YES Problem: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) Proof: DP Processor: DPs: a#(a(x1)) -> a#(b(a(x1))) a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(b(x1))) -> a#(b(b(a(b(x1))))) a#(b(a(x1))) -> a#(b(b(a(x1)))) a#(a(a(a(x1)))) -> a#(b(a(a(a(x1))))) a#(a(a(a(x1)))) -> a#(a(b(a(a(a(x1)))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(b(x1)))) -> a#(b(b(a(a(b(x1)))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(b(b(x1)))) -> a#(b(b(b(a(b(b(x1))))))) a#(b(a(a(x1)))) -> a#(b(b(a(a(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(b(a(b(x1)))) -> a#(b(b(b(a(b(x1)))))) a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) EDG Processor: DPs: a#(a(x1)) -> a#(b(a(x1))) a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(b(x1))) -> a#(b(b(a(b(x1))))) a#(b(a(x1))) -> a#(b(b(a(x1)))) a#(a(a(a(x1)))) -> a#(b(a(a(a(x1))))) a#(a(a(a(x1)))) -> a#(a(b(a(a(a(x1)))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(b(x1)))) -> a#(b(b(a(a(b(x1)))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(b(b(x1)))) -> a#(b(b(b(a(b(b(x1))))))) a#(b(a(a(x1)))) -> a#(b(b(a(a(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(b(a(b(x1)))) -> a#(b(b(b(a(b(x1)))))) a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) graph: a#(b(a(a(x1)))) -> a#(b(b(a(a(x1))))) -> a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(x1)) -> a#(b(a(x1))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(b(x1))) -> a#(b(b(a(b(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(b(a(x1))) -> a#(b(b(a(x1)))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(a(a(x1)))) -> a#(b(a(a(a(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(a(a(x1)))) -> a#(a(b(a(a(a(x1)))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(a(b(x1)))) -> a#(b(b(a(a(b(x1)))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(b(b(x1)))) -> a#(b(b(b(a(b(b(x1))))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(b(a(a(x1)))) -> a#(b(b(a(a(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(b(a(b(x1)))) -> a#(b(b(b(a(b(x1)))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) a#(b(a(x1))) -> a#(b(b(a(x1)))) -> a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) -> a#(b(a(x1))) -> a#(b(b(a(x1)))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) -> a#(b(a(a(x1)))) -> a#(b(b(a(a(x1))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) -> a#(b(a(b(x1)))) -> a#(b(b(b(a(b(x1)))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) -> a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) a#(a(b(a(x1)))) -> 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a#(b(a(a(a(x1))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(a(a(a(x1)))) -> a#(a(b(a(a(a(x1)))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(a(a(b(x1)))) -> a#(b(b(a(a(b(x1)))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(a(b(b(x1)))) -> a#(b(b(b(a(b(b(x1))))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(b(a(a(x1)))) -> a#(b(b(a(a(x1))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(b(a(b(x1)))) -> a#(b(b(b(a(b(x1)))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) -> a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) 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a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(b(x1))) -> a#(b(b(a(b(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(b(a(x1))) -> a#(b(b(a(x1)))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(a(x1)))) -> a#(b(a(a(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(a(x1)))) -> a#(a(b(a(a(a(x1)))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(b(x1)))) -> a#(b(b(a(a(b(x1)))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(b(b(x1)))) -> a#(b(b(b(a(b(b(x1))))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(b(a(a(x1)))) -> a#(b(b(a(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(b(a(b(x1)))) -> a#(b(b(b(a(b(x1)))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) a#(a(a(x1))) -> a#(b(a(a(x1)))) -> a#(b(a(x1))) -> a#(b(b(a(x1)))) a#(a(a(x1))) -> a#(b(a(a(x1)))) -> a#(b(a(a(x1)))) -> a#(b(b(a(a(x1))))) a#(a(a(x1))) -> a#(b(a(a(x1)))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(x1))) -> a#(b(a(a(x1)))) -> a#(b(a(b(x1)))) -> a#(b(b(b(a(b(x1)))))) a#(a(a(x1))) -> a#(b(a(a(x1)))) -> a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(b(x1))) -> a#(b(b(a(b(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(b(a(x1))) -> a#(b(b(a(x1)))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(a(x1)))) -> a#(b(a(a(a(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(a(x1)))) -> a#(a(b(a(a(a(x1)))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(b(x1)))) -> a#(b(b(a(a(b(x1)))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(b(b(x1)))) -> a#(b(b(b(a(b(b(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(b(a(a(x1)))) -> a#(b(b(a(a(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(b(a(b(x1)))) -> a#(b(b(b(a(b(x1)))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) a#(a(x1)) -> a#(b(a(x1))) -> a#(b(a(x1))) -> a#(b(b(a(x1)))) a#(a(x1)) -> a#(b(a(x1))) -> a#(b(a(a(x1)))) -> a#(b(b(a(a(x1))))) a#(a(x1)) -> a#(b(a(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(x1)) -> a#(b(a(x1))) -> a#(b(a(b(x1)))) -> a#(b(b(b(a(b(x1)))))) a#(a(x1)) -> a#(b(a(x1))) -> a#(b(b(a(x1)))) -> a#(b(b(b(a(x1))))) SCC Processor: #sccs: 1 #rules: 10 #arcs: 114/289 DPs: a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(b(x1)))) -> a#(a(b(b(a(a(b(x1))))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(a(x1)))) -> a#(a(b(a(a(a(x1)))))) a#(a(a(a(x1)))) -> a#(b(a(a(a(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(x1)) -> a#(b(a(x1))) TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) Arctic Interpretation Processor: dimension: 1 interpretation: [a#](x0) = x0 + 1, [b](x0) = 0, [a](x0) = 1x0 + 0 orientation: a#(b(a(a(x1)))) = 1 >= 1 = a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) = 1 >= 1 = a#(b(a(b(a(b(a(x1))))))) a#(a(b(a(x1)))) = 1 >= 1 = a#(b(a(b(a(x1))))) a#(a(a(b(x1)))) = 2 >= 1 = a#(a(b(b(a(a(b(x1))))))) a#(a(a(a(x1)))) = 3x1 + 2 >= 2 = a#(a(a(b(a(a(a(x1))))))) a#(a(a(a(x1)))) = 3x1 + 2 >= 1 = a#(a(b(a(a(a(x1)))))) a#(a(a(a(x1)))) = 3x1 + 2 >= 1 = a#(b(a(a(a(x1))))) a#(a(a(x1))) = 2x1 + 1 >= 1 = a#(a(b(a(a(x1))))) a#(a(a(x1))) = 2x1 + 1 >= 1 = a#(b(a(a(x1)))) a#(a(x1)) = 1x1 + 1 >= 1 = a#(b(a(x1))) a(x1) = 1x1 + 0 >= 0 = b(x1) a(a(x1)) = 2x1 + 1 >= 1 = a(b(a(x1))) a(b(x1)) = 1 >= 0 = b(b(b(x1))) a(a(a(x1))) = 3x1 + 2 >= 2 = a(a(b(a(a(x1))))) a(a(b(x1))) = 2 >= 1 = a(b(b(a(b(x1))))) a(b(a(x1))) = 1 >= 0 = b(a(b(b(a(x1))))) a(b(b(x1))) = 1 >= 0 = b(b(b(b(b(x1))))) a(a(a(a(x1)))) = 4x1 + 3 >= 3 = a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) = 3 >= 2 = a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) = 2 >= 1 = a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) = 2 >= 1 = a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) = 1 >= 0 = b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) = 1 >= 0 = b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) = 1 >= 0 = b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) = 1 >= 0 = b(b(b(b(b(b(b(x1))))))) problem: DPs: a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(x1)) -> a#(b(a(x1))) TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) EDG Processor: DPs: a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(x1)) -> a#(b(a(x1))) TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) graph: a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(a(x1))) -> a#(b(a(a(x1)))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> a#(b(a(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) CDG Processor: DPs: a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(x1)) -> a#(b(a(x1))) TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) graph: a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(x1)) -> a#(b(a(x1))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(x1))) -> a#(b(a(a(x1)))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(x1))) -> a#(b(a(a(x1)))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(x1))) -> a#(a(b(a(a(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(a(b(a(x1)))) -> a#(b(a(b(a(b(a(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(x1)) -> a#(b(a(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) SCC Processor: #sccs: 2 #rules: 5 #arcs: 21/49 DPs: a#(a(a(a(x1)))) -> a#(a(a(b(a(a(a(x1))))))) a#(a(a(x1))) -> a#(a(b(a(a(x1))))) TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) KBO Processor: argument filtering: pi(a) = [0] pi(b) = [] pi(a#) = 0 weight function: w0 = 1 w(a#) = w(b) = w(a) = 1 precedence: a# ~ b ~ a problem: DPs: TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) Qed DPs: a#(b(a(a(x1)))) -> a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(x1)) -> a#(b(a(x1))) TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) Matrix Interpretation Processor: dim=3 interpretation: [a#](x0) = [1 1 0]x0, [0 0 0] [b](x0) = [1 0 0]x0 [0 0 0] , [0 0 1] [0] [a](x0) = [1 1 0]x0 + [0] [0 0 0] [1] orientation: a#(b(a(a(x1)))) = [1] >= [0] = a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) = [0 0 1]x1 >= [0] = a#(b(a(b(a(x1))))) a#(a(x1)) = [1 1 1]x1 >= [0 0 1]x1 = a#(b(a(x1))) [0 0 1] [0] [0 0 0] a(x1) = [1 1 0]x1 + [0] >= [1 0 0]x1 = b(x1) [0 0 0] [1] [0 0 0] [0 0 0] [1] [0 0 0] [0] a(a(x1)) = [1 1 1]x1 + [0] >= [0 0 1]x1 + [0] = a(b(a(x1))) [0 0 0] [1] [0 0 0] [1] [0 0 0] [0] [0] a(b(x1)) = [1 0 0]x1 + [0] >= [0] = b(b(b(x1))) [0 0 0] [1] [0] [0 0 0] [1] [1] a(a(a(x1))) = [1 1 1]x1 + [1] >= [1] = a(a(b(a(a(x1))))) [0 0 0] [1] [1] [0 0 0] [1] [0] a(a(b(x1))) = [1 0 0]x1 + [0] >= [0] = a(b(b(a(b(x1))))) [0 0 0] [1] [1] [0 0 0] [0] [0] a(b(a(x1))) = [0 0 1]x1 + [0] >= [0] = b(a(b(b(a(x1))))) [0 0 0] [1] [0] [0] [0] a(b(b(x1))) = [0] >= [0] = b(b(b(b(b(x1))))) [1] [0] [0 0 0] [1] [1] a(a(a(a(x1)))) = [1 1 1]x1 + [2] >= [2] = a(a(a(b(a(a(a(x1))))))) [0 0 0] [1] [1] [0 0 0] [1] [1] a(a(a(b(x1)))) = [1 0 0]x1 + [1] >= [0] = a(a(b(b(a(a(b(x1))))))) [0 0 0] [1] [1] [0 0 0] [1] [0] a(a(b(a(x1)))) = [0 0 1]x1 + [0] >= [0] = a(b(a(b(a(b(a(x1))))))) [0 0 0] [1] [1] [1] [0] a(a(b(b(x1)))) = [0] >= [0] = a(b(b(b(a(b(b(x1))))))) [1] [1] [0] [0] a(b(a(a(x1)))) = [1] >= [1] = b(a(a(b(b(a(a(x1))))))) [1] [0] [0] [0] a(b(a(b(x1)))) = [0] >= [0] = b(a(b(b(b(a(b(x1))))))) [1] [0] [0] [0] a(b(b(a(x1)))) = [0] >= [0] = b(b(a(b(b(b(a(x1))))))) [1] [0] [0] [0] a(b(b(b(x1)))) = [0] >= [0] = b(b(b(b(b(b(b(x1))))))) [1] [0] problem: DPs: a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(x1)) -> a#(b(a(x1))) TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) EDG Processor: DPs: a#(a(b(a(x1)))) -> a#(b(a(b(a(x1))))) a#(a(x1)) -> a#(b(a(x1))) TRS: a(x1) -> b(x1) a(a(x1)) -> a(b(a(x1))) a(b(x1)) -> b(b(b(x1))) a(a(a(x1))) -> a(a(b(a(a(x1))))) a(a(b(x1))) -> a(b(b(a(b(x1))))) a(b(a(x1))) -> b(a(b(b(a(x1))))) a(b(b(x1))) -> b(b(b(b(b(x1))))) a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1))))))) a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1))))))) a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1))))))) a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1))))))) a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1))))))) a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1))))))) a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1))))))) a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1))))))) graph: Qed