YES Problem: 4(2(4(x1))) -> 2(0(0(5(3(3(5(2(0(4(x1)))))))))) 4(4(2(4(2(x1))))) -> 2(0(5(2(1(4(0(2(0(1(x1)))))))))) 0(5(4(2(4(3(x1)))))) -> 5(1(5(5(3(5(3(0(0(0(x1)))))))))) 1(1(4(5(3(3(x1)))))) -> 1(3(1(1(3(0(1(2(2(1(x1)))))))))) 3(1(4(3(1(2(x1)))))) -> 0(0(1(1(4(2(3(0(0(3(x1)))))))))) 3(2(4(2(4(1(x1)))))) -> 0(2(1(1(1(5(3(1(3(3(x1)))))))))) 3(3(0(4(1(2(x1)))))) -> 3(5(1(2(0(2(0(5(3(1(x1)))))))))) 4(1(4(5(0(5(4(x1))))))) -> 4(1(5(3(1(0(5(3(1(0(x1)))))))))) 4(4(0(5(4(2(2(x1))))))) -> 4(0(4(3(4(4(4(5(4(1(x1)))))))))) 5(4(5(3(2(4(3(x1))))))) -> 2(5(5(5(0(4(5(0(1(4(x1)))))))))) Proof: DP Processor: DPs: 4#(2(4(x1))) -> 0#(4(x1)) 4#(2(4(x1))) -> 5#(2(0(4(x1)))) 4#(2(4(x1))) -> 3#(5(2(0(4(x1))))) 4#(2(4(x1))) -> 3#(3(5(2(0(4(x1)))))) 4#(2(4(x1))) -> 5#(3(3(5(2(0(4(x1))))))) 4#(2(4(x1))) -> 0#(5(3(3(5(2(0(4(x1)))))))) 4#(2(4(x1))) -> 0#(0(5(3(3(5(2(0(4(x1))))))))) 4#(4(2(4(2(x1))))) -> 1#(x1) 4#(4(2(4(2(x1))))) -> 0#(1(x1)) 4#(4(2(4(2(x1))))) -> 0#(2(0(1(x1)))) 4#(4(2(4(2(x1))))) -> 4#(0(2(0(1(x1))))) 4#(4(2(4(2(x1))))) -> 1#(4(0(2(0(1(x1)))))) 4#(4(2(4(2(x1))))) -> 5#(2(1(4(0(2(0(1(x1)))))))) 4#(4(2(4(2(x1))))) -> 0#(5(2(1(4(0(2(0(1(x1))))))))) 0#(5(4(2(4(3(x1)))))) -> 0#(x1) 0#(5(4(2(4(3(x1)))))) -> 0#(0(x1)) 0#(5(4(2(4(3(x1)))))) -> 0#(0(0(x1))) 0#(5(4(2(4(3(x1)))))) -> 3#(0(0(0(x1)))) 0#(5(4(2(4(3(x1)))))) -> 5#(3(0(0(0(x1))))) 0#(5(4(2(4(3(x1)))))) -> 3#(5(3(0(0(0(x1)))))) 0#(5(4(2(4(3(x1)))))) -> 5#(3(5(3(0(0(0(x1))))))) 0#(5(4(2(4(3(x1)))))) -> 5#(5(3(5(3(0(0(0(x1)))))))) 0#(5(4(2(4(3(x1)))))) -> 1#(5(5(3(5(3(0(0(0(x1))))))))) 0#(5(4(2(4(3(x1)))))) -> 5#(1(5(5(3(5(3(0(0(0(x1)))))))))) 1#(1(4(5(3(3(x1)))))) -> 1#(x1) 1#(1(4(5(3(3(x1)))))) -> 1#(2(2(1(x1)))) 1#(1(4(5(3(3(x1)))))) -> 0#(1(2(2(1(x1))))) 1#(1(4(5(3(3(x1)))))) -> 3#(0(1(2(2(1(x1)))))) 1#(1(4(5(3(3(x1)))))) -> 1#(3(0(1(2(2(1(x1))))))) 1#(1(4(5(3(3(x1)))))) -> 1#(1(3(0(1(2(2(1(x1)))))))) 1#(1(4(5(3(3(x1)))))) -> 3#(1(1(3(0(1(2(2(1(x1))))))))) 1#(1(4(5(3(3(x1)))))) -> 1#(3(1(1(3(0(1(2(2(1(x1)))))))))) 3#(1(4(3(1(2(x1)))))) -> 3#(x1) 3#(1(4(3(1(2(x1)))))) -> 0#(3(x1)) 3#(1(4(3(1(2(x1)))))) -> 0#(0(3(x1))) 3#(1(4(3(1(2(x1)))))) -> 3#(0(0(3(x1)))) 3#(1(4(3(1(2(x1)))))) -> 4#(2(3(0(0(3(x1)))))) 3#(1(4(3(1(2(x1)))))) -> 1#(4(2(3(0(0(3(x1))))))) 3#(1(4(3(1(2(x1)))))) -> 1#(1(4(2(3(0(0(3(x1)))))))) 3#(1(4(3(1(2(x1)))))) -> 0#(1(1(4(2(3(0(0(3(x1))))))))) 3#(1(4(3(1(2(x1)))))) -> 0#(0(1(1(4(2(3(0(0(3(x1)))))))))) 3#(2(4(2(4(1(x1)))))) -> 3#(x1) 3#(2(4(2(4(1(x1)))))) -> 3#(3(x1)) 3#(2(4(2(4(1(x1)))))) -> 1#(3(3(x1))) 3#(2(4(2(4(1(x1)))))) -> 3#(1(3(3(x1)))) 3#(2(4(2(4(1(x1)))))) -> 5#(3(1(3(3(x1))))) 3#(2(4(2(4(1(x1)))))) -> 1#(5(3(1(3(3(x1)))))) 3#(2(4(2(4(1(x1)))))) -> 1#(1(5(3(1(3(3(x1))))))) 3#(2(4(2(4(1(x1)))))) -> 1#(1(1(5(3(1(3(3(x1)))))))) 3#(2(4(2(4(1(x1)))))) -> 0#(2(1(1(1(5(3(1(3(3(x1)))))))))) 3#(3(0(4(1(2(x1)))))) -> 1#(x1) 3#(3(0(4(1(2(x1)))))) -> 3#(1(x1)) 3#(3(0(4(1(2(x1)))))) -> 5#(3(1(x1))) 3#(3(0(4(1(2(x1)))))) -> 0#(5(3(1(x1)))) 3#(3(0(4(1(2(x1)))))) -> 0#(2(0(5(3(1(x1)))))) 3#(3(0(4(1(2(x1)))))) -> 1#(2(0(2(0(5(3(1(x1)))))))) 3#(3(0(4(1(2(x1)))))) -> 5#(1(2(0(2(0(5(3(1(x1))))))))) 3#(3(0(4(1(2(x1)))))) -> 3#(5(1(2(0(2(0(5(3(1(x1)))))))))) 4#(1(4(5(0(5(4(x1))))))) -> 0#(x1) 4#(1(4(5(0(5(4(x1))))))) -> 1#(0(x1)) 4#(1(4(5(0(5(4(x1))))))) -> 3#(1(0(x1))) 4#(1(4(5(0(5(4(x1))))))) -> 5#(3(1(0(x1)))) 4#(1(4(5(0(5(4(x1))))))) -> 0#(5(3(1(0(x1))))) 4#(1(4(5(0(5(4(x1))))))) -> 1#(0(5(3(1(0(x1)))))) 4#(1(4(5(0(5(4(x1))))))) -> 3#(1(0(5(3(1(0(x1))))))) 4#(1(4(5(0(5(4(x1))))))) -> 5#(3(1(0(5(3(1(0(x1)))))))) 4#(1(4(5(0(5(4(x1))))))) -> 1#(5(3(1(0(5(3(1(0(x1))))))))) 4#(1(4(5(0(5(4(x1))))))) -> 4#(1(5(3(1(0(5(3(1(0(x1)))))))))) 4#(4(0(5(4(2(2(x1))))))) -> 1#(x1) 4#(4(0(5(4(2(2(x1))))))) -> 4#(1(x1)) 4#(4(0(5(4(2(2(x1))))))) -> 5#(4(1(x1))) 4#(4(0(5(4(2(2(x1))))))) -> 4#(5(4(1(x1)))) 4#(4(0(5(4(2(2(x1))))))) -> 4#(4(5(4(1(x1))))) 4#(4(0(5(4(2(2(x1))))))) -> 4#(4(4(5(4(1(x1)))))) 4#(4(0(5(4(2(2(x1))))))) -> 3#(4(4(4(5(4(1(x1))))))) 4#(4(0(5(4(2(2(x1))))))) -> 4#(3(4(4(4(5(4(1(x1)))))))) 4#(4(0(5(4(2(2(x1))))))) -> 0#(4(3(4(4(4(5(4(1(x1))))))))) 4#(4(0(5(4(2(2(x1))))))) -> 4#(0(4(3(4(4(4(5(4(1(x1)))))))))) 5#(4(5(3(2(4(3(x1))))))) -> 4#(x1) 5#(4(5(3(2(4(3(x1))))))) -> 1#(4(x1)) 5#(4(5(3(2(4(3(x1))))))) -> 0#(1(4(x1))) 5#(4(5(3(2(4(3(x1))))))) -> 5#(0(1(4(x1)))) 5#(4(5(3(2(4(3(x1))))))) -> 4#(5(0(1(4(x1))))) 5#(4(5(3(2(4(3(x1))))))) -> 0#(4(5(0(1(4(x1)))))) 5#(4(5(3(2(4(3(x1))))))) -> 5#(0(4(5(0(1(4(x1))))))) 5#(4(5(3(2(4(3(x1))))))) -> 5#(5(0(4(5(0(1(4(x1)))))))) 5#(4(5(3(2(4(3(x1))))))) -> 5#(5(5(0(4(5(0(1(4(x1))))))))) TRS: 4(2(4(x1))) -> 2(0(0(5(3(3(5(2(0(4(x1)))))))))) 4(4(2(4(2(x1))))) -> 2(0(5(2(1(4(0(2(0(1(x1)))))))))) 0(5(4(2(4(3(x1)))))) -> 5(1(5(5(3(5(3(0(0(0(x1)))))))))) 1(1(4(5(3(3(x1)))))) -> 1(3(1(1(3(0(1(2(2(1(x1)))))))))) 3(1(4(3(1(2(x1)))))) -> 0(0(1(1(4(2(3(0(0(3(x1)))))))))) 3(2(4(2(4(1(x1)))))) -> 0(2(1(1(1(5(3(1(3(3(x1)))))))))) 3(3(0(4(1(2(x1)))))) -> 3(5(1(2(0(2(0(5(3(1(x1)))))))))) 4(1(4(5(0(5(4(x1))))))) -> 4(1(5(3(1(0(5(3(1(0(x1)))))))))) 4(4(0(5(4(2(2(x1))))))) -> 4(0(4(3(4(4(4(5(4(1(x1)))))))))) 5(4(5(3(2(4(3(x1))))))) -> 2(5(5(5(0(4(5(0(1(4(x1)))))))))) Matrix Interpretation Processor: dim=4 interpretation: [1#](x0) = [1 0 0 0]x0, [3#](x0) = [1 0 0 0]x0, [5#](x0) = [1 0 0 0]x0, [0#](x0) = [1 0 0 0]x0, [4#](x0) = [1 0 1 0]x0, [1 0 0 0] [0 0 0 0] [1](x0) = [0 0 0 1]x0 [0 0 0 0] , [1 0 0 0] [0] [0 0 0 0] [1] [3](x0) = [0 1 1 0]x0 + [0] [0 0 0 1] [0], [5](x0) = x0 , [1 0 0 0] [0 0 0 0] [0](x0) = [0 0 0 0]x0 [0 0 0 0] , [1 0 0 0] [0] [0 0 0 0] [0] [2](x0) = [0 0 1 1]x0 + [0] [0 0 0 0] [1], [1 0 1 0] [0] [0 0 1 0] [0] [4](x0) = [0 0 0 0]x0 + [0] [0 0 0 0] [1] orientation: 4#(2(4(x1))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 = 0#(4(x1)) 4#(2(4(x1))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 = 5#(2(0(4(x1)))) 4#(2(4(x1))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 = 3#(5(2(0(4(x1))))) 4#(2(4(x1))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 = 3#(3(5(2(0(4(x1)))))) 4#(2(4(x1))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 = 5#(3(3(5(2(0(4(x1))))))) 4#(2(4(x1))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 = 0#(5(3(3(5(2(0(4(x1)))))))) 4#(2(4(x1))) = [1 0 1 0]x1 + [1] >= [1 0 1 0]x1 = 0#(0(5(3(3(5(2(0(4(x1))))))))) 4#(4(2(4(2(x1))))) = [1 0 1 1]x1 + [1] >= [1 0 0 0]x1 = 1#(x1) 4#(4(2(4(2(x1))))) = [1 0 1 1]x1 + [1] >= [1 0 0 0]x1 = 0#(1(x1)) 4#(4(2(4(2(x1))))) = [1 0 1 1]x1 + [1] >= [1 0 0 0]x1 = 0#(2(0(1(x1)))) 4#(4(2(4(2(x1))))) = [1 0 1 1]x1 + [1] >= [1 0 0 0]x1 = 4#(0(2(0(1(x1))))) 4#(4(2(4(2(x1))))) = [1 0 1 1]x1 + [1] >= [1 0 0 0]x1 = 1#(4(0(2(0(1(x1)))))) 4#(4(2(4(2(x1))))) = [1 0 1 1]x1 + [1] >= [1 0 0 0]x1 = 5#(2(1(4(0(2(0(1(x1)))))))) 4#(4(2(4(2(x1))))) = [1 0 1 1]x1 + [1] >= [1 0 0 0]x1 = 0#(5(2(1(4(0(2(0(1(x1))))))))) 0#(5(4(2(4(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 0#(x1) 0#(5(4(2(4(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 0#(0(x1)) 0#(5(4(2(4(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 0#(0(0(x1))) 0#(5(4(2(4(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 3#(0(0(0(x1)))) 0#(5(4(2(4(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 5#(3(0(0(0(x1))))) 0#(5(4(2(4(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 3#(5(3(0(0(0(x1)))))) 0#(5(4(2(4(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 5#(3(5(3(0(0(0(x1))))))) 0#(5(4(2(4(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 5#(5(3(5(3(0(0(0(x1)))))))) 0#(5(4(2(4(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 1#(5(5(3(5(3(0(0(0(x1))))))))) 0#(5(4(2(4(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 5#(1(5(5(3(5(3(0(0(0(x1)))))))))) 1#(1(4(5(3(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 1#(x1) 1#(1(4(5(3(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 1#(2(2(1(x1)))) 1#(1(4(5(3(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 0#(1(2(2(1(x1))))) 1#(1(4(5(3(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 3#(0(1(2(2(1(x1)))))) 1#(1(4(5(3(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 1#(3(0(1(2(2(1(x1))))))) 1#(1(4(5(3(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 1#(1(3(0(1(2(2(1(x1)))))))) 1#(1(4(5(3(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 3#(1(1(3(0(1(2(2(1(x1))))))))) 1#(1(4(5(3(3(x1)))))) = [1 1 1 0]x1 + [1] >= [1 0 0 0]x1 = 1#(3(1(1(3(0(1(2(2(1(x1)))))))))) 3#(1(4(3(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 3#(x1) 3#(1(4(3(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 0#(3(x1)) 3#(1(4(3(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 0#(0(3(x1))) 3#(1(4(3(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 3#(0(0(3(x1)))) 3#(1(4(3(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 4#(2(3(0(0(3(x1)))))) 3#(1(4(3(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 1#(4(2(3(0(0(3(x1))))))) 3#(1(4(3(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 1#(1(4(2(3(0(0(3(x1)))))))) 3#(1(4(3(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 0#(1(1(4(2(3(0(0(3(x1))))))))) 3#(1(4(3(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 0#(0(1(1(4(2(3(0(0(3(x1)))))))))) 3#(2(4(2(4(1(x1)))))) = [1 0 0 1]x1 + [1] >= [1 0 0 0]x1 = 3#(x1) 3#(2(4(2(4(1(x1)))))) = [1 0 0 1]x1 + [1] >= [1 0 0 0]x1 = 3#(3(x1)) 3#(2(4(2(4(1(x1)))))) = [1 0 0 1]x1 + [1] >= [1 0 0 0]x1 = 1#(3(3(x1))) 3#(2(4(2(4(1(x1)))))) = [1 0 0 1]x1 + [1] >= [1 0 0 0]x1 = 3#(1(3(3(x1)))) 3#(2(4(2(4(1(x1)))))) = [1 0 0 1]x1 + [1] >= [1 0 0 0]x1 = 5#(3(1(3(3(x1))))) 3#(2(4(2(4(1(x1)))))) = [1 0 0 1]x1 + [1] >= [1 0 0 0]x1 = 1#(5(3(1(3(3(x1)))))) 3#(2(4(2(4(1(x1)))))) = [1 0 0 1]x1 + [1] >= [1 0 0 0]x1 = 1#(1(5(3(1(3(3(x1))))))) 3#(2(4(2(4(1(x1)))))) = [1 0 0 1]x1 + [1] >= [1 0 0 0]x1 = 1#(1(1(5(3(1(3(3(x1)))))))) 3#(2(4(2(4(1(x1)))))) = [1 0 0 1]x1 + [1] >= [1 0 0 0]x1 = 0#(2(1(1(1(5(3(1(3(3(x1)))))))))) 3#(3(0(4(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 1#(x1) 3#(3(0(4(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 3#(1(x1)) 3#(3(0(4(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 5#(3(1(x1))) 3#(3(0(4(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 0#(5(3(1(x1)))) 3#(3(0(4(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 0#(2(0(5(3(1(x1)))))) 3#(3(0(4(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 1#(2(0(2(0(5(3(1(x1)))))))) 3#(3(0(4(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 5#(1(2(0(2(0(5(3(1(x1))))))))) 3#(3(0(4(1(2(x1)))))) = [1 0 0 0]x1 + [1] >= [1 0 0 0]x1 = 3#(5(1(2(0(2(0(5(3(1(x1)))))))))) 4#(1(4(5(0(5(4(x1))))))) = [1 0 1 0]x1 + [1] >= [1 0 0 0]x1 = 0#(x1) 4#(1(4(5(0(5(4(x1))))))) = [1 0 1 0]x1 + [1] >= [1 0 0 0]x1 = 1#(0(x1)) 4#(1(4(5(0(5(4(x1))))))) = [1 0 1 0]x1 + [1] >= [1 0 0 0]x1 = 3#(1(0(x1))) 4#(1(4(5(0(5(4(x1))))))) = [1 0 1 0]x1 + [1] >= [1 0 0 0]x1 = 5#(3(1(0(x1)))) 4#(1(4(5(0(5(4(x1))))))) = [1 0 1 0]x1 + [1] >= [1 0 0 0]x1 = 0#(5(3(1(0(x1))))) 4#(1(4(5(0(5(4(x1))))))) = [1 0 1 0]x1 + [1] >= [1 0 0 0]x1 = 1#(0(5(3(1(0(x1)))))) 4#(1(4(5(0(5(4(x1))))))) = [1 0 1 0]x1 + [1] >= [1 0 0 0]x1 = 3#(1(0(5(3(1(0(x1))))))) 4#(1(4(5(0(5(4(x1))))))) = [1 0 1 0]x1 + [1] >= [1 0 0 0]x1 = 5#(3(1(0(5(3(1(0(x1)))))))) 4#(1(4(5(0(5(4(x1))))))) = [1 0 1 0]x1 + [1] >= [1 0 0 0]x1 = 1#(5(3(1(0(5(3(1(0(x1))))))))) 4#(1(4(5(0(5(4(x1))))))) = [1 0 1 0]x1 + [1] >= [1 0 0 0]x1 = 4#(1(5(3(1(0(5(3(1(0(x1)))))))))) 4#(4(0(5(4(2(2(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 0 0]x1 = 1#(x1) 4#(4(0(5(4(2(2(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 0 1]x1 = 4#(1(x1)) 4#(4(0(5(4(2(2(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 0 1]x1 = 5#(4(1(x1))) 4#(4(0(5(4(2(2(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 0 1]x1 = 4#(5(4(1(x1)))) 4#(4(0(5(4(2(2(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 0 1]x1 = 4#(4(5(4(1(x1))))) 4#(4(0(5(4(2(2(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 0 1]x1 = 4#(4(4(5(4(1(x1)))))) 4#(4(0(5(4(2(2(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 0 1]x1 = 3#(4(4(4(5(4(1(x1))))))) 4#(4(0(5(4(2(2(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 0 1]x1 = 4#(3(4(4(4(5(4(1(x1)))))))) 4#(4(0(5(4(2(2(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 0 1]x1 = 0#(4(3(4(4(4(5(4(1(x1))))))))) 4#(4(0(5(4(2(2(x1))))))) = [1 0 1 1]x1 + [1] >= [1 0 0 1]x1 = 4#(0(4(3(4(4(4(5(4(1(x1)))))))))) 5#(4(5(3(2(4(3(x1))))))) = [1 1 1 0]x1 + [1] >= [1 0 1 0]x1 = 4#(x1) 5#(4(5(3(2(4(3(x1))))))) = [1 1 1 0]x1 + [1] >= [1 0 1 0]x1 = 1#(4(x1)) 5#(4(5(3(2(4(3(x1))))))) = [1 1 1 0]x1 + [1] >= [1 0 1 0]x1 = 0#(1(4(x1))) 5#(4(5(3(2(4(3(x1))))))) = [1 1 1 0]x1 + [1] >= [1 0 1 0]x1 = 5#(0(1(4(x1)))) 5#(4(5(3(2(4(3(x1))))))) = [1 1 1 0]x1 + [1] >= [1 0 1 0]x1 = 4#(5(0(1(4(x1))))) 5#(4(5(3(2(4(3(x1))))))) = [1 1 1 0]x1 + [1] >= [1 0 1 0]x1 = 0#(4(5(0(1(4(x1)))))) 5#(4(5(3(2(4(3(x1))))))) = [1 1 1 0]x1 + [1] >= [1 0 1 0]x1 = 5#(0(4(5(0(1(4(x1))))))) 5#(4(5(3(2(4(3(x1))))))) = [1 1 1 0]x1 + [1] >= [1 0 1 0]x1 = 5#(5(0(4(5(0(1(4(x1)))))))) 5#(4(5(3(2(4(3(x1))))))) = [1 1 1 0]x1 + [1] >= [1 0 1 0]x1 = 5#(5(5(0(4(5(0(1(4(x1))))))))) [1 0 1 0] [1] [1 0 1 0] [0] [0 0 0 0] [1] [0 0 0 0] [0] 4(2(4(x1))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = 2(0(0(5(3(3(5(2(0(4(x1)))))))))) [0 0 0 0] [1] [0 0 0 0] [1] [1 0 1 1] [1] [1 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] 4(4(2(4(2(x1))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = 2(0(5(2(1(4(0(2(0(1(x1)))))))))) [0 0 0 0] [1] [0 0 0 0] [1] [1 1 1 0] [1] [1 0 0 0] [0 0 0 0] [0] [0 0 0 0] 0(5(4(2(4(3(x1)))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 = 5(1(5(5(3(5(3(0(0(0(x1)))))))))) [0 0 0 0] [0] [0 0 0 0] [1 1 1 0] [1] [1 0 0 0] [0 0 0 0] [0] [0 0 0 0] 1(1(4(5(3(3(x1)))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 = 1(3(1(1(3(0(1(2(2(1(x1)))))))))) [0 0 0 0] [0] [0 0 0 0] [1 0 0 0] [1] [1 0 0 0] [0 0 0 0] [1] [0 0 0 0] 3(1(4(3(1(2(x1)))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 = 0(0(1(1(4(2(3(0(0(3(x1)))))))))) [0 0 0 0] [0] [0 0 0 0] [1 0 0 1] [1] [1 0 0 0] [0 0 0 0] [1] [0 0 0 0] 3(2(4(2(4(1(x1)))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 = 0(2(1(1(1(5(3(1(3(3(x1)))))))))) [0 0 0 0] [1] [0 0 0 0] [1 0 0 0] [1] [1 0 0 0] [0] [0 0 0 0] [1] [0 0 0 0] [1] 3(3(0(4(1(2(x1)))))) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = 3(5(1(2(0(2(0(5(3(1(x1)))))))))) [0 0 0 0] [0] [0 0 0 0] [0] [1 0 1 0] [1] [1 0 0 0] [0] [0 0 0 0] [1] [0 0 0 0] [0] 4(1(4(5(0(5(4(x1))))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = 4(1(5(3(1(0(5(3(1(0(x1)))))))))) [0 0 0 0] [1] [0 0 0 0] [1] [1 0 1 1] [1] [1 0 0 1] [0] [0 0 0 0] [0] [0 0 0 0] [0] 4(4(0(5(4(2(2(x1))))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = 4(0(4(3(4(4(4(5(4(1(x1)))))))))) [0 0 0 0] [1] [0 0 0 0] [1] [1 1 1 0] [1] [1 0 1 0] [0] [0 0 0 0] [1] [0 0 0 0] [0] 5(4(5(3(2(4(3(x1))))))) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = 2(5(5(5(0(4(5(0(1(4(x1)))))))))) [0 0 0 0] [1] [0 0 0 0] [1] problem: DPs: TRS: 4(2(4(x1))) -> 2(0(0(5(3(3(5(2(0(4(x1)))))))))) 4(4(2(4(2(x1))))) -> 2(0(5(2(1(4(0(2(0(1(x1)))))))))) 0(5(4(2(4(3(x1)))))) -> 5(1(5(5(3(5(3(0(0(0(x1)))))))))) 1(1(4(5(3(3(x1)))))) -> 1(3(1(1(3(0(1(2(2(1(x1)))))))))) 3(1(4(3(1(2(x1)))))) -> 0(0(1(1(4(2(3(0(0(3(x1)))))))))) 3(2(4(2(4(1(x1)))))) -> 0(2(1(1(1(5(3(1(3(3(x1)))))))))) 3(3(0(4(1(2(x1)))))) -> 3(5(1(2(0(2(0(5(3(1(x1)))))))))) 4(1(4(5(0(5(4(x1))))))) -> 4(1(5(3(1(0(5(3(1(0(x1)))))))))) 4(4(0(5(4(2(2(x1))))))) -> 4(0(4(3(4(4(4(5(4(1(x1)))))))))) 5(4(5(3(2(4(3(x1))))))) -> 2(5(5(5(0(4(5(0(1(4(x1)))))))))) Qed