YES Problem: a(b(a(a(x1)))) -> c(b(a(b(a(x1))))) a(c(b(x1))) -> a(a(b(c(b(a(x1)))))) Proof: DP Processor: DPs: a#(b(a(a(x1)))) -> a#(b(a(x1))) a#(c(b(x1))) -> a#(x1) a#(c(b(x1))) -> a#(b(c(b(a(x1))))) a#(c(b(x1))) -> a#(a(b(c(b(a(x1)))))) TRS: a(b(a(a(x1)))) -> c(b(a(b(a(x1))))) a(c(b(x1))) -> a(a(b(c(b(a(x1)))))) Matrix Interpretation Processor: dim=4 interpretation: [a#](x0) = [0 0 0 1]x0, [0 0 0 0] [1] [0 0 0 0] [0] [c](x0) = [0 0 0 0]x0 + [0] [0 1 0 0] [1], [0 0 0 0] [0 0 0 1] [b](x0) = [0 0 1 0]x0 [0 1 0 0] , [0 0 0 0] [1] [1 0 1 0] [0] [a](x0) = [1 0 1 0]x0 + [0] [0 0 1 0] [0] orientation: a#(b(a(a(x1)))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 = a#(b(a(x1))) a#(c(b(x1))) = [0 0 0 1]x1 + [1] >= [0 0 0 1]x1 = a#(x1) a#(c(b(x1))) = [0 0 0 1]x1 + [1] >= [0] = a#(b(c(b(a(x1))))) a#(c(b(x1))) = [0 0 0 1]x1 + [1] >= [0] = a#(a(b(c(b(a(x1)))))) [0 0 0 0] [1] [0 0 0 0] [1] [1 0 1 0] [1] [0 0 0 0] [0] a(b(a(a(x1)))) = [1 0 1 0]x1 + [1] >= [0 0 0 0]x1 + [0] = c(b(a(b(a(x1))))) [1 0 1 0] [1] [1 0 1 0] [1] [1] [1] [1] [1] a(c(b(x1))) = [1] >= [1] = a(a(b(c(b(a(x1)))))) [0] [0] problem: DPs: TRS: a(b(a(a(x1)))) -> c(b(a(b(a(x1))))) a(c(b(x1))) -> a(a(b(c(b(a(x1)))))) Qed