/home/nowonder/forschung/aprove/TPDB05/TRS/currying/AG01/#3.57.trs

The program

(VAR x y z k l)
(RULES
  app'(app'(minus, x), 0) -> x
  app'(app'(minus, app'(s, x)), app'(s, y)) -> app'(app'(minus, x), y)
  app'(app'(minus, app'(app'(minus, x), y)), z) -> app'(app'(minus, x), app'(app'(plus, y), z))
  app'(app'(quot, 0), app'(s, y)) -> 0
  app'(app'(quot, app'(s, x)), app'(s, y)) -> app'(s, app'(app'(quot, app'(app'(minus, x), y)), app'(s, y)))
  app'(app'(plus, 0), y) -> y
  app'(app'(plus, app'(s, x)), y) -> app'(s, app'(app'(plus, x), y))
  app'(app'(app, nil), k) -> k
  app'(app'(app, l), nil) -> l
  app'(app'(app, app'(app'(cons, x), l)), k) -> app'(app'(cons, x), app'(app'(app, l), k))
  app'(sum, app'(app'(cons, x), nil)) -> app'(app'(cons, x), nil)
  app'(sum, app'(app'(cons, x), app'(app'(cons, y), l))) -> app'(sum, app'(app'(cons, app'(app'(plus, x), y)), l))
  app'(sum, app'(app'(app, l), app'(app'(cons, x), app'(app'(cons, y), k)))) -> app'(sum, app'(app'(app, l), app'(sum, app'(app'(cons, x), app'(app'(cons, y), k)))))
)

Submit to AProVE Web Frontend

Edit in AProVE Web Frontend