/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 h(x,x) -> h(a(),b())
 g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
 f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
 h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))

Proof:
 DP Processor:
  DPs:
   h#(x,x) -> h#(a(),b())
   g#(g(x,a()),y) -> g#(a(),x)
   g#(g(x,a()),y) -> g#(a(),y)
   g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
   f#(g(x,y)) -> h#(a(),a())
   f#(g(x,y)) -> f#(y)
   f#(g(x,y)) -> f#(f(y))
   f#(g(x,y)) -> g#(f(f(y)),h(a(),a()))
   f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x)
   h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
   h#(h(f(f(x)),y),h(z,v)) -> f#(y)
   h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
   h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
   h#(h(f(f(x)),y),h(z,v)) -> f#(z)
   h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
   h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
  TRS:
   h(x,x) -> h(a(),b())
   g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
   f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
   h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
  TDG Processor:
   DPs:
    h#(x,x) -> h#(a(),b())
    g#(g(x,a()),y) -> g#(a(),x)
    g#(g(x,a()),y) -> g#(a(),y)
    g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
    f#(g(x,y)) -> h#(a(),a())
    f#(g(x,y)) -> f#(y)
    f#(g(x,y)) -> f#(f(y))
    f#(g(x,y)) -> g#(f(f(y)),h(a(),a()))
    f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x)
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
    h#(h(f(f(x)),y),h(z,v)) -> f#(y)
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
    h#(h(f(f(x)),y),h(z,v)) -> f#(z)
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
   TRS:
    h(x,x) -> h(a(),b())
    g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
    f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
    h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
   graph:
    f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x)
    f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> g#(f(f(y)),h(a(),a()))
    f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> f#(f(y))
    f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> f#(y)
    f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> h#(a(),a())
    f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x)
    f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> g#(f(f(y)),h(a(),a()))
    f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> f#(f(y))
    f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> f#(y)
    f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> h#(a(),a())
    f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) ->
    g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
    f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) ->
    g#(g(x,a()),y) -> g#(a(),y)
    f#(g(x,y)) -> g#(f(f(y)),h(a(),a())) ->
    g#(g(x,a()),y) -> g#(a(),x)
    f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) ->
    g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
    f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) ->
    g#(g(x,a()),y) -> g#(a(),y)
    f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x) ->
    g#(g(x,a()),y) -> g#(a(),x)
    f#(g(x,y)) -> h#(a(),a()) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
    f#(g(x,y)) -> h#(a(),a()) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
    f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z)
    f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
    f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
    f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y)
    f#(g(x,y)) -> h#(a(),a()) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
    f#(g(x,y)) -> h#(a(),a()) -> h#(x,x) -> h#(a(),b())
    g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) ->
    g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
    g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) ->
    g#(g(x,a()),y) -> g#(a(),y)
    g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) ->
    g#(g(x,a()),y) -> g#(a(),x)
    g#(g(x,a()),y) -> g#(a(),y) ->
    g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
    g#(g(x,a()),y) -> g#(a(),y) -> g#(g(x,a()),y) -> g#(a(),y)
    g#(g(x,a()),y) -> g#(a(),y) -> g#(g(x,a()),y) -> g#(a(),x)
    g#(g(x,a()),y) -> g#(a(),x) ->
    g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
    g#(g(x,a()),y) -> g#(a(),x) -> g#(g(x,a()),y) -> g#(a(),y)
    g#(g(x,a()),y) -> g#(a(),x) ->
    g#(g(x,a()),y) -> g#(a(),x)
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) ->
    f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x)
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) ->
    f#(g(x,y)) -> g#(f(f(y)),h(a(),a()))
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) ->
    f#(g(x,y)) -> f#(f(y))
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) ->
    f#(g(x,y)) -> f#(y)
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) ->
    f#(g(x,y)) -> h#(a(),a())
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) ->
    f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x)
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) ->
    f#(g(x,y)) -> g#(f(f(y)),h(a(),a()))
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) ->
    f#(g(x,y)) -> f#(f(y))
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> f#(y)
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) ->
    f#(g(x,y)) -> h#(a(),a())
    h#(h(f(f(x)),y),h(z,v)) -> f#(z) ->
    f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x)
    h#(h(f(f(x)),y),h(z,v)) -> f#(z) ->
    f#(g(x,y)) -> g#(f(f(y)),h(a(),a()))
    h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> f#(f(y))
    h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> f#(y)
    h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> h#(a(),a())
    h#(h(f(f(x)),y),h(z,v)) -> f#(y) ->
    f#(g(x,y)) -> g#(g(f(f(y)),h(a(),a())),x)
    h#(h(f(f(x)),y),h(z,v)) -> f#(y) ->
    f#(g(x,y)) -> g#(f(f(y)),h(a(),a()))
    h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> f#(f(y))
    h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> f#(y)
    h#(h(f(f(x)),y),h(z,v)) -> f#(y) ->
    f#(g(x,y)) -> h#(a(),a())
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(z)
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(y)
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) ->
    h#(x,x) -> h#(a(),b())
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(z)
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(y)
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
    h#(x,x) -> h#(a(),b())
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(z)
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
    h#(h(f(f(x)),y),h(z,v)) -> f#(y)
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
    h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) -> h#(x,x) -> h#(a(),b())
    h#(x,x) -> h#(a(),b()) ->
    h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
    h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
    h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(z)
    h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
    h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
    h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> f#(y)
    h#(x,x) -> h#(a(),b()) -> h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
    h#(x,x) -> h#(a(),b()) -> h#(x,x) -> h#(a(),b())
   SCC Processor:
    #sccs: 2
    #rules: 14
    #arcs: 85/256
    DPs:
     f#(g(x,y)) -> f#(f(y))
     f#(g(x,y)) -> h#(a(),a())
     h#(x,x) -> h#(a(),b())
     h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
     h#(h(f(f(x)),y),h(z,v)) -> f#(y)
     f#(g(x,y)) -> f#(y)
     h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
     h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
     h#(h(f(f(x)),y),h(z,v)) -> f#(z)
     h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
     h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
    TRS:
     h(x,x) -> h(a(),b())
     g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
     f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
     h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
    EDG Processor:
     DPs:
      f#(g(x,y)) -> f#(f(y))
      f#(g(x,y)) -> h#(a(),a())
      h#(x,x) -> h#(a(),b())
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
      h#(h(f(f(x)),y),h(z,v)) -> f#(y)
      f#(g(x,y)) -> f#(y)
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
      h#(h(f(f(x)),y),h(z,v)) -> f#(z)
      h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
     TRS:
      h(x,x) -> h(a(),b())
      g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
      f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
      h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
     graph:
      f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> h#(a(),a())
      f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> f#(y)
      f#(g(x,y)) -> f#(f(y)) -> f#(g(x,y)) -> f#(f(y))
      f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> h#(a(),a())
      f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> f#(y)
      f#(g(x,y)) -> f#(y) -> f#(g(x,y)) -> f#(f(y))
      f#(g(x,y)) -> h#(a(),a()) -> h#(x,x) -> h#(a(),b())
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) ->
      f#(g(x,y)) -> h#(a(),a())
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) ->
      f#(g(x,y)) -> f#(y)
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y))) ->
      f#(g(x,y)) -> f#(f(y))
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) ->
      f#(g(x,y)) -> h#(a(),a())
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> f#(y)
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(y)) -> f#(g(x,y)) -> f#(f(y))
      h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> h#(a(),a())
      h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> f#(y)
      h#(h(f(f(x)),y),h(z,v)) -> f#(z) -> f#(g(x,y)) -> f#(f(y))
      h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> h#(a(),a())
      h#(h(f(f(x)),y),h(z,v)) -> f#(y) -> f#(g(x,y)) -> f#(y)
      h#(h(f(f(x)),y),h(z,v)) -> f#(y) ->
      f#(g(x,y)) -> f#(f(y))
      h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y)))) ->
      h#(x,x) -> h#(a(),b())
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
      h#(x,x) -> h#(a(),b())
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
      h#(h(f(f(x)),y),h(z,v)) -> f#(y)
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
      h#(h(f(f(x)),y),h(z,v)) -> f#(z)
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
      h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x)) ->
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
      h#(x,x) -> h#(a(),b())
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
      h#(h(f(f(x)),y),h(z,v)) -> f#(y)
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(y))
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
      h#(h(f(f(x)),y),h(z,v)) -> f#(f(f(y)))
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
      h#(h(f(f(x)),y),h(z,v)) -> f#(z)
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
      h#(h(f(f(x)),y),h(z,v)) -> h#(f(z),f(f(f(y))))
      h#(h(f(f(x)),y),h(z,v)) -> h#(v,x) ->
      h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
     SCC Processor:
      #sccs: 2
      #rules: 4
      #arcs: 36/121
      DPs:
       h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
       h#(h(f(f(x)),y),h(z,v)) -> h#(v,x)
      TRS:
       h(x,x) -> h(a(),b())
       g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
       f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
       h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
      Semantic Labeling Processor:
       dimension: 1
       usable rules:
        
       interpretation:
        [f](x0) = x0,
        
        [g](x0, x1) = 0,
        
        [b] = 0,
        
        [a] = 0,
        
        [h](x0, x1) = x0 + x1 + 1
        labeled:
         h#
        usable (for model):
         h#
         h
         f
         a
         b
         g
        argument filtering:
         pi(h) = []
         pi(a) = []
         pi(b) = []
         pi(g) = 0
         pi(f) = []
         pi(h#) = []
       precedence:
        h# ~ f ~ g ~ b ~ a ~ h
       problem:
        DPs:
         h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
        TRS:
         h(x,x) -> h(a(),b())
         g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
         f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
         h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
       Restore Modifier:
        DPs:
         h#(h(f(f(x)),y),h(z,v)) -> h#(h(f(z),f(f(f(y)))),h(v,x))
        TRS:
         h(x,x) -> h(a(),b())
         g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
         f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
         h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
        Matrix Interpretation Processor: dim=3
         
         usable rules:
          h(x,x) -> h(a(),b())
          g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
          f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
          h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
         interpretation:
          [h#](x0, x1) = [1 0 0]x0 + [0 0 1]x1,
          
                    [0 1 0]     [0]
          [f](x0) = [1 1 0]x0 + [1]
                    [0 0 0]     [0],
          
                        [0]
          [g](x0, x1) = [0]
                        [0],
          
                [0]
          [b] = [0]
                [0],
          
                [0]
          [a] = [0]
                [1],
          
                        [1 0 0]     [0 0 1]     [0]
          [h](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                        [0 1 0]     [0 1 0]     [1]
         orientation:
          h#(h(f(f(x)),y),h(z,v)) = [0 1 0]v + [1 1 0]x + [0 0 1]y + [0 1 0]z + [2] >= [0 1 0]v + [0 1 0]x + [0 1 0]z + [1] = h#(h(f(z),f(f(f(y)))),h(v,x))
          
                   [1 0 1]    [0]    [0]             
          h(x,x) = [0 0 0]x + [0] >= [0] = h(a(),b())
                   [0 2 0]    [1]    [1]             
          
                          [0]    [0]                       
          g(g(x,a()),y) = [0] >= [0] = g(g(a(),y),g(a(),x))
                          [0]    [0]                       
          
                      [0]    [0]                             
          f(g(x,y)) = [1] >= [0] = g(g(f(f(y)),h(a(),a())),x)
                      [0]    [0]                             
          
                                   [0 1 0]    [1 1 0]    [0 0 1]    [0 1 0]    [2]    [0 1 0]    [0 1 0]    [0 1 0]    [1]                               
          h(h(f(f(x)),y),h(z,v)) = [0 0 0]v + [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]v + [0 0 0]x + [0 0 0]z + [0] = h(h(f(z),f(f(f(y)))),h(v,x))
                                   [0 0 0]    [0 0 0]    [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [0 0 0]    [1]                               
         problem:
          DPs:
           
          TRS:
           h(x,x) -> h(a(),b())
           g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
           f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
           h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
         Qed
      
      DPs:
       f#(g(x,y)) -> f#(f(y))
       f#(g(x,y)) -> f#(y)
      TRS:
       h(x,x) -> h(a(),b())
       g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
       f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
       h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
      Bounds Processor:
       bound: 1
       enrichment: match-dp
       automaton:
        final states: {1}
        transitions:
         f370() -> 2*
         f{#,0}(2) -> 1*
         f{#,0}(14) -> 1*
         f{#,0}(3) -> 1*
         f0(14) -> 8*
         f0(3) -> 8*
         g0(8,7) -> 9*
         g0(9,2) -> 3*
         g0(9,9) -> 8*
         h0(6,6) -> 7*
         a0() -> 6*
         b0() -> 6*
         f{#,1}(14) -> 1*
         f{#,1}(13) -> 1*
         f1(2) -> 14*,3,13
       problem:
        DPs:
         f#(g(x,y)) -> f#(y)
        TRS:
         h(x,x) -> h(a(),b())
         g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
         f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
         h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
       Bounds Processor:
        bound: 0
        enrichment: match-dp
        automaton:
         final states: {1}
         transitions:
          f470() -> 2*
          f{#,0}(2) -> 1*
        problem:
         DPs:
          
         TRS:
          h(x,x) -> h(a(),b())
          g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
          f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
          h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
        Qed
    
    DPs:
     g#(g(x,a()),y) -> g#(a(),x)
     g#(g(x,a()),y) -> g#(a(),y)
     g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
    TRS:
     h(x,x) -> h(a(),b())
     g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
     f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
     h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
    EDG Processor:
     DPs:
      g#(g(x,a()),y) -> g#(a(),x)
      g#(g(x,a()),y) -> g#(a(),y)
      g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
     TRS:
      h(x,x) -> h(a(),b())
      g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
      f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
      h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
     graph:
      g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) ->
      g#(g(x,a()),y) -> g#(a(),x)
      g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) ->
      g#(g(x,a()),y) -> g#(a(),y)
      g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x)) -> g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 3/9
      DPs:
       g#(g(x,a()),y) -> g#(g(a(),y),g(a(),x))
      TRS:
       h(x,x) -> h(a(),b())
       g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
       f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
       h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
      Bounds Processor:
       bound: 0
       enrichment: match-dp
       automaton:
        final states: {1}
        transitions:
         g0(3,3) -> 6*
         g0(3,9) -> 7*
         g0(3,2) -> 9*,5,4
         g0(3,4) -> 7*
         f490() -> 2*
         a0() -> 3*
         g{#,0}(7,6) -> 1*
         g{#,0}(9,4) -> 1*
         g{#,0}(5,9) -> 1*
         g{#,0}(9,9) -> 1*
         g{#,0}(5,4) -> 1*
       problem:
        DPs:
         
        TRS:
         h(x,x) -> h(a(),b())
         g(g(x,a()),y) -> g(g(a(),y),g(a(),x))
         f(g(x,y)) -> g(g(f(f(y)),h(a(),a())),x)
         h(h(f(f(x)),y),h(z,v)) -> h(h(f(z),f(f(f(y)))),h(v,x))
       Qed