YES

Succeeded in reading "/export/starexec/sandbox2/benchmark/theBenchmark.ari".
    (CONDITIONTYPE ORIENTED)
    (VAR y x x1)
    (RULES
      gcd(add(x,y),y) -> gcd(x,y)
      gcd(y,add(x,y)) -> gcd(x,y)
      gcd(x,0) -> x
      gcd(0,x) -> x
      gcd(x,y) -> gcd(y,x) | leq(y,x) == false
      add(0,y) -> y
      add(s(x),y) -> s(add(x,y))
    )

No "->="-rules.

Decomposed conditions and removed infeasible rules if possible.
    (VAR y x x1)
    (RULES
      add(0,y) -> y
      add(s(x),y) -> s(add(x,y))
      gcd(add(x,y),y) -> gcd(x,y)
      gcd(y,add(x,y)) -> gcd(x,y)
      gcd(x,0) -> x
      gcd(0,x) -> x
    )

(VAR x1)
(CONDITION 
leq(0,x1) == false
)

Optimized the infeasibility problem if possible.

(VAR x1)
(CONDITION 
leq(0,x1) == false
)

This is ultra-RL and deterministic.

This is not operationally terminating and confluent.

This is a constructor-based system.

(RTG_of_NARROWINGTREE
(START
  Gamma[leq(0,x1) == false : { e, 1, 1.1 }]
)
(NONTERMINALS
  Gamma[leq(0,x1) == false : { e, 1, 1.1 }]
)
(RULES
  Gamma[leq(0,x1) == false : { e, 1, 1.1 }] -> EmptySet
)
)

YES