MAYBE

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

Proof:
 DP Processor:
  DPs:
   f#(g(x),g(y)) -> p#(x)
   f#(g(x),g(y)) -> g#(s(p(x)))
   f#(g(x),g(y)) -> f#(g(x),s(y))
   f#(g(x),g(y)) -> p#(f(g(x),s(y)))
   f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x))))
   p#(0()) -> g#(0())
  TRS:
   f(g(x),g(y)) -> f(p(f(g(x),s(y))),g(s(p(x))))
   p(0()) -> g(0())
   g(s(p(x))) -> p(x)
  TDG Processor:
   DPs:
    f#(g(x),g(y)) -> p#(x)
    f#(g(x),g(y)) -> g#(s(p(x)))
    f#(g(x),g(y)) -> f#(g(x),s(y))
    f#(g(x),g(y)) -> p#(f(g(x),s(y)))
    f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x))))
    p#(0()) -> g#(0())
   TRS:
    f(g(x),g(y)) -> f(p(f(g(x),s(y))),g(s(p(x))))
    p(0()) -> g(0())
    g(s(p(x))) -> p(x)
   graph:
    f#(g(x),g(y)) -> p#(f(g(x),s(y))) -> p#(0()) -> g#(0())
    f#(g(x),g(y)) -> p#(x) -> p#(0()) -> g#(0())
    f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x)))) ->
    f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x))))
    f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x)))) ->
    f#(g(x),g(y)) -> p#(f(g(x),s(y)))
    f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x)))) ->
    f#(g(x),g(y)) -> f#(g(x),s(y))
    f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x)))) ->
    f#(g(x),g(y)) -> g#(s(p(x)))
    f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x)))) ->
    f#(g(x),g(y)) -> p#(x)
    f#(g(x),g(y)) -> f#(g(x),s(y)) ->
    f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x))))
    f#(g(x),g(y)) -> f#(g(x),s(y)) ->
    f#(g(x),g(y)) -> p#(f(g(x),s(y)))
    f#(g(x),g(y)) -> f#(g(x),s(y)) -> f#(g(x),g(y)) -> f#(g(x),s(y))
    f#(g(x),g(y)) -> f#(g(x),s(y)) -> f#(g(x),g(y)) -> g#(s(p(x)))
    f#(g(x),g(y)) -> f#(g(x),s(y)) -> f#(g(x),g(y)) -> p#(x)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 12/36
    DPs:
     f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x))))
     f#(g(x),g(y)) -> f#(g(x),s(y))
    TRS:
     f(g(x),g(y)) -> f(p(f(g(x),s(y))),g(s(p(x))))
     p(0()) -> g(0())
     g(s(p(x))) -> p(x)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0, x1) = x1,
      
      [0] = 0,
      
      [p](x0) = 1,
      
      [s](x0) = 0,
      
      [f](x0, x1) = 0,
      
      [g](x0) = 1
     orientation:
      f#(g(x),g(y)) = 1 >= 1 = f#(p(f(g(x),s(y))),g(s(p(x))))
      
      f#(g(x),g(y)) = 1 >= 0 = f#(g(x),s(y))
      
      f(g(x),g(y)) = 0 >= 0 = f(p(f(g(x),s(y))),g(s(p(x))))
      
      p(0()) = 1 >= 1 = g(0())
      
      g(s(p(x))) = 1 >= 1 = p(x)
     problem:
      DPs:
       f#(g(x),g(y)) -> f#(p(f(g(x),s(y))),g(s(p(x))))
      TRS:
       f(g(x),g(y)) -> f(p(f(g(x),s(y))),g(s(p(x))))
       p(0()) -> g(0())
       g(s(p(x))) -> p(x)
     Open