MAYBE

Succeeded in reading "/export/starexec/sandbox2/benchmark/theBenchmark.ari".
    (CONDITIONTYPE ORIENTED)
    (VAR x y z x3 x2 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 x3 x2 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 x3 x2 x x1)
(CONDITION 
iadd(x1) == tp2(x,x2), iadd(x2) == tp2(x3,x1)
)

Optimized the infeasibility problem if possible.

(VAR x3 x2 x x1)
(CONDITION 
iadd(x1) == tp2(x,x2), iadd(x2) == tp2(x3,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(x1) == tp2(x,x2) : { e, 1 } & iadd(x2) == tp2(x3,x1) : { e, 1 }]
)
(NONTERMINALS
  Gamma[iadd(x1) == tp2(x,x2) : { e, 1 } & iadd(x2) == tp2(x3,x1) : { e, 1 }]
  Gamma[iadd(x231) == tp2 : { e, 1 }]
  Gamma[u1(iadd2) == tp4 : { e, 1 }]
)
(RULES
  Gamma[iadd(x1) == tp2(x,x2) : { e, 1 } & iadd(x2) == tp2(x3,x1) : { e, 1 }] -> ((Rec(Gamma[iadd(x231) == tp2 : { e, 1 }], { tp1 -> tp2, x1 -> x231 }) & { tp1 -> tp2(x,x2) }) & (Rec(Gamma[iadd(x231) == tp2 : { e, 1 }], { tp3 -> tp2, x2 -> x231 }) & { tp3 -> tp2(x3,x1) }))
  Gamma[iadd(x231) == tp2 : { e, 1 }] -> { tp2 -> iadd(x231) }
  Gamma[iadd(x231) == tp2 : { e, 1 }] -> { tp2 -> tp2(0,y23), x231 -> y23 }
  Gamma[iadd(x231) == tp2 : { e, 1 }] -> ((Rec(Gamma[iadd(x231) == tp2 : { e, 1 }], { iadd1 -> tp2, z15 -> x231 }) & Rec(Gamma[u1(iadd2) == tp4 : { e, 1 }], { tp2 -> tp4, iadd1 -> iadd2 })) . { x231 -> s(z15) })
  Gamma[iadd(x231) == tp2 : { e, 1 }] -> { tp2 -> tp2(x251,y25), x231 -> add(x251,y25) }
  Gamma[u1(iadd2) == tp4 : { e, 1 }] -> { tp4 -> u1(iadd2) }
  Gamma[u1(iadd2) == tp4 : { e, 1 }] -> { tp4 -> tp2(s(x277),y44), iadd2 -> tp2(x277,y44) }
)
)

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

This is not ultra-RL and deterministic.


MAYBE