MAYBE

Succeeded in reading "/export/starexec/sandbox2/benchmark/theBenchmark.ari".
    (CONDITIONTYPE ORIENTED)
    (VAR x y z x1)
    (RULES
      gcd(z,y) -> gcd(x,y) | iadd(z) == tp2(x,y)
      gcd(y,z) -> gcd(x,y) | iadd(z) == tp2(x,y)
      gcd(x,0) -> x
      gcd(0,x) -> x
      iadd(y) -> tp2(0,y)
      iadd(s(z)) -> u1(iadd(z))
      u1(tp2(x,y)) -> tp2(s(x),y)
      iadd(add(x,y)) -> tp2(x,y)
    )

No "->="-rules.

Decomposed conditions and removed infeasible rules if possible.
    (CONDITIONTYPE ORIENTED)
    (VAR x y z x1)
    (RULES
      gcd(z,y) -> gcd(x,y) | iadd(z) == tp2(x,y)
      gcd(y,z) -> gcd(x,y) | iadd(z) == tp2(x,y)
      gcd(x,0) -> x
      gcd(0,x) -> x
      iadd(y) -> tp2(0,y)
      iadd(s(z)) -> u1(iadd(z))
      u1(tp2(x,y)) -> tp2(s(x),y)
      iadd(add(x,y)) -> tp2(x,y)
    )

(VAR x1 x)
(CONDITION 
iadd(0) == tp2(x,x1)
)

Optimized the infeasibility problem if possible.

(VAR x1 x)
(CONDITION 
iadd(0) == tp2(x,x1)
)

This is ultra-RL and deterministic.

This is not operationally terminating and confluent.

This is a constructor-based system.

(RTG_of_NARROWINGTREE
(START
  Gamma[iadd(0) == tp2(x,x1) : { e, 1, 1.1 }]
)
(NONTERMINALS
  Gamma[iadd(0) == tp2(x,x1) : { e, 1, 1.1 }]
)
(RULES
  Gamma[iadd(0) == tp2(x,x1) : { e, 1, 1.1 }] -> { x1 -> y3, x -> 0 }
)
)

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

This is not ultra-RL and deterministic.


MAYBE