YES Problem: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) Proof: DP Processor: DPs: b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) EDG Processor: DPs: b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) graph: b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) CDG Processor: DPs: b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) graph: b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(a(a(b(b(b(a(b(x1))))))))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(a(b(b(b(a(b(x1)))))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) SCC Processor: #sccs: 1 #rules: 7 #arcs: 30/81 DPs: b#(a(b(a(a(b(b(x1))))))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) -> b#(b(b(a(b(x1))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) Matrix Interpretation Processor: dim=4 interpretation: [b#](x0) = [1 0 1 1]x0, [0 0 0 0] [0] [0 0 0 0] [1] [a](x0) = [1 0 0 0]x0 + [0] [0 1 1 0] [0], [1 0 1 0] [0 0 0 0] [b](x0) = [0 0 0 1]x0 [0 0 0 0] orientation: b#(a(b(a(a(b(b(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 1 1]x1 = b#(a(b(x1))) b#(a(b(b(x1)))) = [1 0 1 1]x1 >= [1 0 1 1]x1 = b#(a(b(x1))) b#(a(b(b(x1)))) = [1 0 1 1]x1 >= [1 0 1 1]x1 = b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) = [1 0 1 1]x1 >= [1 0 1 1]x1 = b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) = [1 0 1 1]x1 >= [1 0 1 1]x1 = b#(a(b(b(a(b(x1)))))) b#(a(b(a(a(b(b(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 1 1]x1 = b#(b(a(b(x1)))) b#(a(b(a(a(b(b(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 1 1]x1 = b#(b(b(a(b(x1))))) [1 0 1 1] [1 0 1 1] [0 0 0 0] [0 0 0 0] b(b(b(a(b(x1))))) = [0 0 0 0]x1 >= [0 0 0 0]x1 = b(a(b(b(a(b(x1)))))) [0 0 0 0] [0 0 0 0] [1 0 1 1] [1 0 1 1] [0 0 0 0] [0 0 0 0] b(a(b(b(x1)))) = [0 0 0 0]x1 >= [0 0 0 0]x1 = b(b(a(b(a(b(x1)))))) [0 0 0 0] [0 0 0 0] [0 0 0 0] [0] [0] [0 0 0 0] [0] [0] b(a(b(a(a(b(b(x1))))))) = [1 0 1 1]x1 + [1] >= [1] = b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) [0 0 0 0] [0] [0] problem: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) EDG Processor: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) graph: b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) -> b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(b(b(a(b(x1))))) -> b#(a(b(b(a(b(x1)))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) Matrix Interpretation Processor: dim=4 interpretation: [b#](x0) = [1 1 0 0]x0, [0 1 0 0] [0 0 0 0] [a](x0) = [0 0 0 0]x0 [0 0 1 0] , [0 0 0 1] [0] [1 1 0 0] [0] [b](x0) = [0 0 0 1]x0 + [0] [0 0 0 0] [1] orientation: b#(a(b(b(x1)))) = [1 1 0 1]x1 >= [1 1 0 0]x1 = b#(a(b(x1))) b#(a(b(b(x1)))) = [1 1 0 1]x1 >= [1 1 0 0]x1 = b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) = [1 1 0 1]x1 >= [1 1 0 1]x1 = b#(b(a(b(a(b(x1)))))) b#(b(b(a(b(x1))))) = [1 1 0 1]x1 + [1] >= [1 1 0 1]x1 = b#(a(b(b(a(b(x1)))))) [0 0 0 0] [1] [0 0 0 0] [1] [1 1 0 1] [1] [1 1 0 1] [0] b(b(b(a(b(x1))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(a(b(b(a(b(x1)))))) [0 0 0 0] [1] [0 0 0 0] [1] [0 0 0 0] [1] [0 0 0 0] [1] [1 1 0 1] [0] [1 1 0 1] [0] b(a(b(b(x1)))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = b(b(a(b(a(b(x1)))))) [0 0 0 0] [1] [0 0 0 0] [1] [0] [0] [0] [0] b(a(b(a(a(b(b(x1))))))) = [0] >= [0] = b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) [1] [1] problem: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) EDG Processor: DPs: b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) graph: b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(b(a(b(x1)))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) -> b#(a(b(b(x1)))) -> b#(a(b(x1))) SCC Processor: #sccs: 1 #rules: 2 #arcs: 6/9 DPs: b#(a(b(b(x1)))) -> b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) -> b#(a(b(x1))) TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) Arctic Interpretation Processor: dimension: 1 interpretation: [b#](x0) = 9x0 + 0, [a](x0) = -3x0 + 0, [b](x0) = 3x0 + 10 orientation: b#(a(b(b(x1)))) = 12x1 + 19 >= 9x1 + 16 = b#(a(b(a(b(x1))))) b#(a(b(b(x1)))) = 12x1 + 19 >= 9x1 + 16 = b#(a(b(x1))) b(b(b(a(b(x1))))) = 9x1 + 16 >= 6x1 + 13 = b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) = 6x1 + 13 >= 6x1 + 13 = b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) = 3x1 + 10 >= 3x1 + 10 = b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) problem: DPs: TRS: b(b(b(a(b(x1))))) -> b(a(b(b(a(b(x1)))))) b(a(b(b(x1)))) -> b(b(a(b(a(b(x1)))))) b(a(b(a(a(b(b(x1))))))) -> b(a(a(b(a(a(b(b(b(a(b(x1))))))))))) Qed