(0(),1(),g(x,y),z) -> f(g(x,y),g(x,y),g(x,y),h(x))
       g(0(),1()) -> 0()
       g(0(),1()) -> 1()
       h(g(x,y)) -> h(x)
      Open
      
      DPs:
       h#(g(x,y)) -> h#(x)
      TRS:
       f(0(),1(),g(x,y),z) -> f(g(x,y),g(x,y),g(x,y),h(x))
       g(0(),1()) -> 0()
       g(0(),1()) -> 1()
       h(g(x,y)) -> h(x)
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [h#](x0) = x0 + 1,
        
        [h](x0) = x0 + 1,
        
        [f](x0, x1, x2, x3) = x2 + 1,
        
        [g](x0, x1) = x0 + x1 + 1,
        
        [1] = 1,
        
        [0] = 0
       orientation:
        h#(g(x,y)) = x + y + 2 >= x + 1 = h#(x)
        
        f(0(),1(),g(x,y),z) = x + y + 2 >= x + y + 2 = f(g(x,y),g(x,y),g(x,y),h(x))
        
        g(0(),1()) = 2 >= 0 = 0()
        
        g(0(),1()) = 2 >= 1 = 1()
        
        h(g(x,y)) = x + y + 2 >= x + 1 = h(x)
       problem:
        DPs:
         
        TRS:
         f(0(),1(),g(x,y),z) -> f(g(x,y),g(x,y),g(x,y),h(x))
         g(0(),1()) -> 0()
         g(0(),1()) -> 1()
         h(g(x,y)) -> h(x)
       Qed