YES

Succeeded in reading "/export/starexec/sandbox/benchmark/theBenchmark.ari".
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      f(a,x) -> a
      f(b,x) -> b
      g(a,x) -> c | f(x,a) == a
      g(x,a) -> d | f(x,b) == b
      c -> c
    )

No "->="-rules.

Decomposed conditions and removed infeasible rules if possible.
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      f(a,x) -> a
      f(b,x) -> b
      g(a,x) -> c | f(x,a) == a
      g(x,a) -> d | f(x,b) == b
      c -> c
    )

(CONDITION 
f(a,b) == b, f(a,a) == a
)

Optimized the infeasibility problem if possible.

(CONDITION 
f(a,b) == b, f(a,a) == a
)

This is ultra-RL and deterministic.

This is not operationally terminating and confluent.

This is a constructor-based system.

(RTG_of_NARROWINGTREE
(START
  Gamma[f(a,b) == b : { e, 1, 1.1, 1.2 } & f(a,a) == a : { e, 1, 1.1, 1.2 }]
)
(NONTERMINALS
  Gamma[f(a,b) == b : { e, 1, 1.1, 1.2 } & f(a,a) == a : { e, 1, 1.1, 1.2 }]
)
(RULES
  Gamma[f(a,b) == b : { e, 1, 1.1, 1.2 } & f(a,a) == a : { e, 1, 1.1, 1.2 }] -> EmptySet
)
)

YES