YES Problem: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))) Proof: DP Processor: DPs: 0#(1(2(1(x1)))) -> 0#(1(2(x1))) 0#(1(2(1(x1)))) -> 0#(1(2(0(1(2(x1)))))) 0#(1(2(1(x1)))) -> 0#(1(2(0(1(2(0(1(2(x1))))))))) 0#(1(2(1(x1)))) -> 0#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))) 0#(1(2(1(x1)))) -> 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))) 0#(1(2(1(x1)))) -> 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))) 0#(1(2(1(x1)))) -> 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))) 0#(1(2(1(x1)))) -> 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))) 0#(1(2(1(x1)))) -> 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))) 0#(1(2(1(x1)))) -> 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))) 0#(1(2(1(x1)))) -> 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))) TRS: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))) Matrix Interpretation Processor: dim=4 interpretation: [0#](x0) = [1 0 0 1]x0, [1 0 0 1] [0 0 0 0] [0](x0) = [1 0 0 1]x0 [0 0 1 0] , [0 0 1 0] [1 0 0 0] [2](x0) = [0 0 0 0]x0 [0 1 0 0] , [1 0 0 0] [0] [0 0 1 0] [0] [1](x0) = [0 1 0 0]x0 + [1] [0 0 0 1] [0] orientation: 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(x1))) 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(0(1(2(x1)))))) 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(0(1(2(0(1(2(x1))))))))) 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))) 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))) 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))) 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))) 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))) 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))) 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))) 0#(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 = 0#(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))) [0 1 1 0] [1] [0 1 1 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 + [1] = 1(2(1(1(0(1(2(0(1(2(x1)))))))))) [1 0 0 0] [1] [0 0 0 0] [1] [0 1 1 0] [1] [0 1 1 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 + [1] = 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) [1 0 0 0] [1] [0 0 0 0] [1] [0 1 1 0] [1] [0 1 1 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 + [1] = 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))) [1 0 0 0] [1] [0 0 0 0] [1] [0 1 1 0] [1] [0 1 1 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 + [1] = 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))) [1 0 0 0] [1] [0 0 0 0] [1] [0 1 1 0] [1] [0 1 1 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 + [1] = 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))) [1 0 0 0] [1] [0 0 0 0] [1] [0 1 1 0] [1] [0 1 1 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 + [1] = 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))) [1 0 0 0] [1] [0 0 0 0] [1] [0 1 1 0] [1] [0 1 1 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 + [1] = 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))) [1 0 0 0] [1] [0 0 0 0] [1] [0 1 1 0] [1] [0 1 1 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 + [1] = 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))) [1 0 0 0] [1] [0 0 0 0] [1] [0 1 1 0] [1] [0 1 1 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 + [1] = 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))) [1 0 0 0] [1] [0 0 0 0] [1] [0 1 1 0] [1] [0 1 1 0] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(1(x1)))) = [0 1 1 0]x1 + [1] >= [0 1 1 0]x1 + [1] = 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0 ( 1(2(x1))))))))))))))))))))))))))))))))))))) [1 0 0 0] [1] [0 0 0 0] [1] problem: DPs: TRS: 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))) 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))) Qed