39.96/10.58 YES 39.96/10.59 39.96/10.59 Problem: 39.96/10.59 strict: 39.96/10.59 b(b(c(x1))) -> b(c(c(x1))) 39.96/10.59 a(a(a(x1))) -> c(b(a(x1))) 39.96/10.59 b(b(c(x1))) -> b(a(a(x1))) 39.96/10.59 c(b(c(x1))) -> a(a(a(x1))) 39.96/10.59 weak: 39.96/10.59 a(b(b(x1))) -> a(c(a(x1))) 39.96/10.59 a(c(b(x1))) -> b(a(c(x1))) 39.96/10.59 b(a(a(x1))) -> b(a(c(x1))) 39.96/10.59 39.96/10.59 Proof: 39.96/10.59 Root-Labeling Processor: 39.96/10.59 strict: 39.96/10.59 b(b)(b(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) 39.96/10.59 b(b)(b(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) 39.96/10.59 b(b)(b(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) 39.96/10.59 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(c)(c(b)(b(a)(a(b)(x1)))) 39.96/10.59 b(a)(a(a)(a(a)(a(c)(x1)))) -> b(c)(c(b)(b(a)(a(c)(x1)))) 39.96/10.59 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(c)(c(b)(b(a)(a(a)(x1)))) 39.96/10.59 c(a)(a(a)(a(a)(a(b)(x1)))) -> c(c)(c(b)(b(a)(a(b)(x1)))) 39.96/10.59 c(a)(a(a)(a(a)(a(c)(x1)))) -> c(c)(c(b)(b(a)(a(c)(x1)))) 39.96/10.59 c(a)(a(a)(a(a)(a(a)(x1)))) -> c(c)(c(b)(b(a)(a(a)(x1)))) 39.96/10.59 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(c)(c(b)(b(a)(a(b)(x1)))) 39.96/10.59 a(a)(a(a)(a(a)(a(c)(x1)))) -> a(c)(c(b)(b(a)(a(c)(x1)))) 39.96/10.59 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(c)(c(b)(b(a)(a(a)(x1)))) 39.96/10.59 b(b)(b(c)(c(b)(x1))) -> b(a)(a(a)(a(b)(x1))) 39.96/10.59 b(b)(b(c)(c(c)(x1))) -> b(a)(a(a)(a(c)(x1))) 39.96/10.59 b(b)(b(c)(c(a)(x1))) -> b(a)(a(a)(a(a)(x1))) 39.96/10.59 b(c)(c(b)(b(c)(c(b)(x1)))) -> b(a)(a(a)(a(a)(a(b)(x1)))) 39.96/10.59 b(c)(c(b)(b(c)(c(c)(x1)))) -> b(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.59 b(c)(c(b)(b(c)(c(a)(x1)))) -> b(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.59 c(c)(c(b)(b(c)(c(b)(x1)))) -> c(a)(a(a)(a(a)(a(b)(x1)))) 39.96/10.59 c(c)(c(b)(b(c)(c(c)(x1)))) -> c(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.59 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.59 a(c)(c(b)(b(c)(c(b)(x1)))) -> a(a)(a(a)(a(a)(a(b)(x1)))) 39.96/10.59 a(c)(c(b)(b(c)(c(c)(x1)))) -> a(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.59 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.59 weak: 39.96/10.59 a(b)(b(b)(b(b)(x1))) -> a(c)(c(a)(a(b)(x1))) 39.96/10.59 a(b)(b(b)(b(c)(x1))) -> a(c)(c(a)(a(c)(x1))) 39.96/10.59 a(b)(b(b)(b(a)(x1))) -> a(c)(c(a)(a(a)(x1))) 39.96/10.59 b(a)(a(c)(c(b)(b(b)(x1)))) -> b(b)(b(a)(a(c)(c(b)(x1)))) 39.96/10.59 b(a)(a(c)(c(b)(b(c)(x1)))) -> b(b)(b(a)(a(c)(c(c)(x1)))) 39.96/10.59 b(a)(a(c)(c(b)(b(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.59 c(a)(a(c)(c(b)(b(b)(x1)))) -> c(b)(b(a)(a(c)(c(b)(x1)))) 39.96/10.59 c(a)(a(c)(c(b)(b(c)(x1)))) -> c(b)(b(a)(a(c)(c(c)(x1)))) 39.96/10.59 c(a)(a(c)(c(b)(b(a)(x1)))) -> c(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.59 a(a)(a(c)(c(b)(b(b)(x1)))) -> a(b)(b(a)(a(c)(c(b)(x1)))) 39.96/10.59 a(a)(a(c)(c(b)(b(c)(x1)))) -> a(b)(b(a)(a(c)(c(c)(x1)))) 39.96/10.59 a(a)(a(c)(c(b)(b(a)(x1)))) -> a(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.59 b(a)(a(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 39.96/10.59 b(a)(a(a)(a(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 39.96/10.59 b(a)(a(a)(a(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 39.96/10.59 RT Transformation Processor: 39.96/10.59 b(b)(b(c)(c(b)(x1))) -> b(c)(c(c)(c(b)(x1))) 39.96/10.59 b(b)(b(c)(c(c)(x1))) -> b(c)(c(c)(c(c)(x1))) 39.96/10.59 b(b)(b(c)(c(a)(x1))) -> b(c)(c(c)(c(a)(x1))) 39.96/10.59 b(a)(a(a)(a(a)(a(b)(x1)))) -> b(c)(c(b)(b(a)(a(b)(x1)))) 39.96/10.59 b(a)(a(a)(a(a)(a(c)(x1)))) -> b(c)(c(b)(b(a)(a(c)(x1)))) 39.96/10.59 b(a)(a(a)(a(a)(a(a)(x1)))) -> b(c)(c(b)(b(a)(a(a)(x1)))) 39.96/10.59 c(a)(a(a)(a(a)(a(b)(x1)))) -> c(c)(c(b)(b(a)(a(b)(x1)))) 39.96/10.59 c(a)(a(a)(a(a)(a(c)(x1)))) -> c(c)(c(b)(b(a)(a(c)(x1)))) 39.96/10.59 c(a)(a(a)(a(a)(a(a)(x1)))) -> c(c)(c(b)(b(a)(a(a)(x1)))) 39.96/10.59 a(a)(a(a)(a(a)(a(b)(x1)))) -> a(c)(c(b)(b(a)(a(b)(x1)))) 39.96/10.59 a(a)(a(a)(a(a)(a(c)(x1)))) -> a(c)(c(b)(b(a)(a(c)(x1)))) 39.96/10.59 a(a)(a(a)(a(a)(a(a)(x1)))) -> a(c)(c(b)(b(a)(a(a)(x1)))) 39.96/10.59 b(b)(b(c)(c(b)(x1))) -> b(a)(a(a)(a(b)(x1))) 39.96/10.59 b(b)(b(c)(c(c)(x1))) -> b(a)(a(a)(a(c)(x1))) 39.96/10.59 b(b)(b(c)(c(a)(x1))) -> b(a)(a(a)(a(a)(x1))) 39.96/10.59 b(c)(c(b)(b(c)(c(b)(x1)))) -> b(a)(a(a)(a(a)(a(b)(x1)))) 39.96/10.59 b(c)(c(b)(b(c)(c(c)(x1)))) -> b(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.59 b(c)(c(b)(b(c)(c(a)(x1)))) -> b(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.59 c(c)(c(b)(b(c)(c(b)(x1)))) -> c(a)(a(a)(a(a)(a(b)(x1)))) 39.96/10.59 c(c)(c(b)(b(c)(c(c)(x1)))) -> c(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.59 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.59 a(c)(c(b)(b(c)(c(b)(x1)))) -> a(a)(a(a)(a(a)(a(b)(x1)))) 39.96/10.59 a(c)(c(b)(b(c)(c(c)(x1)))) -> a(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.59 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.59 a(b)(b(b)(b(b)(x1))) -> a(c)(c(a)(a(b)(x1))) 39.96/10.59 a(b)(b(b)(b(c)(x1))) -> a(c)(c(a)(a(c)(x1))) 39.96/10.59 a(b)(b(b)(b(a)(x1))) -> a(c)(c(a)(a(a)(x1))) 39.96/10.59 b(a)(a(c)(c(b)(b(b)(x1)))) -> b(b)(b(a)(a(c)(c(b)(x1)))) 39.96/10.59 b(a)(a(c)(c(b)(b(c)(x1)))) -> b(b)(b(a)(a(c)(c(c)(x1)))) 39.96/10.60 b(a)(a(c)(c(b)(b(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.60 c(a)(a(c)(c(b)(b(b)(x1)))) -> c(b)(b(a)(a(c)(c(b)(x1)))) 39.96/10.60 c(a)(a(c)(c(b)(b(c)(x1)))) -> c(b)(b(a)(a(c)(c(c)(x1)))) 39.96/10.60 c(a)(a(c)(c(b)(b(a)(x1)))) -> c(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.60 a(a)(a(c)(c(b)(b(b)(x1)))) -> a(b)(b(a)(a(c)(c(b)(x1)))) 39.96/10.60 a(a)(a(c)(c(b)(b(c)(x1)))) -> a(b)(b(a)(a(c)(c(c)(x1)))) 39.96/10.60 a(a)(a(c)(c(b)(b(a)(x1)))) -> a(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.60 b(a)(a(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 39.96/10.60 b(a)(a(a)(a(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 39.96/10.60 b(a)(a(a)(a(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 39.96/10.60 Matrix Interpretation Processor: dim=1 39.96/10.60 39.96/10.60 interpretation: 39.96/10.60 [a(c)](x0) = 2x0 + 1, 39.96/10.60 39.96/10.60 [a(b)](x0) = 2x0 + 1, 39.96/10.60 39.96/10.60 [a(a)](x0) = 2x0 + 1, 39.96/10.60 39.96/10.60 [b(a)](x0) = 2x0, 39.96/10.60 39.96/10.60 [c(a)](x0) = 2x0, 39.96/10.60 39.96/10.60 [c(c)](x0) = 2x0, 39.96/10.60 39.96/10.60 [c(b)](x0) = 2x0 + 1, 39.96/10.60 39.96/10.60 [b(c)](x0) = 2x0 + 3, 39.96/10.60 39.96/10.60 [b(b)](x0) = 2x0 + 2 39.96/10.60 orientation: 39.96/10.60 b(b)(b(c)(c(b)(x1))) = 8x1 + 12 >= 8x1 + 7 = b(c)(c(c)(c(b)(x1))) 39.96/10.60 39.96/10.60 b(b)(b(c)(c(c)(x1))) = 8x1 + 8 >= 8x1 + 3 = b(c)(c(c)(c(c)(x1))) 39.96/10.60 39.96/10.60 b(b)(b(c)(c(a)(x1))) = 8x1 + 8 >= 8x1 + 3 = b(c)(c(c)(c(a)(x1))) 39.96/10.60 39.96/10.60 b(a)(a(a)(a(a)(a(b)(x1)))) = 16x1 + 14 >= 16x1 + 13 = b(c)(c(b)(b(a)(a(b)(x1)))) 39.96/10.60 39.96/10.60 b(a)(a(a)(a(a)(a(c)(x1)))) = 16x1 + 14 >= 16x1 + 13 = b(c)(c(b)(b(a)(a(c)(x1)))) 39.96/10.60 39.96/10.60 b(a)(a(a)(a(a)(a(a)(x1)))) = 16x1 + 14 >= 16x1 + 13 = b(c)(c(b)(b(a)(a(a)(x1)))) 39.96/10.60 39.96/10.60 c(a)(a(a)(a(a)(a(b)(x1)))) = 16x1 + 14 >= 16x1 + 10 = c(c)(c(b)(b(a)(a(b)(x1)))) 39.96/10.60 39.96/10.60 c(a)(a(a)(a(a)(a(c)(x1)))) = 16x1 + 14 >= 16x1 + 10 = c(c)(c(b)(b(a)(a(c)(x1)))) 39.96/10.60 39.96/10.60 c(a)(a(a)(a(a)(a(a)(x1)))) = 16x1 + 14 >= 16x1 + 10 = c(c)(c(b)(b(a)(a(a)(x1)))) 39.96/10.60 39.96/10.60 a(a)(a(a)(a(a)(a(b)(x1)))) = 16x1 + 15 >= 16x1 + 11 = a(c)(c(b)(b(a)(a(b)(x1)))) 39.96/10.60 39.96/10.60 a(a)(a(a)(a(a)(a(c)(x1)))) = 16x1 + 15 >= 16x1 + 11 = a(c)(c(b)(b(a)(a(c)(x1)))) 39.96/10.60 39.96/10.60 a(a)(a(a)(a(a)(a(a)(x1)))) = 16x1 + 15 >= 16x1 + 11 = a(c)(c(b)(b(a)(a(a)(x1)))) 39.96/10.60 39.96/10.60 b(b)(b(c)(c(b)(x1))) = 8x1 + 12 >= 8x1 + 6 = b(a)(a(a)(a(b)(x1))) 39.96/10.60 39.96/10.60 b(b)(b(c)(c(c)(x1))) = 8x1 + 8 >= 8x1 + 6 = b(a)(a(a)(a(c)(x1))) 39.96/10.60 39.96/10.60 b(b)(b(c)(c(a)(x1))) = 8x1 + 8 >= 8x1 + 6 = b(a)(a(a)(a(a)(x1))) 39.96/10.60 39.96/10.60 b(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 + 25 >= 16x1 + 14 = b(a)(a(a)(a(a)(a(b)(x1)))) 39.96/10.60 39.96/10.60 b(c)(c(b)(b(c)(c(c)(x1)))) = 16x1 + 17 >= 16x1 + 14 = b(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.60 39.96/10.60 b(c)(c(b)(b(c)(c(a)(x1)))) = 16x1 + 17 >= 16x1 + 14 = b(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.60 39.96/10.60 c(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 + 22 >= 16x1 + 14 = c(a)(a(a)(a(a)(a(b)(x1)))) 39.96/10.60 39.96/10.60 c(c)(c(b)(b(c)(c(c)(x1)))) = 16x1 + 14 >= 16x1 + 14 = c(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.60 39.96/10.60 c(c)(c(b)(b(c)(c(a)(x1)))) = 16x1 + 14 >= 16x1 + 14 = c(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.60 39.96/10.60 a(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 + 23 >= 16x1 + 15 = a(a)(a(a)(a(a)(a(b)(x1)))) 39.96/10.60 39.96/10.60 a(c)(c(b)(b(c)(c(c)(x1)))) = 16x1 + 15 >= 16x1 + 15 = a(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.60 39.96/10.60 a(c)(c(b)(b(c)(c(a)(x1)))) = 16x1 + 15 >= 16x1 + 15 = a(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.60 39.96/10.60 a(b)(b(b)(b(b)(x1))) = 8x1 + 13 >= 8x1 + 5 = a(c)(c(a)(a(b)(x1))) 39.96/10.60 39.96/10.60 a(b)(b(b)(b(c)(x1))) = 8x1 + 17 >= 8x1 + 5 = a(c)(c(a)(a(c)(x1))) 39.96/10.60 39.96/10.60 a(b)(b(b)(b(a)(x1))) = 8x1 + 5 >= 8x1 + 5 = a(c)(c(a)(a(a)(x1))) 39.96/10.60 39.96/10.60 b(a)(a(c)(c(b)(b(b)(x1)))) = 16x1 + 22 >= 16x1 + 14 = b(b)(b(a)(a(c)(c(b)(x1)))) 39.96/10.60 39.96/10.60 b(a)(a(c)(c(b)(b(c)(x1)))) = 16x1 + 30 >= 16x1 + 6 = b(b)(b(a)(a(c)(c(c)(x1)))) 39.96/10.60 39.96/10.60 b(a)(a(c)(c(b)(b(a)(x1)))) = 16x1 + 6 >= 16x1 + 6 = b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.60 39.96/10.60 c(a)(a(c)(c(b)(b(b)(x1)))) = 16x1 + 22 >= 16x1 + 13 = c(b)(b(a)(a(c)(c(b)(x1)))) 39.96/10.60 39.96/10.60 c(a)(a(c)(c(b)(b(c)(x1)))) = 16x1 + 30 >= 16x1 + 5 = c(b)(b(a)(a(c)(c(c)(x1)))) 39.96/10.60 39.96/10.60 c(a)(a(c)(c(b)(b(a)(x1)))) = 16x1 + 6 >= 16x1 + 5 = c(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.60 39.96/10.60 a(a)(a(c)(c(b)(b(b)(x1)))) = 16x1 + 23 >= 16x1 + 13 = a(b)(b(a)(a(c)(c(b)(x1)))) 39.96/10.60 39.96/10.60 a(a)(a(c)(c(b)(b(c)(x1)))) = 16x1 + 31 >= 16x1 + 5 = a(b)(b(a)(a(c)(c(c)(x1)))) 39.96/10.60 39.96/10.60 a(a)(a(c)(c(b)(b(a)(x1)))) = 16x1 + 7 >= 16x1 + 5 = a(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.61 39.96/10.61 b(a)(a(a)(a(b)(x1))) = 8x1 + 6 >= 8x1 + 6 = b(a)(a(c)(c(b)(x1))) 39.96/10.61 39.96/10.61 b(a)(a(a)(a(c)(x1))) = 8x1 + 6 >= 8x1 + 2 = b(a)(a(c)(c(c)(x1))) 39.96/10.61 39.96/10.61 b(a)(a(a)(a(a)(x1))) = 8x1 + 6 >= 8x1 + 2 = b(a)(a(c)(c(a)(x1))) 39.96/10.61 problem: 39.96/10.61 c(c)(c(b)(b(c)(c(c)(x1)))) -> c(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.61 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.61 a(c)(c(b)(b(c)(c(c)(x1)))) -> a(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.61 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.61 a(b)(b(b)(b(a)(x1))) -> a(c)(c(a)(a(a)(x1))) 39.96/10.61 b(a)(a(c)(c(b)(b(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.61 b(a)(a(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 39.96/10.61 Matrix Interpretation Processor: dim=3 39.96/10.61 39.96/10.61 interpretation: 39.96/10.61 [1 0 0] 39.96/10.61 [a(c)](x0) = [1 0 0]x0 39.96/10.61 [0 0 1] , 39.96/10.61 39.96/10.61 [1 0 1] 39.96/10.61 [a(b)](x0) = [0 1 0]x0 39.96/10.61 [0 0 0] , 39.96/10.61 39.96/10.61 [1 0 0] 39.96/10.61 [a(a)](x0) = [0 0 0]x0 39.96/10.61 [1 0 0] , 39.96/10.61 39.96/10.61 [1 0 0] 39.96/10.61 [b(a)](x0) = [1 0 0]x0 39.96/10.61 [1 0 0] , 39.96/10.61 39.96/10.61 [1 0 0] 39.96/10.61 [c(a)](x0) = [0 0 1]x0 39.96/10.61 [0 1 0] , 39.96/10.61 39.96/10.61 [1 0 0] [0] 39.96/10.61 [c(c)](x0) = [0 0 1]x0 + [0] 39.96/10.61 [0 0 0] [1], 39.96/10.61 39.96/10.61 [1 0 0] 39.96/10.61 [c(b)](x0) = [0 0 0]x0 39.96/10.61 [0 0 1] , 39.96/10.61 39.96/10.61 [1 0 1] 39.96/10.61 [b(c)](x0) = [0 0 0]x0 39.96/10.61 [1 0 0] , 39.96/10.61 39.96/10.61 [1 0 0] 39.96/10.61 [b(b)](x0) = [0 1 0]x0 39.96/10.61 [0 0 0] 39.96/10.61 orientation: 39.96/10.61 [1 0 0] [1] [1 0 0] 39.96/10.61 c(c)(c(b)(b(c)(c(c)(x1)))) = [1 0 0]x1 + [0] >= [1 0 0]x1 = c(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.61 [0 0 0] [1] [0 0 0] 39.96/10.61 39.96/10.61 [1 1 0] [0] [1 0 0] 39.96/10.61 c(c)(c(b)(b(c)(c(a)(x1)))) = [1 0 0]x1 + [0] >= [1 0 0]x1 = c(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.61 [0 0 0] [1] [0 0 0] 39.96/10.61 39.96/10.61 [1 0 0] [1] [1 0 0] 39.96/10.61 a(c)(c(b)(b(c)(c(c)(x1)))) = [1 0 0]x1 + [1] >= [0 0 0]x1 = a(a)(a(a)(a(a)(a(c)(x1)))) 39.96/10.61 [1 0 0] [0] [1 0 0] 39.96/10.61 39.96/10.61 [1 1 0] [1 0 0] 39.96/10.61 a(c)(c(b)(b(c)(c(a)(x1)))) = [1 1 0]x1 >= [0 0 0]x1 = a(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.61 [1 0 0] [1 0 0] 39.96/10.61 39.96/10.61 [1 0 0] [1 0 0] 39.96/10.61 a(b)(b(b)(b(a)(x1))) = [1 0 0]x1 >= [1 0 0]x1 = a(c)(c(a)(a(a)(x1))) 39.96/10.61 [0 0 0] [0 0 0] 39.96/10.61 39.96/10.61 [1 0 0] [1 0 0] 39.96/10.61 b(a)(a(c)(c(b)(b(a)(x1)))) = [1 0 0]x1 >= [1 0 0]x1 = b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.61 [1 0 0] [0 0 0] 39.96/10.61 39.96/10.61 [1 0 1] [1 0 0] 39.96/10.61 b(a)(a(a)(a(b)(x1))) = [1 0 1]x1 >= [1 0 0]x1 = b(a)(a(c)(c(b)(x1))) 39.96/10.61 [1 0 1] [1 0 0] 39.96/10.61 problem: 39.96/10.61 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.61 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.61 a(b)(b(b)(b(a)(x1))) -> a(c)(c(a)(a(a)(x1))) 39.96/10.61 b(a)(a(c)(c(b)(b(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.61 b(a)(a(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 39.96/10.61 Matrix Interpretation Processor: dim=3 39.96/10.61 39.96/10.61 interpretation: 39.96/10.61 [1 0 0] [1] 39.96/10.61 [a(c)](x0) = [0 0 1]x0 + [0] 39.96/10.61 [0 0 0] [1], 39.96/10.61 39.96/10.61 [1 1 1] [0] 39.96/10.61 [a(b)](x0) = [1 0 1]x0 + [1] 39.96/10.61 [0 0 0] [1], 39.96/10.61 39.96/10.61 [1 0 1] 39.96/10.61 [a(a)](x0) = [0 0 0]x0 39.96/10.61 [0 1 0] , 39.96/10.61 39.96/10.61 [1 0 0] [0] 39.96/10.61 [b(a)](x0) = [0 0 0]x0 + [1] 39.96/10.61 [0 0 1] [0], 39.96/10.61 39.96/10.61 [1 0 0] 39.96/10.61 [c(a)](x0) = [0 1 1]x0 39.96/10.61 [1 0 0] , 39.96/10.61 39.96/10.61 [1 0 0] [1] 39.96/10.61 [c(c)](x0) = [0 0 0]x0 + [0] 39.96/10.61 [1 0 0] [0], 39.96/10.61 39.96/10.61 [1 0 1] [0] 39.96/10.61 [c(b)](x0) = [0 0 0]x0 + [0] 39.96/10.61 [0 0 0] [1], 39.96/10.61 39.96/10.61 [1 0 0] 39.96/10.61 [b(c)](x0) = [0 0 0]x0 39.96/10.61 [0 1 0] , 39.96/10.61 39.96/10.61 39.96/10.61 [b(b)](x0) = x0 39.96/10.61 39.96/10.61 orientation: 39.96/10.61 [1 1 1] [1] [1 1 1] 39.96/10.61 c(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.61 [1 1 1] [0] [1 1 1] 39.96/10.61 39.96/10.61 [1 1 1] [1] [1 1 1] 39.96/10.61 a(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = a(a)(a(a)(a(a)(a(a)(x1)))) 39.96/10.61 [0 0 0] [1] [0 0 0] 39.96/10.61 39.96/10.61 [1 0 1] [1] [1 0 1] [1] 39.96/10.61 a(b)(b(b)(b(a)(x1))) = [1 0 1]x1 + [1] >= [1 0 1]x1 + [0] = a(c)(c(a)(a(a)(x1))) 39.96/10.61 [0 0 0] [1] [0 0 0] [1] 39.96/10.61 39.96/10.61 [1 0 1] [1] [1 0 0] [1] 39.96/10.61 b(a)(a(c)(c(b)(b(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.61 [0 0 0] [1] [0 0 0] [1] 39.96/10.61 39.96/10.61 [1 1 1] [1] [1 0 1] [1] 39.96/10.61 b(a)(a(a)(a(b)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a)(a(c)(c(b)(x1))) 39.96/10.61 [1 0 1] [1] [0 0 0] [1] 39.96/10.61 problem: 39.96/10.61 a(b)(b(b)(b(a)(x1))) -> a(c)(c(a)(a(a)(x1))) 39.96/10.61 b(a)(a(c)(c(b)(b(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.61 b(a)(a(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 39.96/10.61 Matrix Interpretation Processor: dim=1 39.96/10.61 39.96/10.61 interpretation: 39.96/10.61 [a(c)](x0) = 2x0, 39.96/10.61 39.96/10.61 [a(b)](x0) = 4x0 + 4, 39.96/10.61 39.96/10.61 [a(a)](x0) = 2x0 + 1, 39.96/10.61 39.96/10.61 [b(a)](x0) = x0, 39.96/10.61 39.96/10.61 [c(a)](x0) = 2x0, 39.96/10.61 39.96/10.61 [c(b)](x0) = 4x0, 39.96/10.61 39.96/10.61 [b(b)](x0) = 2x0 39.96/10.61 orientation: 39.96/10.61 a(b)(b(b)(b(a)(x1))) = 8x1 + 4 >= 8x1 + 4 = a(c)(c(a)(a(a)(x1))) 39.96/10.61 39.96/10.61 b(a)(a(c)(c(b)(b(a)(x1)))) = 8x1 >= 8x1 = b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.61 39.96/10.61 b(a)(a(a)(a(b)(x1))) = 8x1 + 9 >= 8x1 = b(a)(a(c)(c(b)(x1))) 39.96/10.61 problem: 39.96/10.61 a(b)(b(b)(b(a)(x1))) -> a(c)(c(a)(a(a)(x1))) 39.96/10.61 b(a)(a(c)(c(b)(b(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.61 Matrix Interpretation Processor: dim=3 39.96/10.61 39.96/10.61 interpretation: 39.96/10.61 [1 1 1] [0] 39.96/10.61 [a(c)](x0) = [0 0 0]x0 + [1] 39.96/10.61 [0 0 0] [0], 39.96/10.61 39.96/10.61 [1 1 0] [1] 39.96/10.61 [a(b)](x0) = [0 0 0]x0 + [1] 39.96/10.61 [0 0 0] [0], 39.96/10.61 39.96/10.61 [1 0 0] 39.96/10.61 [a(a)](x0) = [0 1 0]x0 39.96/10.61 [0 0 0] , 39.96/10.61 39.96/10.61 [1 0 0] [0] 39.96/10.61 [b(a)](x0) = [0 0 0]x0 + [1] 39.96/10.61 [0 1 0] [0], 39.96/10.61 39.96/10.61 [1 0 0] 39.96/10.61 [c(a)](x0) = [0 1 0]x0 39.96/10.61 [0 0 0] , 39.96/10.61 39.96/10.61 [1 1 0] 39.96/10.61 [c(b)](x0) = [0 0 0]x0 39.96/10.61 [0 0 1] , 39.96/10.61 39.96/10.61 [1 0 0] 39.96/10.61 [b(b)](x0) = [0 0 1]x0 39.96/10.61 [0 1 0] 39.96/10.61 orientation: 39.96/10.61 [1 1 0] [1] [1 1 0] [0] 39.96/10.61 a(b)(b(b)(b(a)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(c)(c(a)(a(a)(x1))) 39.96/10.61 [0 0 0] [0] [0 0 0] [0] 39.96/10.61 39.96/10.61 [1 1 0] [1] [1 1 0] [0] 39.96/10.61 b(a)(a(c)(c(b)(b(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b)(b(a)(a(c)(c(a)(x1)))) 39.96/10.61 [0 0 0] [1] [0 0 0] [1] 39.96/10.61 problem: 39.96/10.61 39.96/10.61 Qed 39.96/10.62 EOF