/home/nowonder/forschung/aprove/TPDB05/TRS/currying/AG01/#3.13.trs

The program

(VAR x y h i u v)
(RULES
  app(app(eq, 0), 0) -> true
  app(app(eq, 0), app(s, x)) -> false
  app(app(eq, app(s, x)), 0) -> false
  app(app(eq, app(s, x)), app(s, y)) -> app(app(eq, x), y)
  app(app(or, true), y) -> true
  app(app(or, false), y) -> y
  app(app(union, empty), h) -> h
  app(app(union, app(app(app(edge, x), y), i)), h) -> app(app(app(edge, x), y), app(app(union, i), h))
  app(app(app(app(reach, x), y), empty), h) -> false
  app(app(app(app(reach, x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_1, app(app(eq, x), u)), x), y), app(app(app(edge, u), v), i)), h)
  app(app(app(app(app(if_reach_1, true), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(app(if_reach_2, app(app(eq, y), v)), x), y), app(app(app(edge, u), v), i)), h)
  app(app(app(app(app(if_reach_1, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(app(app(reach, x), y), i), app(app(app(edge, u), v), h))
  app(app(app(app(app(if_reach_2, true), x), y), app(app(app(edge, u), v), i)), h) -> true
  app(app(app(app(app(if_reach_2, false), x), y), app(app(app(edge, u), v), i)), h) -> app(app(or, app(app(app(app(reach, x), y), i), h)), app(app(app(app(reach, v), y), app(app(union, i), h)), empty))
)

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