YES Problem: 0(0(1(0(2(x1))))) -> 0(0(1(2(2(x1))))) 0(0(1(0(2(x1))))) -> 0(0(2(1(2(x1))))) 0(0(1(0(2(x1))))) -> 0(1(0(2(2(x1))))) 0(0(1(0(2(x1))))) -> 0(1(1(2(2(x1))))) 0(0(1(0(2(x1))))) -> 0(1(2(0(2(x1))))) 0(0(1(0(2(x1))))) -> 0(1(2(2(0(x1))))) 0(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 0(0(1(0(2(x1))))) -> 0(2(1(0(2(x1))))) 0(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 0(0(1(0(2(x1))))) -> 0(2(2(1(0(x1))))) 0(0(1(0(2(x1))))) -> 0(2(2(1(2(x1))))) 0(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 0(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 0(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 0(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 0(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 0(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 0(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 0(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 0(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 0(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 0(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 0(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 0(1(2(0(2(x1))))) -> 0(1(0(2(2(x1))))) 0(1(2(0(2(x1))))) -> 0(1(1(2(2(x1))))) 0(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 0(1(2(0(2(x1))))) -> 0(2(1(0(2(x1))))) 0(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 0(1(2(0(2(x1))))) -> 0(2(2(1(0(x1))))) 0(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 0(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 0(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 0(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 0(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 1(0(1(0(2(x1))))) -> 0(1(2(2(2(x1))))) 1(0(1(0(2(x1))))) -> 0(2(1(2(2(x1))))) 1(0(1(0(2(x1))))) -> 1(0(0(2(2(x1))))) 1(0(1(0(2(x1))))) -> 1(0(1(2(2(x1))))) 1(0(1(0(2(x1))))) -> 1(0(2(0(2(x1))))) 1(0(1(0(2(x1))))) -> 1(0(2(1(2(x1))))) 1(0(1(0(2(x1))))) -> 1(0(2(2(0(x1))))) 1(0(1(0(2(x1))))) -> 1(0(2(2(2(x1))))) 1(0(1(0(2(x1))))) -> 1(1(0(2(2(x1))))) 1(0(1(0(2(x1))))) -> 1(2(0(2(2(x1))))) 1(0(1(0(2(x1))))) -> 1(2(1(0(2(x1))))) 1(0(1(0(2(x1))))) -> 1(2(2(0(2(x1))))) 1(0(1(0(2(x1))))) -> 1(2(2(2(0(x1))))) 1(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 1(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 1(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 1(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 1(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 1(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 1(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 1(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 1(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 1(0(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 1(0(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 1(0(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 1(0(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 1(0(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 1(0(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 1(1(2(0(2(x1))))) -> 0(1(2(2(2(x1))))) 1(1(2(0(2(x1))))) -> 0(2(1(2(2(x1))))) 1(1(2(0(2(x1))))) -> 0(2(2(1(2(x1))))) 1(1(2(0(2(x1))))) -> 1(0(0(2(2(x1))))) 1(1(2(0(2(x1))))) -> 1(0(1(2(2(x1))))) 1(1(2(0(2(x1))))) -> 1(0(2(0(2(x1))))) 1(1(2(0(2(x1))))) -> 1(0(2(1(2(x1))))) 1(1(2(0(2(x1))))) -> 1(0(2(2(0(x1))))) 1(1(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 1(1(2(0(2(x1))))) -> 1(1(0(2(2(x1))))) 1(1(2(0(2(x1))))) -> 1(2(0(2(2(x1))))) 1(1(2(0(2(x1))))) -> 1(2(1(0(2(x1))))) 1(1(2(0(2(x1))))) -> 1(2(2(0(2(x1))))) 1(1(2(0(2(x1))))) -> 1(2(2(2(0(x1))))) 1(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 1(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 1(1(2(0(2(x1))))) -> 2(1(2(0(2(x1))))) 1(1(2(0(2(x1))))) -> 2(2(0(1(2(x1))))) 1(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 1(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) 1(2(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 2(0(1(0(2(x1))))) -> 2(0(1(2(2(x1))))) 2(0(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 2(0(1(0(2(x1))))) -> 2(1(0(2(2(x1))))) 2(0(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 2(0(1(0(2(x1))))) -> 2(1(2(2(0(x1))))) 2(0(1(0(2(x1))))) -> 2(2(0(1(2(x1))))) 2(0(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 2(0(1(0(2(x1))))) -> 2(2(1(2(0(x1))))) 2(0(1(0(2(x1))))) -> 2(2(2(1(0(x1))))) 2(1(1(0(2(x1))))) -> 2(0(1(0(2(x1))))) 2(1(1(0(2(x1))))) -> 2(0(2(1(2(x1))))) 2(1(1(0(2(x1))))) -> 2(1(2(0(2(x1))))) 2(1(1(0(2(x1))))) -> 2(2(1(0(2(x1))))) 2(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 2(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 2(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 2(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) Proof: Matrix Interpretation Processor: dim=1 interpretation: [0](x0) = 2x0 + 1, [2](x0) = x0, [1](x0) = 2x0 + 1 orientation: 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 0(0(1(2(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 0(0(2(1(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 0(1(0(2(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 0(1(1(2(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 0(1(2(0(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 0(1(2(2(0(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 0(1(2(2(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 0(2(1(0(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 0(2(1(2(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 0(2(2(1(0(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 0(2(2(1(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(0(0(2(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(0(2(0(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(0(2(2(0(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 1(0(2(2(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(1(0(2(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 1(2(0(2(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(2(1(0(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 1(2(2(0(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 1(2(2(2(0(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(1(0(2(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(2(1(0(2(x1))))) 0(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(2(2(1(0(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 0(1(0(2(2(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 0(1(1(2(2(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 0(1(2(2(2(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 0(2(1(0(2(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 0(2(1(2(2(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 0(2(2(1(0(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 0(2(2(1(2(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(0(2(2(2(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(2(0(2(2(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(2(2(0(2(x1))))) 0(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(2(2(2(0(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 0(1(2(2(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 0(2(1(2(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(0(0(2(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(0(1(2(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(0(2(0(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(0(2(1(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(0(2(2(0(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 1(0(2(2(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(1(0(2(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 1(2(0(2(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 8x1 + 7 = 1(2(1(0(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 1(2(2(0(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 1(2(2(2(0(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(0(1(2(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(0(2(1(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(1(0(2(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(1(2(0(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(1(2(2(0(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(2(0(1(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(2(1(0(2(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(2(1(2(0(x1))))) 1(0(1(0(2(x1))))) = 16x1 + 15 >= 4x1 + 3 = 2(2(2(1(0(x1))))) 1(0(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(0(2(2(2(x1))))) 1(0(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(2(0(2(2(x1))))) 1(0(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(2(2(0(2(x1))))) 1(0(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(2(2(2(0(x1))))) 1(0(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(1(0(2(2(x1))))) 1(0(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(2(1(0(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 0(1(2(2(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 0(2(1(2(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 0(2(2(1(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 1(0(0(2(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 1(0(1(2(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 1(0(2(0(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 1(0(2(1(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 1(0(2(2(0(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(0(2(2(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 1(1(0(2(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(2(0(2(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 1(2(1(0(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(2(2(0(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 1(2(2(2(0(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(0(1(2(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(1(0(2(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(1(2(0(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(2(0(1(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(2(1(0(2(x1))))) 1(1(2(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(2(2(1(0(x1))))) 1(2(2(0(2(x1))))) = 4x1 + 3 >= 4x1 + 3 = 1(0(2(2(2(x1))))) 2(0(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(0(1(2(2(x1))))) 2(0(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(0(2(1(2(x1))))) 2(0(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(1(0(2(2(x1))))) 2(0(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(1(2(0(2(x1))))) 2(0(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(1(2(2(0(x1))))) 2(0(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(2(0(1(2(x1))))) 2(0(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(2(1(0(2(x1))))) 2(0(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(2(1(2(0(x1))))) 2(0(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(2(2(1(0(x1))))) 2(1(1(0(2(x1))))) = 8x1 + 7 >= 8x1 + 7 = 2(0(1(0(2(x1))))) 2(1(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(0(2(1(2(x1))))) 2(1(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(1(2(0(2(x1))))) 2(1(1(0(2(x1))))) = 8x1 + 7 >= 4x1 + 3 = 2(2(1(0(2(x1))))) 2(1(2(0(2(x1))))) = 4x1 + 3 >= 4x1 + 3 = 2(0(1(2(2(x1))))) 2(1(2(0(2(x1))))) = 4x1 + 3 >= 4x1 + 3 = 2(1(0(2(2(x1))))) 2(1(2(0(2(x1))))) = 4x1 + 3 >= 4x1 + 3 = 2(2(1(0(2(x1))))) 2(1(2(0(2(x1))))) = 4x1 + 3 >= 4x1 + 3 = 2(2(2(1(0(x1))))) problem: 0(1(2(0(2(x1))))) -> 0(1(0(2(2(x1))))) 0(1(2(0(2(x1))))) -> 0(1(1(2(2(x1))))) 0(1(2(0(2(x1))))) -> 0(2(1(0(2(x1))))) 0(1(2(0(2(x1))))) -> 0(2(2(1(0(x1))))) 1(1(2(0(2(x1))))) -> 1(0(0(2(2(x1))))) 1(1(2(0(2(x1))))) -> 1(0(1(2(2(x1))))) 1(1(2(0(2(x1))))) -> 1(0(2(0(2(x1))))) 1(1(2(0(2(x1))))) -> 1(0(2(1(2(x1))))) 1(1(2(0(2(x1))))) -> 1(0(2(2(0(x1))))) 1(1(2(0(2(x1))))) -> 1(1(0(2(2(x1))))) 1(1(2(0(2(x1))))) -> 1(2(1(0(2(x1))))) 1(2(2(0(2(x1))))) -> 1(0(2(2(2(x1))))) 2(1(1(0(2(x1))))) -> 2(0(1(0(2(x1))))) 2(1(2(0(2(x1))))) -> 2(0(1(2(2(x1))))) 2(1(2(0(2(x1))))) -> 2(1(0(2(2(x1))))) 2(1(2(0(2(x1))))) -> 2(2(1(0(2(x1))))) 2(1(2(0(2(x1))))) -> 2(2(2(1(0(x1))))) Bounds Processor: bound: 0 enrichment: match automaton: final states: {44,43,42,41,39,36,35,34,30,26,23,21,19,14,10,7,1} transitions: 10(4) -> 8* 10(3) -> 27* 10(25) -> 23* 10(11) -> 12* 10(20) -> 19* 10(5) -> 6* 10(33) -> 30* 10(13) -> 35* 10(6) -> 34* 10(29) -> 26* 10(15) -> 16* 10(8) -> 9* 10(38) -> 36* 10(22) -> 21* 20(6) -> 42* 20(17) -> 18* 20(13) -> 43* 20(12) -> 13* 20(27) -> 28* 20(31) -> 32* 20(4) -> 37* 20(2) -> 3* 20(16) -> 17* 20(40) -> 39* 20(15) -> 31* 20(18) -> 44* 20(3) -> 4* 20(22) -> 41* 20(11) -> 24* 00(28) -> 29* 00(13) -> 10* 00(3) -> 11* 00(4) -> 5* 00(24) -> 25* 00(6) -> 1* 00(18) -> 14* 00(12) -> 40* 00(32) -> 33* 00(2) -> 15* 00(8) -> 22* 00(9) -> 7* 00(5) -> 20* 00(37) -> 38* f30() -> 2* 43 -> 3,28 42 -> 3,28 7 -> 15* 14 -> 15* 36 -> 27,8 44 -> 3,28 1 -> 15* 39 -> 3* 41 -> 3,28 10 -> 15* problem: Qed