YES

Succeeded in reading "/export/starexec/sandbox/benchmark/theBenchmark.ari".
    (CONDITIONTYPE ORIENTED)
    (VAR x x1)
    (RULES
      even(0) -> true
      even(s(x)) -> false | odd(x) == false
      even(s(x)) -> true | odd(x) == true
      odd(0) -> false
      odd(s(x)) -> false | even(x) == false
      odd(s(x)) -> true | even(x) == true
    )

No "->="-rules.

Decomposed conditions and removed infeasible rules if possible.
    (CONDITIONTYPE ORIENTED)
    (VAR x x1)
    (RULES
      even(0) -> true
      even(s(x)) -> false | odd(x) == false
      even(s(x)) -> true | odd(x) == true
      odd(0) -> false
      odd(s(x)) -> false | even(x) == false
      odd(s(x)) -> true | even(x) == true
    )

(VAR x1)
(CONDITION 
even(x1) == false, even(x1) == true
)

Optimized the infeasibility problem if possible.

(VAR x1)
(CONDITION 
even(x1) == false, even(x1) == true
)

This is ultra-RL and deterministic.

This is operationally terminating and confluent.

(RTG_of_NARROWINGTREE
(START
  Gamma[even(x1) == false : { e, 1 } & even(x1) == true : { e, 1 }]
)
(NONTERMINALS
  Gamma[even(x1) == false : { e, 1 } & even(x1) == true : { e, 1 }]
  Gamma[even(x443) == false : { e, 1 }]
  Gamma[even(x448) == true : { e, 1 }]
  Gamma[odd(x458) == false : { e, 1 }]
  Gamma[odd(x464) == true : { e, 1 }]
)
(RULES
  Gamma[even(x1) == false : { e, 1 } & even(x1) == true : { e, 1 }] -> EmptySet
  Gamma[even(x443) == false : { e, 1 }] -> (Rec(Gamma[odd(x458) == false : { e, 1 }], { x449 -> x458 }) . { x443 -> s(x449) })
  Gamma[even(x448) == true : { e, 1 }] -> { x448 -> 0 }
  Gamma[even(x448) == true : { e, 1 }] -> (Rec(Gamma[odd(x464) == true : { e, 1 }], { x468 -> x464 }) . { x448 -> s(x468) })
  Gamma[odd(x458) == false : { e, 1 }] -> { x458 -> 0 }
  Gamma[odd(x458) == false : { e, 1 }] -> (Rec(Gamma[even(x443) == false : { e, 1 }], { x485 -> x443 }) . { x458 -> s(x485) })
  Gamma[odd(x464) == true : { e, 1 }] -> (Rec(Gamma[even(x448) == true : { e, 1 }], { x502 -> x448 }) . { x464 -> s(x502) })
)
)

YES