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))))))) Matrix Interpretation Processor: dim=3 interpretation: [a#](x0) = [3 1 2]x0, [0 0 0] [b](x0) = [0 0 0]x0 [1 0 0] , [0 1 0] [0] [a](x0) = [1 0 0]x0 + [1] [1 0 1] [0] orientation: a#(b(a(a(x1)))) = [2 0 0]x1 + [2] >= [1] = a#(a(b(b(a(a(x1)))))) a#(a(b(a(x1)))) = [0 2 0]x1 + [1] >= [0] = a#(b(a(b(a(b(a(x1))))))) a#(a(b(a(x1)))) = [0 2 0]x1 + [1] >= [0] = a#(b(a(b(a(x1))))) a#(a(a(b(x1)))) = [2 0 0]x1 + [4] >= [1] = a#(a(b(b(a(a(b(x1))))))) a#(a(a(a(x1)))) = [5 5 2]x1 + [7] >= [0 2 0]x1 + [6] = a#(a(a(b(a(a(a(x1))))))) a#(a(a(a(x1)))) = [5 5 2]x1 + [7] >= [0 2 0]x1 + [3] = a#(a(b(a(a(a(x1)))))) a#(a(a(a(x1)))) = [5 5 2]x1 + [7] >= [0 2 0]x1 + [2] = a#(b(a(a(a(x1))))) a#(a(a(x1))) = [5 3 2]x1 + [4] >= [2 0 0]x1 + [3] = a#(a(b(a(a(x1))))) a#(a(a(x1))) = [5 3 2]x1 + [4] >= [2 0 0]x1 + [2] = a#(b(a(a(x1)))) a#(a(x1)) = [3 3 2]x1 + [1] >= [0 2 0]x1 = a#(b(a(x1))) [0 1 0] [0] [0 0 0] a(x1) = [1 0 0]x1 + [1] >= [0 0 0]x1 = b(x1) [1 0 1] [0] [1 0 0] [1 0 0] [1] [0 0 0] [0] a(a(x1)) = [0 1 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b(a(x1))) [1 1 1] [0] [0 1 0] [0] [0 0 0] [0] [0] a(b(x1)) = [0 0 0]x1 + [1] >= [0] = b(b(b(x1))) [1 0 0] [0] [0] [0 1 0] [1] [0 0 0] [1] a(a(a(x1))) = [1 0 0]x1 + [2] >= [0 0 0]x1 + [1] = a(a(b(a(a(x1))))) [2 1 1] [1] [1 0 0] [1] [0 0 0] [1] [0] a(a(b(x1))) = [0 0 0]x1 + [1] >= [1] = a(b(b(a(b(x1))))) [1 0 0] [0] [0] [0 0 0] [0] [0] a(b(a(x1))) = [0 0 0]x1 + [1] >= [0] = b(a(b(b(a(x1))))) [0 1 0] [0] [0] [0] [0] a(b(b(x1))) = [1] >= [0] = b(b(b(b(b(x1))))) [0] [0] [1 0 0] [2] [0 0 0] [1] a(a(a(a(x1)))) = [0 1 0]x1 + [2] >= [0 0 0]x1 + [2] = a(a(a(b(a(a(a(x1))))))) [2 2 1] [2] [0 1 0] [2] [0 0 0] [1] [1] a(a(a(b(x1)))) = [0 0 0]x1 + [2] >= [1] = a(a(b(b(a(a(b(x1))))))) [1 0 0] [1] [0] [0 0 0] [1] [0] a(a(b(a(x1)))) = [0 0 0]x1 + [1] >= [1] = a(b(a(b(a(b(a(x1))))))) [0 1 0] [0] [0] [1] [0] a(a(b(b(x1)))) = [1] >= [1] = a(b(b(b(a(b(b(x1))))))) [0] [0] [0 0 0] [0] [0] a(b(a(a(x1)))) = [0 0 0]x1 + [1] >= [0] = b(a(a(b(b(a(a(x1))))))) [1 0 0] [1] [1] [0] [0] a(b(a(b(x1)))) = [1] >= [0] = b(a(b(b(b(a(b(x1))))))) [0] [0] [0] [0] a(b(b(a(x1)))) = [1] >= [0] = b(b(a(b(b(b(a(x1))))))) [0] [0] [0] [0] a(b(b(b(x1)))) = [1] >= [0] = b(b(b(b(b(b(b(x1))))))) [0] [0] 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