/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 i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 ) Problem 1: Dependency Pairs Processor: -> Pairs: I(0(x1)) -> P(s(p(s(0(p(s(p(s(x1))))))))) I(0(x1)) -> P(s(p(s(x1)))) I(0(x1)) -> P(s(0(p(s(p(s(x1))))))) I(0(x1)) -> P(s(x1)) I(s(x1)) -> J(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))) I(s(x1)) -> P(p(p(p(s(s(s(s(x1)))))))) I(s(x1)) -> P(p(p(s(s(s(s(x1))))))) I(s(x1)) -> P(p(s(s(s(s(x1)))))) I(s(x1)) -> P(s(p(p(p(p(s(s(s(s(x1)))))))))) I(s(x1)) -> P(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))) I(s(x1)) -> P(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) I(s(x1)) -> P(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))) I(s(x1)) -> P(s(s(s(s(x1))))) J(0(x1)) -> P(p(s(s(0(p(s(p(s(x1))))))))) J(0(x1)) -> P(s(p(p(s(s(0(p(s(p(s(x1))))))))))) J(0(x1)) -> P(s(p(s(x1)))) J(0(x1)) -> P(s(s(0(p(s(p(s(x1)))))))) J(0(x1)) -> P(s(x1)) J(s(x1)) -> I(p(s(p(s(x1))))) J(s(x1)) -> P(p(s(s(i(p(s(p(s(x1))))))))) J(s(x1)) -> P(s(p(s(x1)))) J(s(x1)) -> P(s(s(i(p(s(p(s(x1)))))))) J(s(x1)) -> P(s(x1)) P(p(s(x1))) -> P(x1) -> Rules: i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 Problem 1: SCC Processor: -> Pairs: I(0(x1)) -> P(s(p(s(0(p(s(p(s(x1))))))))) I(0(x1)) -> P(s(p(s(x1)))) I(0(x1)) -> P(s(0(p(s(p(s(x1))))))) I(0(x1)) -> P(s(x1)) I(s(x1)) -> J(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))) I(s(x1)) -> P(p(p(p(s(s(s(s(x1)))))))) I(s(x1)) -> P(p(p(s(s(s(s(x1))))))) I(s(x1)) -> P(p(s(s(s(s(x1)))))) I(s(x1)) -> P(s(p(p(p(p(s(s(s(s(x1)))))))))) I(s(x1)) -> P(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))) I(s(x1)) -> P(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) I(s(x1)) -> P(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))) I(s(x1)) -> P(s(s(s(s(x1))))) J(0(x1)) -> P(p(s(s(0(p(s(p(s(x1))))))))) J(0(x1)) -> P(s(p(p(s(s(0(p(s(p(s(x1))))))))))) J(0(x1)) -> P(s(p(s(x1)))) J(0(x1)) -> P(s(s(0(p(s(p(s(x1)))))))) J(0(x1)) -> P(s(x1)) J(s(x1)) -> I(p(s(p(s(x1))))) J(s(x1)) -> P(p(s(s(i(p(s(p(s(x1))))))))) J(s(x1)) -> P(s(p(s(x1)))) J(s(x1)) -> P(s(s(i(p(s(p(s(x1)))))))) J(s(x1)) -> P(s(x1)) P(p(s(x1))) -> P(x1) -> Rules: i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: P(p(s(x1))) -> P(x1) ->->-> Rules: i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 ->->Cycle: ->->-> Pairs: I(s(x1)) -> J(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))) J(s(x1)) -> I(p(s(p(s(x1))))) ->->-> Rules: i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: P(p(s(x1))) -> P(x1) -> Rules: i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 ->Projection: pi(P) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pair Processor: -> Pairs: I(s(x1)) -> J(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))) J(s(x1)) -> I(p(s(p(s(x1))))) -> Rules: i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 -> Usable rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [p](X) = 1/3.X + 1/4 [0](X) = 0 [s](X) = 3.X + 4 [I](X) = 4/3.X + 1/2 [J](X) = 1/2.X + 3 Problem 1.2: SCC Processor: -> Pairs: J(s(x1)) -> I(p(s(p(s(x1))))) -> Rules: i(0(x1)) -> p(s(p(s(0(p(s(p(s(x1))))))))) i(s(x1)) -> p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))))))) j(0(x1)) -> p(s(p(p(s(s(0(p(s(p(s(x1))))))))))) j(s(x1)) -> s(s(s(s(p(p(s(s(i(p(s(p(s(x1))))))))))))) p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 ->Strongly Connected Components: There is no strongly connected component The problem is finite.