/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR x1) (RULES a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 ) Problem 1: Dependency Pairs Processor: -> Pairs: A(s(x1)) -> B(p(p(s(s(x1))))) A(s(x1)) -> P(p(s(s(x1)))) A(s(x1)) -> P(s(b(p(p(s(s(x1))))))) A(s(x1)) -> P(s(s(x1))) B(s(x1)) -> C(p(s(p(s(x1))))) B(s(x1)) -> P(p(s(s(c(p(s(p(s(x1))))))))) B(s(x1)) -> P(s(p(s(x1)))) B(s(x1)) -> P(s(s(c(p(s(p(s(x1)))))))) B(s(x1)) -> P(s(x1)) C(s(x1)) -> A(p(s(p(s(x1))))) C(s(x1)) -> P(s(a(p(s(p(s(x1))))))) C(s(x1)) -> P(s(p(s(a(p(s(p(s(x1))))))))) C(s(x1)) -> P(s(p(s(x1)))) C(s(x1)) -> P(s(x1)) P(p(s(x1))) -> P(x1) -> Rules: a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 Problem 1: SCC Processor: -> Pairs: A(s(x1)) -> B(p(p(s(s(x1))))) A(s(x1)) -> P(p(s(s(x1)))) A(s(x1)) -> P(s(b(p(p(s(s(x1))))))) A(s(x1)) -> P(s(s(x1))) B(s(x1)) -> C(p(s(p(s(x1))))) B(s(x1)) -> P(p(s(s(c(p(s(p(s(x1))))))))) B(s(x1)) -> P(s(p(s(x1)))) B(s(x1)) -> P(s(s(c(p(s(p(s(x1)))))))) B(s(x1)) -> P(s(x1)) C(s(x1)) -> A(p(s(p(s(x1))))) C(s(x1)) -> P(s(a(p(s(p(s(x1))))))) C(s(x1)) -> P(s(p(s(a(p(s(p(s(x1))))))))) C(s(x1)) -> P(s(p(s(x1)))) C(s(x1)) -> P(s(x1)) P(p(s(x1))) -> P(x1) -> Rules: a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: P(p(s(x1))) -> P(x1) ->->-> Rules: a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 ->->Cycle: ->->-> Pairs: A(s(x1)) -> B(p(p(s(s(x1))))) B(s(x1)) -> C(p(s(p(s(x1))))) C(s(x1)) -> A(p(s(p(s(x1))))) ->->-> Rules: a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(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: a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 ->Projection: pi(P) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(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: A(s(x1)) -> B(p(p(s(s(x1))))) B(s(x1)) -> C(p(s(p(s(x1))))) C(s(x1)) -> A(p(s(p(s(x1))))) -> Rules: a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 -> Usable rules: p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation: [p](X) = 1/2.X [s](X) = 2.X + 2 [A](X) = 2.X + 1/2 [B](X) = 2.X + 1 [C](X) = 2.X + 1/2 Problem 1.2: SCC Processor: -> Pairs: B(s(x1)) -> C(p(s(p(s(x1))))) C(s(x1)) -> A(p(s(p(s(x1))))) -> Rules: a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 ->Strongly Connected Components: There is no strongly connected component The problem is finite.