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