MAYBE

Succeeded in reading "/export/starexec/sandbox/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 x x1)
(CONDITION 
iadd(x1) == tp2(x,0)
)

Optimized the infeasibility problem if possible.

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

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(x1) == tp2(x,0) : { e, 1 }]
)
(NONTERMINALS
  Gamma[iadd(x1) == tp2(x,0) : { e, 1 }]
  Gamma[iadd(x231) == tp2 : { e, 1 }]
  Gamma[u1(iadd2) == tp3 : { e, 1 }]
)
(RULES
  Gamma[iadd(x1) == tp2(x,0) : { e, 1 }] -> (Rec(Gamma[iadd(x231) == tp2 : { e, 1 }], { tp1 -> tp2, x1 -> x231 }) & { tp1 -> tp2(x,0) })
  Gamma[iadd(x231) == tp2 : { e, 1 }] -> { tp2 -> iadd(x231) }
  Gamma[iadd(x231) == tp2 : { e, 1 }] -> { tp2 -> tp2(0,y13), x231 -> y13 }
  Gamma[iadd(x231) == tp2 : { e, 1 }] -> ((Rec(Gamma[iadd(x231) == tp2 : { e, 1 }], { iadd1 -> tp2, z9 -> x231 }) & Rec(Gamma[u1(iadd2) == tp3 : { e, 1 }], { tp2 -> tp3, iadd1 -> iadd2 })) . { x231 -> s(z9) })
  Gamma[iadd(x231) == tp2 : { e, 1 }] -> { tp2 -> tp2(x238,y15), x231 -> add(x238,y15) }
  Gamma[u1(iadd2) == tp3 : { e, 1 }] -> { tp3 -> u1(iadd2) }
  Gamma[u1(iadd2) == tp3 : { e, 1 }] -> { tp3 -> tp2(s(x264),y34), iadd2 -> tp2(x264,y34) }
)
)

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

This is not ultra-RL and deterministic.


MAYBE