YES Problem: a(a(a(a(x1)))) -> a(a(b(b(b(b(b(b(x1)))))))) b(b(a(a(x1)))) -> b(b(b(b(c(c(x1)))))) a(a(b(b(b(b(c(c(x1)))))))) -> a(a(a(a(a(a(b(b(x1)))))))) Proof: String Reversal Processor: a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1)))))))) a(a(b(b(x1)))) -> c(c(b(b(b(b(x1)))))) c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1)))))))) DP Processor: DPs: a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1)))))))) a(a(b(b(x1)))) -> c(c(b(b(b(b(x1)))))) c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1)))))))) TDG Processor: DPs: a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1)))))))) a(a(b(b(x1)))) -> c(c(b(b(b(b(x1)))))) c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1)))))))) graph: c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) -> a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) -> a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) -> a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) -> a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) -> a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) -> a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) -> a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) -> a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) EDG Processor: DPs: a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1)))))))) a(a(b(b(x1)))) -> c(c(b(b(b(b(x1)))))) c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1)))))))) graph: c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) -> a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) -> a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) -> a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) -> a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) -> a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) -> a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) -> a#(a(b(b(x1)))) -> c#(b(b(b(b(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) -> a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) -> c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) SCC Processor: #sccs: 1 #rules: 5 #arcs: 12/36 DPs: c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(a(x1)))))) a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(a(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(a(x1)))) c#(c(b(b(b(b(a(a(x1)))))))) -> a#(a(a(x1))) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1)))))))) a(a(b(b(x1)))) -> c(c(b(b(b(b(x1)))))) c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1)))))))) Matrix Interpretation Processor: dim=4 interpretation: [c#](x0) = [0 1 0 0]x0, [a#](x0) = [1 0 0 0]x0, [0 0 0 1] [0 1 0 0] [c](x0) = [0 0 0 1]x0 [0 1 0 0] , [0 0 0 0] [0 0 1 0] [b](x0) = [0 0 0 1]x0 [0 1 0 0] , [0 0 0 1] [0] [0 0 0 1] [0] [a](x0) = [0 0 0 1]x0 + [1] [0 0 0 1] [0] orientation: c#(c(b(b(b(b(a(a(x1)))))))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = a#(a(a(a(a(a(x1)))))) a#(a(b(b(x1)))) = [0 0 1 0]x1 >= [0 0 1 0]x1 = c#(c(b(b(b(b(x1)))))) c#(c(b(b(b(b(a(a(x1)))))))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = a#(a(a(a(a(x1))))) c#(c(b(b(b(b(a(a(x1)))))))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = a#(a(a(a(x1)))) c#(c(b(b(b(b(a(a(x1)))))))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = a#(a(a(x1))) [0 0 0 1] [0] [0 0 0 0] [0] [0 0 0 1] [0] [0 0 0 1] [0] a(a(a(a(x1)))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [1] = b(b(b(b(b(b(a(a(x1)))))))) [0 0 0 1] [0] [0 0 0 1] [0] [0 0 1 0] [0] [0 0 1 0] [0 0 1 0] [0] [0 0 1 0] a(a(b(b(x1)))) = [0 0 1 0]x1 + [1] >= [0 0 1 0]x1 = c(c(b(b(b(b(x1)))))) [0 0 1 0] [0] [0 0 1 0] [0 0 0 1] [1] [0 0 0 0] [0] [0 0 0 1] [1] [0 0 0 1] [0] c(c(b(b(b(b(a(a(x1)))))))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 + [0] = b(b(a(a(a(a(a(a(x1)))))))) [0 0 0 1] [1] [0 0 0 1] [1] problem: DPs: a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1)))))))) a(a(b(b(x1)))) -> c(c(b(b(b(b(x1)))))) c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1)))))))) EDG Processor: DPs: a#(a(b(b(x1)))) -> c#(c(b(b(b(b(x1)))))) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(a(a(x1)))))))) a(a(b(b(x1)))) -> c(c(b(b(b(b(x1)))))) c(c(b(b(b(b(a(a(x1)))))))) -> b(b(a(a(a(a(a(a(x1)))))))) graph: Qed