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)
  CDG 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)
   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))
   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