NO


Succeeded in reading "/export/starexec/sandbox2/benchmark/theBenchmark.ari".
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      f(x) -> x | x == e
      g(d,x,x) -> A
      h(x,x) -> g(x,x,f(k))
      a -> c
      a -> d
      b -> c
      b -> d
      c -> e
      c -> l
      k -> l
      k -> m
      d -> m
    )

No "->="-rules.

Decomposed conditions if possible.
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      f(x) -> x | x == e
      g(d,x,x) -> A
      h(x,x) -> g(x,x,f(k))
      a -> c
      a -> d
      b -> c
      b -> d
      c -> e
      c -> l
      k -> l
      k -> m
      d -> m
    )

Removed infeasible rules as much as possible.
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      f(x) -> x | x == e
      g(d,x,x) -> A
      h(x,x) -> g(x,x,f(k))
      a -> c
      a -> d
      b -> c
      b -> d
      c -> e
      c -> l
      k -> l
      k -> m
      d -> m
    )

Try to disprove confluence of the following (C)TRS:
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      f(x) -> x | x == e
      g(d,x,x) -> A
      h(x,x) -> g(x,x,f(k))
      a -> c
      a -> d
      b -> c
      b -> d
      c -> e
      c -> l
      k -> l
      k -> m
      d -> m
    )

Succeeded in disproving confluence.

Disproved via the following (C)TRS:
(CONDITIONTYPE ORIENTED)
(VAR x)
(RULES
  f(x) -> x | x == e
  g(d,x,x) -> A
  h(x,x) -> g(x,x,f(k))
  a -> c
  a -> d
  b -> c
  b -> d
  c -> e
  c -> l
  k -> l
  k -> m
  d -> m
)

NO