MAYBE

Succeeded in reading "/export/starexec/sandbox2/benchmark/theBenchmark.ari".
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      s(p(x)) -> x
      p(s(x)) -> x
      pos(0) -> false
      pos(s(0)) -> true
      pos(s(x)) -> true | pos(x) == true
      pos(p(x)) -> false | pos(x) == false
    )

No "->="-rules.

Decomposed conditions and removed infeasible rules if possible.
    (CONDITIONTYPE ORIENTED)
    (VAR x)
    (RULES
      s(p(x)) -> x
      p(s(x)) -> x
      pos(0) -> false
      pos(s(0)) -> true
      pos(s(x)) -> true | pos(x) == true
      pos(p(x)) -> false | pos(x) == false
    )

(VAR x)
(CONDITION 
pos(s(x)) == false
)

Optimized the infeasibility problem if possible.

(VAR x)
(CONDITION 
pos(s(x)) == 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[pos(s(x)) == false : { e, 1, 1.1 }]
)
(NONTERMINALS
  Gamma[pos(s(x)) == false : { e, 1, 1.1 }]
  Gamma[s(x117) == s2 : { e, 1 }]
  Gamma[pos(s3) == false : { e, 1 }]
  Gamma[pos(x138) == true : { e, 1 }]
)
(RULES
  Gamma[pos(s(x)) == false : { e, 1, 1.1 }] -> (Rec(Gamma[s(x117) == s2 : { e, 1 }], { s1 -> s2, x -> x117 }) & Rec(Gamma[pos(s3) == false : { e, 1 }], { s1 -> s3 }))
  Gamma[s(x117) == s2 : { e, 1 }] -> { s2 -> s(x117) }
  Gamma[s(x117) == s2 : { e, 1 }] -> { x122 -> x126, s2 -> x126, x117 -> p(x126) }
  Gamma[pos(s3) == false : { e, 1 }] -> { s3 -> 0 }
  Gamma[pos(s3) == false : { e, 1 }] -> (Rec(Gamma[pos(s3) == false : { e, 1 }], { x131 -> s3 }) . { s3 -> p(x131) })
  Gamma[pos(x138) == true : { e, 1 }] -> { x138 -> s(0) }
  Gamma[pos(x138) == true : { e, 1 }] -> (Rec(Gamma[pos(x138) == true : { e, 1 }], { x148 -> x138 }) . { x138 -> s(x148) })
)
)

Failed to prove infeasibility of the linearized conditions by means of narrowing trees.

This is not ultra-RL and deterministic.


MAYBE