YES


Succeeded in reading "/export/starexec/sandbox2/benchmark/theBenchmark.ari".
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      p(q(x)) -> 0
      c -> c
      a(x) -> b | p(x) == 0
    )

No "->="-rules.

Decomposed conditions if possible.
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      p(q(x)) -> 0
      c -> c
      a(x) -> b | p(x) == 0
    )

Removed infeasible rules as much as possible.
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      p(q(x)) -> 0
      c -> c
      a(x) -> b | p(x) == 0
    )

Try to disprove confluence of the following (C)TRS:
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      p(q(x)) -> 0
      c -> c
      a(x) -> b | p(x) == 0
    )

Failed either to apply SR and U for normal 1CTRSs to the above CTRS or to prove confluence of any converted TRSs.

Try to apply SR and U for 3DCTRSs to the above CTRS.

Succeeded in applying U for 3DCTRSs to the above CTRS.
U(R) =
    (VAR x1)
    (RULES
      p(q(x1)) -> 0
      c -> c
      a(x1) -> u1(p(x1),x1)
      u1(0,x1) -> b
    )

U for 3DCTRSs is sound for the above CTRS.

U(R) is confluent.

YES