YES Succeeded in reading "/export/starexec/sandbox/benchmark/theBenchmark.ari". (CONDITIONTYPE ORIENTED) (VAR x) (RULES zero(0) -> true zero(s(x)) -> false even(x) -> true | zero(x) == true even(s(x)) -> true | odd(x) == true even(s(x)) -> false | even(x) == true odd(x) -> false | zero(x) == true odd(s(x)) -> true | even(x) == true odd(s(x)) -> false | odd(x) == true ) No "->="-rules. Decomposed conditions and removed infeasible rules if possible. (CONDITIONTYPE ORIENTED) (VAR x) (RULES zero(0) -> true zero(s(x)) -> false even(x) -> true | zero(x) == true even(s(x)) -> true | odd(x) == true even(s(x)) -> false | even(x) == true odd(x) -> false | zero(x) == true odd(s(x)) -> true | even(x) == true odd(s(x)) -> false | odd(x) == true ) (VAR x) (CONDITION zero(s(x)) == true, even(x) == true ) Optimized the infeasibility problem if possible. (VAR x) (CONDITION zero(s(x)) == true, even(x) == true ) This is ultra-RL and deterministic. This is operationally terminating and confluent. (RTG_of_NARROWINGTREE (START Gamma[zero(s(x)) == true : { e, 1, 1.1 } & even(x) == true : { e, 1 }] ) (NONTERMINALS Gamma[zero(s(x)) == true : { e, 1, 1.1 } & even(x) == true : { e, 1 }] Gamma[even(x1459) == true : { e, 1 }] Gamma[zero(x1474) == true : { e, 1 }] Gamma[odd(x1483) == true : { e, 1 }] ) (RULES Gamma[zero(s(x)) == true : { e, 1, 1.1 } & even(x) == true : { e, 1 }] -> EmptySet Gamma[even(x1459) == true : { e, 1 }] -> (Rec(Gamma[zero(x1474) == true : { e, 1 }], { x1461 -> x1474 }) . { x1459 -> x1461 }) Gamma[even(x1459) == true : { e, 1 }] -> (Rec(Gamma[odd(x1483) == true : { e, 1 }], { x1462 -> x1483 }) . { x1459 -> s(x1462) }) Gamma[zero(x1474) == true : { e, 1 }] -> { x1474 -> 0 } Gamma[odd(x1483) == true : { e, 1 }] -> (Rec(Gamma[even(x1459) == true : { e, 1 }], { x1509 -> x1459 }) . { x1483 -> s(x1509) }) ) ) YES