MAYBE

Problem:
 h(X,Z) -> f(X,s(X),Z)
 f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
 g(0(),Y) -> 0()
 g(X,s(Y)) -> g(X,Y)

Proof:
 DP Processor:
  DPs:
   h#(X,Z) -> f#(X,s(X),Z)
   f#(X,Y,g(X,Y)) -> h#(0(),g(X,Y))
   g#(X,s(Y)) -> g#(X,Y)
  TRS:
   h(X,Z) -> f(X,s(X),Z)
   f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
   g(0(),Y) -> 0()
   g(X,s(Y)) -> g(X,Y)
  TDG Processor:
   DPs:
    h#(X,Z) -> f#(X,s(X),Z)
    f#(X,Y,g(X,Y)) -> h#(0(),g(X,Y))
    g#(X,s(Y)) -> g#(X,Y)
   TRS:
    h(X,Z) -> f(X,s(X),Z)
    f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
    g(0(),Y) -> 0()
    g(X,s(Y)) -> g(X,Y)
   graph:
    g#(X,s(Y)) -> g#(X,Y) -> g#(X,s(Y)) -> g#(X,Y)
    f#(X,Y,g(X,Y)) -> h#(0(),g(X,Y)) -> h#(X,Z) -> f#(X,s(X),Z)
    h#(X,Z) -> f#(X,s(X),Z) -> f#(X,Y,g(X,Y)) -> h#(0(),g(X,Y))
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 3/9
    DPs:
     f#(X,Y,g(X,Y)) -> h#(0(),g(X,Y))
     h#(X,Z) -> f#(X,s(X),Z)
    TRS:
     h(X,Z) -> f(X,s(X),Z)
     f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
     g(0(),Y) -> 0()
     g(X,s(Y)) -> g(X,Y)
    Open
    
    DPs:
     g#(X,s(Y)) -> g#(X,Y)
    TRS:
     h(X,Z) -> f(X,s(X),Z)
     f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
     g(0(),Y) -> 0()
     g(X,s(Y)) -> g(X,Y)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [g#](x0, x1) = x1 + 1,
      
      [0] = 0,
      
      [g](x0, x1) = 0,
      
      [f](x0, x1, x2) = 0,
      
      [s](x0) = x0 + 1,
      
      [h](x0, x1) = 0
     orientation:
      g#(X,s(Y)) = Y + 2 >= Y + 1 = g#(X,Y)
      
      h(X,Z) = 0 >= 0 = f(X,s(X),Z)
      
      f(X,Y,g(X,Y)) = 0 >= 0 = h(0(),g(X,Y))
      
      g(0(),Y) = 0 >= 0 = 0()
      
      g(X,s(Y)) = 0 >= 0 = g(X,Y)
     problem:
      DPs:
       
      TRS:
       h(X,Z) -> f(X,s(X),Z)
       f(X,Y,g(X,Y)) -> h(0(),g(X,Y))
       g(0(),Y) -> 0()
       g(X,s(Y)) -> g(X,Y)
     Qed