YES Problem: b(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) Proof: DP Processor: DPs: b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(x1))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(b(a(b(x1)))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(b(a(b(b(a(b(x1))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(a(b(b(a(b(b(a(b(x1))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(b(a(b(b(a(b(b(a(b(x1)))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) TRS: b(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) EDG Processor: DPs: b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(x1))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(b(a(b(x1)))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(b(a(b(b(a(b(x1))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(a(b(b(a(b(b(a(b(x1))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(b(a(b(b(a(b(b(a(b(x1)))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) TRS: b(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) graph: b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(x1))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(b(a(b(x1)))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(b(a(b(b(a(b(x1))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(a(b(b(a(b(b(a(b(x1))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(b(a(b(b(a(b(b(a(b(x1)))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(x1))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(b(a(b(x1)))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(b(a(b(b(a(b(x1))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(a(b(b(a(b(b(a(b(x1))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(b(a(b(b(a(b(b(a(b(x1)))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(x1))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(b(a(b(x1)))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(a(b(b(a(b(b(a(b(x1))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(a(b(b(a(b(b(a(b(x1))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(b(a(b(b(a(b(b(a(b(x1)))))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) -> b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) SCC Processor: #sccs: 1 #rules: 3 #arcs: 27/81 DPs: b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(b(a(b(x1)))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(b(a(b(x1))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b#(b(a(b(x1)))) TRS: b(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) Matrix Interpretation Processor: dim=3 interpretation: [b#](x0) = [1 0 0]x0, [0 0 1] [a](x0) = [1 0 0]x0 [1 0 0] , [0 1 0] [0] [b](x0) = [0 0 1]x0 + [0] [1 0 0] [1] orientation: b#(b(a(b(b(a(b(b(b(b(x1)))))))))) = [0 1 0]x1 + [1] >= [0 1 0]x1 = b#(b(a(b(b(a(b(b(a(b(x1)))))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) = [0 1 0]x1 + [1] >= [0 1 0]x1 = b#(b(a(b(b(a(b(x1))))))) b#(b(a(b(b(a(b(b(b(b(x1)))))))))) = [0 1 0]x1 + [1] >= [0 1 0]x1 = b#(b(a(b(x1)))) [0 1 0] [1] [0 1 0] [1] b(b(a(b(b(a(b(b(b(b(x1)))))))))) = [0 1 0]x1 + [3] >= [0 1 0]x1 + [3] = b(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) [0 1 0] [2] [0 1 0] [2] problem: DPs: TRS: b(b(a(b(b(a(b(b(b(b(x1)))))))))) -> b(b(b(b(b(a(b(b(a(b(b(a(b(x1))))))))))))) Qed