YES

Succeeded in reading "/export/starexec/sandbox2/benchmark/theBenchmark.ari".
    (CONDITIONTYPE ORIENTED)
    (VAR y x x1)
    (RULES
      f(c(x),c(c(y))) -> a(a(x)) | c(f(x,y)) == c(a(b))
      f(c(c(c(x))),y) -> a(y) | c(f(c(x),c(c(y)))) == c(a(a(b)))
      h(b) -> b
      h(a(a(x))) -> a(b) | h(x) == b
    )

No "->="-rules.

Decomposed conditions and removed infeasible rules if possible.
    (CONDITIONTYPE ORIENTED)
    (VAR y x x1)
    (RULES
      h(b) -> b
      h(a(a(x))) -> a(b) | h(x) == b
    )

(VAR y x1)
(CONDITION 
c(f(c(c(x1)),y)) == c(a(b)), c(f(c(x1),c(c(c(c(y)))))) == c(a(a(b)))
)

Optimized the infeasibility problem if possible.

(VAR y x1)
(CONDITION 
f(c(c(x1)),y) == a(b), f(c(x1),c(c(c(c(y))))) == a(a(b))
)

This is ultra-RL and deterministic.

This is operationally terminating and confluent.

(RTG_of_NARROWINGTREE
(START
  Gamma[f(c(c(x1)),y) == a(b) : { e, 1, 1.1, 1.1.1 } & f(c(x1),c(c(c(c(y))))) == a(a(b)) : { e, 1, 1.1, 1.2, 1.2.1, 1.2.1.1, 1.2.1.1.1 }]
)
(NONTERMINALS
  Gamma[f(c(c(x1)),y) == a(b) : { e, 1, 1.1, 1.1.1 } & f(c(x1),c(c(c(c(y))))) == a(a(b)) : { e, 1, 1.1, 1.2, 1.2.1, 1.2.1.1, 1.2.1.1.1 }]
)
(RULES
  Gamma[f(c(c(x1)),y) == a(b) : { e, 1, 1.1, 1.1.1 } & f(c(x1),c(c(c(c(y))))) == a(a(b)) : { e, 1, 1.1, 1.2, 1.2.1, 1.2.1.1, 1.2.1.1.1 }] -> EmptySet
)
)

YES