/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 p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) ) Problem 1: Dependency Pairs Processor: -> Pairs: P(p(s(x1))) -> P(x1) TOWER(0(x1)) -> P(s(p(s(x1)))) TOWER(0(x1)) -> P(s(x1)) TOWER(s(x1)) -> P(s(p(s(tower(p(s(p(s(x1))))))))) TOWER(s(x1)) -> P(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) TOWER(s(x1)) -> P(s(p(s(x1)))) TOWER(s(x1)) -> P(s(tower(p(s(p(s(x1))))))) TOWER(s(x1)) -> P(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))) TOWER(s(x1)) -> P(s(x1)) TOWER(s(x1)) -> TOWER(p(s(p(s(x1))))) TOWER(s(x1)) -> TWOTO(p(s(p(s(tower(p(s(p(s(x1)))))))))) TWICE(s(x1)) -> P(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) TWICE(s(x1)) -> P(p(p(s(s(s(x1)))))) TWICE(s(x1)) -> P(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) TWICE(s(x1)) -> P(p(s(s(s(x1))))) TWICE(s(x1)) -> P(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))) TWICE(s(x1)) -> P(s(s(s(x1)))) TWICE(s(x1)) -> TWICE(p(p(p(s(s(s(x1))))))) TWOTO(s(x1)) -> P(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) TWOTO(s(x1)) -> P(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) TWOTO(s(x1)) -> P(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) TWOTO(s(x1)) -> P(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) TWOTO(s(x1)) -> P(p(s(s(s(twoto(p(s(p(s(x1)))))))))) TWOTO(s(x1)) -> P(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))) TWOTO(s(x1)) -> P(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))) TWOTO(s(x1)) -> P(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))) TWOTO(s(x1)) -> P(s(p(s(x1)))) TWOTO(s(x1)) -> P(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))) TWOTO(s(x1)) -> P(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))) TWOTO(s(x1)) -> P(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))) TWOTO(s(x1)) -> P(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))) TWOTO(s(x1)) -> P(s(s(s(twoto(p(s(p(s(x1))))))))) TWOTO(s(x1)) -> P(s(x1)) TWOTO(s(x1)) -> TWICE(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) TWOTO(s(x1)) -> TWOTO(p(s(p(s(x1))))) -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) Problem 1: SCC Processor: -> Pairs: P(p(s(x1))) -> P(x1) TOWER(0(x1)) -> P(s(p(s(x1)))) TOWER(0(x1)) -> P(s(x1)) TOWER(s(x1)) -> P(s(p(s(tower(p(s(p(s(x1))))))))) TOWER(s(x1)) -> P(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) TOWER(s(x1)) -> P(s(p(s(x1)))) TOWER(s(x1)) -> P(s(tower(p(s(p(s(x1))))))) TOWER(s(x1)) -> P(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))) TOWER(s(x1)) -> P(s(x1)) TOWER(s(x1)) -> TOWER(p(s(p(s(x1))))) TOWER(s(x1)) -> TWOTO(p(s(p(s(tower(p(s(p(s(x1)))))))))) TWICE(s(x1)) -> P(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) TWICE(s(x1)) -> P(p(p(s(s(s(x1)))))) TWICE(s(x1)) -> P(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))) TWICE(s(x1)) -> P(p(s(s(s(x1))))) TWICE(s(x1)) -> P(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))) TWICE(s(x1)) -> P(s(s(s(x1)))) TWICE(s(x1)) -> TWICE(p(p(p(s(s(s(x1))))))) TWOTO(s(x1)) -> P(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))) TWOTO(s(x1)) -> P(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))) TWOTO(s(x1)) -> P(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) TWOTO(s(x1)) -> P(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))) TWOTO(s(x1)) -> P(p(s(s(s(twoto(p(s(p(s(x1)))))))))) TWOTO(s(x1)) -> P(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))) TWOTO(s(x1)) -> P(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))) TWOTO(s(x1)) -> P(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))) TWOTO(s(x1)) -> P(s(p(s(x1)))) TWOTO(s(x1)) -> P(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))) TWOTO(s(x1)) -> P(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))) TWOTO(s(x1)) -> P(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))) TWOTO(s(x1)) -> P(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))) TWOTO(s(x1)) -> P(s(s(s(twoto(p(s(p(s(x1))))))))) TWOTO(s(x1)) -> P(s(x1)) TWOTO(s(x1)) -> TWICE(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))) TWOTO(s(x1)) -> TWOTO(p(s(p(s(x1))))) -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(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(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) ->->Cycle: ->->-> Pairs: TWICE(s(x1)) -> TWICE(p(p(p(s(s(s(x1))))))) ->->-> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) ->->Cycle: ->->-> Pairs: TWOTO(s(x1)) -> TWOTO(p(s(p(s(x1))))) ->->-> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) ->->Cycle: ->->-> Pairs: TOWER(s(x1)) -> TOWER(p(s(p(s(x1))))) ->->-> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) The problem is decomposed in 4 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(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(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(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(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: TWICE(s(x1)) -> TWICE(p(p(p(s(s(s(x1))))))) -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(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: 2 ->Interpretation: [p](X) = 1/2.X [0](X) = 0 [s](X) = 2.X + 2 [TWICE](X) = X Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.3: Reduction Pair Processor: -> Pairs: TWOTO(s(x1)) -> TWOTO(p(s(p(s(x1))))) -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(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) = 1/4.X + 1/2 [0](X) = 0 [s](X) = 4.X + 4 [TWOTO](X) = X Problem 1.3: SCC Processor: -> Pairs: Empty -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.4: Reduction Pair Processor: -> Pairs: TOWER(s(x1)) -> TOWER(p(s(p(s(x1))))) -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(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) = 1/4.X + 1/2 [0](X) = 0 [s](X) = 4.X + 4 [TOWER](X) = X Problem 1.4: SCC Processor: -> Pairs: Empty -> Rules: p(p(s(x1))) -> p(x1) p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) p(s(x1)) -> x1 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) twice(0(x1)) -> 0(x1) twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) twoto(0(x1)) -> s(0(x1)) twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite.