YES Problem: 0(1(2(3(4(5(1(x1))))))) -> 0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))) 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))))))))) Proof: DP Processor: DPs: 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) TRS: 0(1(2(3(4(5(1(x1))))))) -> 0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))) 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))))))))) EDG Processor: DPs: 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) TRS: 0(1(2(3(4(5(1(x1))))))) -> 0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))) 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))))))))) graph: 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) -> 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) SCC Processor: #sccs: 1 #rules: 4 #arcs: 20/25 DPs: 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) 0#(1(2(3(4(5(1(x1))))))) -> 0#(1(2(3(4(5(x1)))))) TRS: 0(1(2(3(4(5(1(x1))))))) -> 0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))) 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))))))))) Matrix Interpretation Processor: dim=4 interpretation: [0#](x0) = [1 0 1 0]x0, [1 0 0 1] [0 0 0 0] [0](x0) = [0 0 1 0]x0 [0 0 1 0] , [1 0 0 0] [0 0 0 0] [2](x0) = [0 1 0 0]x0 [0 0 0 0] , [0 0 1 0] [0] [0 0 0 1] [0] [3](x0) = [0 0 0 0]x0 + [0] [0 0 0 0] [1], [0 0 0 0] [0] [0 0 0 0] [1] [4](x0) = [0 0 0 1]x0 + [0] [0 0 1 0] [0], [0 0 0 0] [0 0 1 0] [5](x0) = [0 0 0 1]x0 [0 1 0 0] , [1 0 0 0] [0] [0 1 0 1] [0] [1](x0) = [0 0 1 0]x0 + [0] [0 0 0 0] [1] orientation: 0#(1(2(3(4(5(1(x1))))))) = [0 1 0 1]x1 + [1] >= [0 0 0 1]x1 = 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) = [0 1 0 1]x1 + [1] >= [0 0 0 1]x1 = 0#(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))) 0#(1(2(3(4(5(1(x1))))))) = [0 1 0 1]x1 + [1] >= [0 0 0 1]x1 = 0#(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))) 0#(1(2(3(4(5(1(x1))))))) = [0 1 0 1]x1 + [1] >= [0 1 0 1]x1 = 0#(1(2(3(4(5(x1)))))) [0 1 0 1] [1] [0 0 0 1] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(3(4(5(1(x1))))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) [0 0 0 0] [1] [0 0 0 0] [1] [0 1 0 1] [1] [0 0 0 1] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(3(4(5(1(x1))))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))) [0 0 0 0] [1] [0 0 0 0] [1] [0 1 0 1] [1] [0 0 0 1] [1] [0 0 0 0] [0] [0 0 0 0] [0] 0(1(2(3(4(5(1(x1))))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))))))))) [0 0 0 0] [1] [0 0 0 0] [1] problem: DPs: TRS: 0(1(2(3(4(5(1(x1))))))) -> 0(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))) 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))) 0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1))))))))))))))))))))))))))))))) Qed