/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(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ) Problem 1: Dependency Pairs Processor: -> Pairs: A(a(a(a(a(x1))))) -> A(a(a(b(a(a(a(x1))))))) A(a(a(a(a(x1))))) -> A(a(b(a(a(a(x1)))))) A(a(a(a(a(x1))))) -> A(b(a(a(a(x1))))) A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(b(a(a(b(x1)))))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(b(a(b(x1))))) A(a(b(a(x1)))) -> A(b(x1)) A(a(b(b(a(x1))))) -> A(b(b(b(a(b(b(x1))))))) A(a(b(b(a(x1))))) -> A(b(b(x1))) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(a(a(x1))))) -> A(b(b(a(a(x1))))) A(b(a(a(x1)))) -> A(b(b(a(x1)))) A(b(a(b(a(x1))))) -> A(b(b(b(a(b(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) A(b(b(a(a(x1))))) -> A(b(b(b(a(x1))))) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: SCC Processor: -> Pairs: A(a(a(a(a(x1))))) -> A(a(a(b(a(a(a(x1))))))) A(a(a(a(a(x1))))) -> A(a(b(a(a(a(x1)))))) A(a(a(a(a(x1))))) -> A(b(a(a(a(x1))))) A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(b(a(a(b(x1)))))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(b(a(b(x1))))) A(a(b(a(x1)))) -> A(b(x1)) A(a(b(b(a(x1))))) -> A(b(b(b(a(b(b(x1))))))) A(a(b(b(a(x1))))) -> A(b(b(x1))) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(a(a(x1))))) -> A(b(b(a(a(x1))))) A(b(a(a(x1)))) -> A(b(b(a(x1)))) A(b(a(b(a(x1))))) -> A(b(b(b(a(b(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) A(b(b(a(a(x1))))) -> A(b(b(b(a(x1))))) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(a(a(a(x1))))) -> A(a(a(b(a(a(a(x1))))))) A(a(a(a(a(x1))))) -> A(a(b(a(a(a(x1)))))) A(a(a(a(a(x1))))) -> A(b(a(a(a(x1))))) A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(a(a(a(x1))))) -> A(a(a(b(a(a(a(x1))))))) A(a(a(a(a(x1))))) -> A(a(b(a(a(a(x1)))))) A(a(a(a(a(x1))))) -> A(b(a(a(a(x1))))) A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 2.X + 3/4 [b](X) = 1/3.X + 1/4 [A](X) = 4.X Problem 1: SCC Processor: -> Pairs: A(a(a(a(a(x1))))) -> A(a(b(a(a(a(x1)))))) A(a(a(a(a(x1))))) -> A(b(a(a(a(x1))))) A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(a(a(a(x1))))) -> A(a(b(a(a(a(x1)))))) A(a(a(a(a(x1))))) -> A(b(a(a(a(x1))))) A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(a(a(a(x1))))) -> A(a(b(a(a(a(x1)))))) A(a(a(a(a(x1))))) -> A(b(a(a(a(x1))))) A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 3/2.X + 3 [b](X) = 1/2.X + 1/4 [A](X) = 2.X Problem 1: SCC Processor: -> Pairs: A(a(a(a(a(x1))))) -> A(b(a(a(a(x1))))) A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(a(a(a(x1))))) -> A(b(a(a(a(x1))))) A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(a(a(a(x1))))) -> A(b(a(a(a(x1))))) A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 3/2.X + 4 [b](X) = 1/2.X [A](X) = 4.X Problem 1: SCC Processor: -> Pairs: A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(a(a(x1)))) -> A(a(b(a(a(x1))))) A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 3.X + 4/3 [b](X) = 1/4.X + 1/4 [A](X) = 3.X Problem 1: SCC Processor: -> Pairs: A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(a(a(x1)))) -> A(b(a(a(x1)))) A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 2.X + 3 [b](X) = 1/3.X + 1/2 [A](X) = 2.X Problem 1: SCC Processor: -> Pairs: A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(a(b(a(x1))))) -> A(a(b(b(a(a(b(x1))))))) A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 3/2.X + 4 [b](X) = 1/2.X + 1/2 [A](X) = 3.X Problem 1: SCC Processor: -> Pairs: A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(a(b(a(x1))))) -> A(a(b(x1))) A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 2.X + 2 [b](X) = 1/4.X [A](X) = 4.X Problem 1: SCC Processor: -> Pairs: A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(a(b(a(x1))))) -> A(b(x1)) A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 3/2.X + 2/3 [b](X) = 1/2.X [A](X) = 2.X Problem 1: SCC Processor: -> Pairs: A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(a(x1))) -> A(b(a(x1))) A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 3/2.X + 1/3 [b](X) = 1/2.X [A](X) = 2.X Problem 1: SCC Processor: -> Pairs: A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(b(a(a(x1))))) -> A(b(a(b(a(b(a(x1))))))) A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 2.X + 2 [b](X) = 1/4.X + 1/3 [A](X) = 1/4.X Problem 1: SCC Processor: -> Pairs: A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(b(a(a(x1))))) -> A(b(a(b(a(x1))))) A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 2.X + 1 [b](X) = 1/3.X [A](X) = 2.X Problem 1: SCC Processor: -> Pairs: A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(b(a(a(x1))))) -> A(b(a(x1))) A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 2.X + 4 [b](X) = 1/3.X [A](X) = 1/4.X Problem 1: SCC Processor: -> Pairs: A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(a(b(a(x1)))) -> A(b(x1)) A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 2.X + 1/3 [b](X) = 1/3.X [A](X) = 4/3.X Problem 1: SCC Processor: -> Pairs: A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(b(a(a(a(x1))))) -> A(a(b(b(a(a(x1)))))) A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [a](X) = 3/2.X + 2 [b](X) = 1/2.X + 1/4 [A](X) = 2/3.X Problem 1: SCC Processor: -> Pairs: A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(b(a(b(a(x1))))) -> A(b(x1)) ->->-> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) Problem 1: Reduction Pair Processor: -> Pairs: A(b(a(b(a(x1))))) -> A(b(x1)) -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) -> Usable rules: Empty ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [a](X) = 2.X + 2 [b](X) = 2.X + 2 [A](X) = 2.X Problem 1: SCC Processor: -> Pairs: Empty -> Rules: a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(a(x1)))) -> a(a(b(a(a(x1))))) a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1))))))) a(a(a(x1))) -> a(b(a(x1))) a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(a(x1)))) -> a(b(b(a(b(x1))))) a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1))))))) a(a(x1)) -> b(x1) a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(a(x1)))) -> b(a(b(b(a(x1))))) a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1))))))) a(b(a(x1))) -> b(b(b(x1))) a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(a(x1)))) -> b(b(b(b(b(x1))))) a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite.