/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR x1) (RULES p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(x1)))) p(s(x1)) -> x1 q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1))))))))) q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1))))))))))) r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1)))))))))) ) Problem 1: Dependency Pairs Processor: -> Pairs: P(p(s(x1))) -> P(x1) Q(0(x1)) -> P(p(s(s(0(s(s(s(s(x1))))))))) Q(0(x1)) -> P(s(s(0(s(s(s(s(x1)))))))) Q(s(x1)) -> P(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) Q(s(x1)) -> P(p(s(s(x1)))) Q(s(x1)) -> P(s(s(s(s(s(s(r(p(p(s(s(x1)))))))))))) Q(s(x1)) -> P(s(s(x1))) Q(s(x1)) -> R(p(p(s(s(x1))))) R(0(x1)) -> P(p(p(s(s(s(x1)))))) R(0(x1)) -> P(p(s(s(s(x1))))) R(0(x1)) -> P(s(p(s(0(p(p(p(s(s(s(x1))))))))))) R(0(x1)) -> P(s(0(p(p(p(s(s(s(x1))))))))) R(0(x1)) -> P(s(s(s(x1)))) R(s(x1)) -> P(s(p(s(s(q(p(s(p(s(x1)))))))))) R(s(x1)) -> P(s(p(s(x1)))) R(s(x1)) -> P(s(s(q(p(s(p(s(x1)))))))) R(s(x1)) -> P(s(x1)) R(s(x1)) -> Q(p(s(p(s(x1))))) -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(x1)))) p(s(x1)) -> x1 q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1))))))))) q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1))))))))))) r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1)))))))))) Problem 1: SCC Processor: -> Pairs: P(p(s(x1))) -> P(x1) Q(0(x1)) -> P(p(s(s(0(s(s(s(s(x1))))))))) Q(0(x1)) -> P(s(s(0(s(s(s(s(x1)))))))) Q(s(x1)) -> P(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) Q(s(x1)) -> P(p(s(s(x1)))) Q(s(x1)) -> P(s(s(s(s(s(s(r(p(p(s(s(x1)))))))))))) Q(s(x1)) -> P(s(s(x1))) Q(s(x1)) -> R(p(p(s(s(x1))))) R(0(x1)) -> P(p(p(s(s(s(x1)))))) R(0(x1)) -> P(p(s(s(s(x1))))) R(0(x1)) -> P(s(p(s(0(p(p(p(s(s(s(x1))))))))))) R(0(x1)) -> P(s(0(p(p(p(s(s(s(x1))))))))) R(0(x1)) -> P(s(s(s(x1)))) R(s(x1)) -> P(s(p(s(s(q(p(s(p(s(x1)))))))))) R(s(x1)) -> P(s(p(s(x1)))) R(s(x1)) -> P(s(s(q(p(s(p(s(x1)))))))) R(s(x1)) -> P(s(x1)) R(s(x1)) -> Q(p(s(p(s(x1))))) -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(x1)))) p(s(x1)) -> x1 q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1))))))))) q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1))))))))))) r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: P(p(s(x1))) -> P(x1) ->->-> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(x1)))) p(s(x1)) -> x1 q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1))))))))) q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1))))))))))) r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1)))))))))) ->->Cycle: ->->-> Pairs: Q(s(x1)) -> R(p(p(s(s(x1))))) R(s(x1)) -> Q(p(s(p(s(x1))))) ->->-> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(x1)))) p(s(x1)) -> x1 q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1))))))))) q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1))))))))))) r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1)))))))))) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: P(p(s(x1))) -> P(x1) -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(x1)))) p(s(x1)) -> x1 q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1))))))))) q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1))))))))))) r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1)))))))))) ->Projection: pi(P) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(x1)))) p(s(x1)) -> x1 q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1))))))))) q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1))))))))))) r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1)))))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pair Processor: -> Pairs: Q(s(x1)) -> R(p(p(s(s(x1))))) R(s(x1)) -> Q(p(s(p(s(x1))))) -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(x1)))) p(s(x1)) -> x1 q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1))))))))) q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1))))))))))) r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1)))))))))) -> Usable rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(x1)))) p(s(x1)) -> x1 ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation: [p](X) = 1/2.X [0](X) = 0 [s](X) = 2.X + 2 [Q](X) = 2.X + 1 [R](X) = 2.X + 1 Problem 1.2: SCC Processor: -> Pairs: R(s(x1)) -> Q(p(s(p(s(x1))))) -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(x1)))) p(s(x1)) -> x1 q(0(x1)) -> p(p(s(s(0(s(s(s(s(x1))))))))) q(s(x1)) -> p(p(s(s(s(s(s(s(r(p(p(s(s(x1))))))))))))) r(0(x1)) -> p(s(p(s(0(p(p(p(s(s(s(x1))))))))))) r(s(x1)) -> p(s(p(s(s(q(p(s(p(s(x1)))))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite.