41.41/10.83 YES 41.41/10.84 41.41/10.84 Problem: 41.41/10.84 strict: 41.41/10.84 c(c(c(x1))) -> a(a(c(x1))) 41.41/10.84 b(a(a(x1))) -> b(b(c(x1))) 41.41/10.84 c(a(c(x1))) -> a(c(c(x1))) 41.41/10.84 b(c(c(x1))) -> b(c(b(x1))) 41.41/10.84 weak: 41.41/10.84 a(a(b(x1))) -> c(b(a(x1))) 41.41/10.84 a(b(a(x1))) -> a(c(c(x1))) 41.41/10.84 41.41/10.84 Proof: 41.41/10.84 Root-Labeling Processor: 41.41/10.84 strict: 41.41/10.84 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.84 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.84 c(c)(c(c)(c(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.84 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.84 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.84 a(c)(c(c)(c(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.84 b(c)(c(c)(c(c)(c(c)(x1)))) -> b(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.84 b(c)(c(c)(c(c)(c(a)(x1)))) -> b(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.84 b(c)(c(c)(c(c)(c(b)(x1)))) -> b(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.84 b(a)(a(a)(a(c)(x1))) -> b(b)(b(c)(c(c)(x1))) 41.41/10.84 b(a)(a(a)(a(a)(x1))) -> b(b)(b(c)(c(a)(x1))) 41.41/10.84 b(a)(a(a)(a(b)(x1))) -> b(b)(b(c)(c(b)(x1))) 41.41/10.84 c(c)(c(a)(a(c)(c(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.84 c(c)(c(a)(a(c)(c(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.84 c(c)(c(a)(a(c)(c(b)(x1)))) -> c(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.84 a(c)(c(a)(a(c)(c(c)(x1)))) -> a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.84 a(c)(c(a)(a(c)(c(a)(x1)))) -> a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.84 a(c)(c(a)(a(c)(c(b)(x1)))) -> a(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.84 b(c)(c(a)(a(c)(c(c)(x1)))) -> b(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.84 b(c)(c(a)(a(c)(c(a)(x1)))) -> b(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.84 b(c)(c(a)(a(c)(c(b)(x1)))) -> b(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.84 b(c)(c(c)(c(c)(x1))) -> b(c)(c(b)(b(c)(x1))) 41.41/10.84 b(c)(c(c)(c(a)(x1))) -> b(c)(c(b)(b(a)(x1))) 41.41/10.84 b(c)(c(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(x1))) 41.41/10.84 weak: 41.41/10.84 c(a)(a(a)(a(b)(b(c)(x1)))) -> c(c)(c(b)(b(a)(a(c)(x1)))) 41.41/10.84 c(a)(a(a)(a(b)(b(a)(x1)))) -> c(c)(c(b)(b(a)(a(a)(x1)))) 41.41/10.84 c(a)(a(a)(a(b)(b(b)(x1)))) -> c(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.84 a(a)(a(a)(a(b)(b(c)(x1)))) -> a(c)(c(b)(b(a)(a(c)(x1)))) 41.41/10.84 a(a)(a(a)(a(b)(b(a)(x1)))) -> a(c)(c(b)(b(a)(a(a)(x1)))) 41.41/10.84 a(a)(a(a)(a(b)(b(b)(x1)))) -> a(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.84 b(a)(a(a)(a(b)(b(c)(x1)))) -> b(c)(c(b)(b(a)(a(c)(x1)))) 41.41/10.84 b(a)(a(a)(a(b)(b(a)(x1)))) -> b(c)(c(b)(b(a)(a(a)(x1)))) 41.41/10.84 b(a)(a(a)(a(b)(b(b)(x1)))) -> b(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.84 a(b)(b(a)(a(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 41.41/10.84 a(b)(b(a)(a(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 41.41/10.84 a(b)(b(a)(a(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 41.41/10.84 RT Transformation Processor: 41.41/10.84 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.84 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.84 c(c)(c(c)(c(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.84 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.84 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.84 a(c)(c(c)(c(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.84 b(c)(c(c)(c(c)(c(c)(x1)))) -> b(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.84 b(c)(c(c)(c(c)(c(a)(x1)))) -> b(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.84 b(c)(c(c)(c(c)(c(b)(x1)))) -> b(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.84 b(a)(a(a)(a(c)(x1))) -> b(b)(b(c)(c(c)(x1))) 41.41/10.84 b(a)(a(a)(a(a)(x1))) -> b(b)(b(c)(c(a)(x1))) 41.41/10.84 b(a)(a(a)(a(b)(x1))) -> b(b)(b(c)(c(b)(x1))) 41.41/10.84 c(c)(c(a)(a(c)(c(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.84 c(c)(c(a)(a(c)(c(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.84 c(c)(c(a)(a(c)(c(b)(x1)))) -> c(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.84 a(c)(c(a)(a(c)(c(c)(x1)))) -> a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.84 a(c)(c(a)(a(c)(c(a)(x1)))) -> a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.84 a(c)(c(a)(a(c)(c(b)(x1)))) -> a(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.84 b(c)(c(a)(a(c)(c(c)(x1)))) -> b(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.84 b(c)(c(a)(a(c)(c(a)(x1)))) -> b(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.84 b(c)(c(a)(a(c)(c(b)(x1)))) -> b(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.84 b(c)(c(c)(c(c)(x1))) -> b(c)(c(b)(b(c)(x1))) 41.41/10.84 b(c)(c(c)(c(a)(x1))) -> b(c)(c(b)(b(a)(x1))) 41.41/10.84 b(c)(c(c)(c(b)(x1))) -> b(c)(c(b)(b(b)(x1))) 41.41/10.84 c(a)(a(a)(a(b)(b(c)(x1)))) -> c(c)(c(b)(b(a)(a(c)(x1)))) 41.41/10.84 c(a)(a(a)(a(b)(b(a)(x1)))) -> c(c)(c(b)(b(a)(a(a)(x1)))) 41.41/10.84 c(a)(a(a)(a(b)(b(b)(x1)))) -> c(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.84 a(a)(a(a)(a(b)(b(c)(x1)))) -> a(c)(c(b)(b(a)(a(c)(x1)))) 41.41/10.84 a(a)(a(a)(a(b)(b(a)(x1)))) -> a(c)(c(b)(b(a)(a(a)(x1)))) 41.41/10.84 a(a)(a(a)(a(b)(b(b)(x1)))) -> a(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.84 b(a)(a(a)(a(b)(b(c)(x1)))) -> b(c)(c(b)(b(a)(a(c)(x1)))) 41.41/10.85 b(a)(a(a)(a(b)(b(a)(x1)))) -> b(c)(c(b)(b(a)(a(a)(x1)))) 41.41/10.85 b(a)(a(a)(a(b)(b(b)(x1)))) -> b(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.85 a(b)(b(a)(a(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 41.41/10.85 a(b)(b(a)(a(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 41.41/10.85 a(b)(b(a)(a(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 41.41/10.85 Matrix Interpretation Processor: dim=1 41.41/10.85 41.41/10.85 interpretation: 41.41/10.85 [a(b)](x0) = 4x0 + 6, 41.41/10.85 41.41/10.85 [b(b)](x0) = x0, 41.41/10.85 41.41/10.85 [b(a)](x0) = x0, 41.41/10.85 41.41/10.85 [b(c)](x0) = x0, 41.41/10.85 41.41/10.85 [c(b)](x0) = 2x0 + 2, 41.41/10.85 41.41/10.85 [a(c)](x0) = 2x0, 41.41/10.85 41.41/10.85 [a(a)](x0) = 2x0 + 2, 41.41/10.85 41.41/10.85 [c(a)](x0) = 2x0 + 3, 41.41/10.85 41.41/10.85 [c(c)](x0) = 2x0 + 1 41.41/10.85 orientation: 41.41/10.85 c(c)(c(c)(c(c)(c(c)(x1)))) = 16x1 + 15 >= 16x1 + 15 = c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.85 41.41/10.85 c(c)(c(c)(c(c)(c(a)(x1)))) = 16x1 + 31 >= 16x1 + 31 = c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.85 41.41/10.85 c(c)(c(c)(c(c)(c(b)(x1)))) = 16x1 + 23 >= 16x1 + 23 = c(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.85 41.41/10.85 a(c)(c(c)(c(c)(c(c)(x1)))) = 16x1 + 14 >= 16x1 + 14 = a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.85 41.41/10.85 a(c)(c(c)(c(c)(c(a)(x1)))) = 16x1 + 30 >= 16x1 + 30 = a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.85 41.41/10.85 a(c)(c(c)(c(c)(c(b)(x1)))) = 16x1 + 22 >= 16x1 + 22 = a(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.85 41.41/10.85 b(c)(c(c)(c(c)(c(c)(x1)))) = 8x1 + 7 >= 8x1 + 6 = b(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.85 41.41/10.85 b(c)(c(c)(c(c)(c(a)(x1)))) = 8x1 + 15 >= 8x1 + 14 = b(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.85 41.41/10.85 b(c)(c(c)(c(c)(c(b)(x1)))) = 8x1 + 11 >= 8x1 + 10 = b(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.85 41.41/10.85 b(a)(a(a)(a(c)(x1))) = 4x1 + 2 >= 2x1 + 1 = b(b)(b(c)(c(c)(x1))) 41.41/10.85 41.41/10.85 b(a)(a(a)(a(a)(x1))) = 4x1 + 6 >= 2x1 + 3 = b(b)(b(c)(c(a)(x1))) 41.41/10.85 41.41/10.85 b(a)(a(a)(a(b)(x1))) = 8x1 + 14 >= 2x1 + 2 = b(b)(b(c)(c(b)(x1))) 41.41/10.85 41.41/10.85 c(c)(c(a)(a(c)(c(c)(x1)))) = 16x1 + 15 >= 16x1 + 15 = c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.85 41.41/10.85 c(c)(c(a)(a(c)(c(a)(x1)))) = 16x1 + 31 >= 16x1 + 31 = c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.85 41.41/10.85 c(c)(c(a)(a(c)(c(b)(x1)))) = 16x1 + 23 >= 16x1 + 23 = c(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.85 41.41/10.85 a(c)(c(a)(a(c)(c(c)(x1)))) = 16x1 + 14 >= 16x1 + 14 = a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.85 41.41/10.85 a(c)(c(a)(a(c)(c(a)(x1)))) = 16x1 + 30 >= 16x1 + 30 = a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.85 41.41/10.85 a(c)(c(a)(a(c)(c(b)(x1)))) = 16x1 + 22 >= 16x1 + 22 = a(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.85 41.41/10.85 b(c)(c(a)(a(c)(c(c)(x1)))) = 8x1 + 7 >= 8x1 + 6 = b(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.85 41.41/10.85 b(c)(c(a)(a(c)(c(a)(x1)))) = 8x1 + 15 >= 8x1 + 14 = b(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.85 41.41/10.85 b(c)(c(a)(a(c)(c(b)(x1)))) = 8x1 + 11 >= 8x1 + 10 = b(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.85 41.41/10.85 b(c)(c(c)(c(c)(x1))) = 4x1 + 3 >= 2x1 + 2 = b(c)(c(b)(b(c)(x1))) 41.41/10.85 41.41/10.85 b(c)(c(c)(c(a)(x1))) = 4x1 + 7 >= 2x1 + 2 = b(c)(c(b)(b(a)(x1))) 41.41/10.85 41.41/10.85 b(c)(c(c)(c(b)(x1))) = 4x1 + 5 >= 2x1 + 2 = b(c)(c(b)(b(b)(x1))) 41.41/10.85 41.41/10.85 c(a)(a(a)(a(b)(b(c)(x1)))) = 16x1 + 31 >= 8x1 + 5 = c(c)(c(b)(b(a)(a(c)(x1)))) 41.41/10.85 41.41/10.85 c(a)(a(a)(a(b)(b(a)(x1)))) = 16x1 + 31 >= 8x1 + 13 = c(c)(c(b)(b(a)(a(a)(x1)))) 41.41/10.85 41.41/10.85 c(a)(a(a)(a(b)(b(b)(x1)))) = 16x1 + 31 >= 16x1 + 29 = c(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.85 41.41/10.85 a(a)(a(a)(a(b)(b(c)(x1)))) = 16x1 + 30 >= 8x1 + 4 = a(c)(c(b)(b(a)(a(c)(x1)))) 41.41/10.85 41.41/10.85 a(a)(a(a)(a(b)(b(a)(x1)))) = 16x1 + 30 >= 8x1 + 12 = a(c)(c(b)(b(a)(a(a)(x1)))) 41.41/10.85 41.41/10.85 a(a)(a(a)(a(b)(b(b)(x1)))) = 16x1 + 30 >= 16x1 + 28 = a(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.85 41.41/10.85 b(a)(a(a)(a(b)(b(c)(x1)))) = 8x1 + 14 >= 4x1 + 2 = b(c)(c(b)(b(a)(a(c)(x1)))) 41.41/10.85 41.41/10.85 b(a)(a(a)(a(b)(b(a)(x1)))) = 8x1 + 14 >= 4x1 + 6 = b(c)(c(b)(b(a)(a(a)(x1)))) 41.41/10.85 41.41/10.85 b(a)(a(a)(a(b)(b(b)(x1)))) = 8x1 + 14 >= 8x1 + 14 = b(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.85 41.41/10.85 a(b)(b(a)(a(c)(x1))) = 8x1 + 6 >= 8x1 + 6 = a(c)(c(c)(c(c)(x1))) 41.41/10.85 41.41/10.85 a(b)(b(a)(a(a)(x1))) = 8x1 + 14 >= 8x1 + 14 = a(c)(c(c)(c(a)(x1))) 41.41/10.85 41.41/10.85 a(b)(b(a)(a(b)(x1))) = 16x1 + 30 >= 8x1 + 10 = a(c)(c(c)(c(b)(x1))) 41.41/10.85 problem: 41.41/10.85 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.85 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.85 c(c)(c(c)(c(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.85 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.85 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.86 a(c)(c(c)(c(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.86 c(c)(c(a)(a(c)(c(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.86 c(c)(c(a)(a(c)(c(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.86 c(c)(c(a)(a(c)(c(b)(x1)))) -> c(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.86 a(c)(c(a)(a(c)(c(c)(x1)))) -> a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.86 a(c)(c(a)(a(c)(c(a)(x1)))) -> a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.86 a(c)(c(a)(a(c)(c(b)(x1)))) -> a(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.86 b(a)(a(a)(a(b)(b(b)(x1)))) -> b(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.86 a(b)(b(a)(a(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 41.41/10.86 a(b)(b(a)(a(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 41.41/10.86 Matrix Interpretation Processor: dim=1 41.41/10.86 41.41/10.86 interpretation: 41.41/10.86 [a(b)](x0) = 2x0 + 1, 41.41/10.86 41.41/10.86 [b(b)](x0) = x0 + 2, 41.41/10.86 41.41/10.86 [b(a)](x0) = 2x0 + 4, 41.41/10.86 41.41/10.86 [b(c)](x0) = x0, 41.41/10.86 41.41/10.86 [c(b)](x0) = 2x0 + 2, 41.41/10.86 41.41/10.86 [a(c)](x0) = 2x0, 41.41/10.86 41.41/10.86 [a(a)](x0) = 2x0 + 2, 41.41/10.86 41.41/10.86 [c(a)](x0) = 2x0 + 3, 41.41/10.86 41.41/10.86 [c(c)](x0) = 2x0 + 1 41.41/10.86 orientation: 41.41/10.86 c(c)(c(c)(c(c)(c(c)(x1)))) = 16x1 + 15 >= 16x1 + 15 = c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.86 41.41/10.86 c(c)(c(c)(c(c)(c(a)(x1)))) = 16x1 + 31 >= 16x1 + 31 = c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.86 41.41/10.86 c(c)(c(c)(c(c)(c(b)(x1)))) = 16x1 + 23 >= 16x1 + 23 = c(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.86 41.41/10.86 a(c)(c(c)(c(c)(c(c)(x1)))) = 16x1 + 14 >= 16x1 + 14 = a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.86 41.41/10.86 a(c)(c(c)(c(c)(c(a)(x1)))) = 16x1 + 30 >= 16x1 + 30 = a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.86 41.41/10.86 a(c)(c(c)(c(c)(c(b)(x1)))) = 16x1 + 22 >= 16x1 + 22 = a(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.86 41.41/10.86 c(c)(c(a)(a(c)(c(c)(x1)))) = 16x1 + 15 >= 16x1 + 15 = c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.86 41.41/10.86 c(c)(c(a)(a(c)(c(a)(x1)))) = 16x1 + 31 >= 16x1 + 31 = c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.86 41.41/10.86 c(c)(c(a)(a(c)(c(b)(x1)))) = 16x1 + 23 >= 16x1 + 23 = c(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.86 41.41/10.86 a(c)(c(a)(a(c)(c(c)(x1)))) = 16x1 + 14 >= 16x1 + 14 = a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.86 41.41/10.86 a(c)(c(a)(a(c)(c(a)(x1)))) = 16x1 + 30 >= 16x1 + 30 = a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.86 41.41/10.86 a(c)(c(a)(a(c)(c(b)(x1)))) = 16x1 + 22 >= 16x1 + 22 = a(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.86 41.41/10.86 b(a)(a(a)(a(b)(b(b)(x1)))) = 8x1 + 28 >= 8x1 + 14 = b(c)(c(b)(b(a)(a(b)(x1)))) 41.41/10.86 41.41/10.86 a(b)(b(a)(a(c)(x1))) = 8x1 + 9 >= 8x1 + 6 = a(c)(c(c)(c(c)(x1))) 41.41/10.86 41.41/10.86 a(b)(b(a)(a(a)(x1))) = 8x1 + 17 >= 8x1 + 14 = a(c)(c(c)(c(a)(x1))) 41.41/10.86 problem: 41.41/10.86 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.86 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.86 c(c)(c(c)(c(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.86 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.86 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.86 a(c)(c(c)(c(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.86 c(c)(c(a)(a(c)(c(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.86 c(c)(c(a)(a(c)(c(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.86 c(c)(c(a)(a(c)(c(b)(x1)))) -> c(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.86 a(c)(c(a)(a(c)(c(c)(x1)))) -> a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.86 a(c)(c(a)(a(c)(c(a)(x1)))) -> a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.86 a(c)(c(a)(a(c)(c(b)(x1)))) -> a(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.86 Matrix Interpretation Processor: dim=1 41.41/10.86 41.41/10.86 interpretation: 41.41/10.86 [c(b)](x0) = x0 + 2, 41.41/10.86 41.41/10.86 [a(c)](x0) = x0, 41.41/10.86 41.41/10.86 [a(a)](x0) = x0, 41.41/10.86 41.41/10.86 [c(a)](x0) = 2x0, 41.41/10.86 41.41/10.86 [c(c)](x0) = 2x0 41.41/10.86 orientation: 41.41/10.86 c(c)(c(c)(c(c)(c(c)(x1)))) = 16x1 >= 4x1 = c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.86 41.41/10.86 c(c)(c(c)(c(c)(c(a)(x1)))) = 16x1 >= 4x1 = c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.86 41.41/10.86 c(c)(c(c)(c(c)(c(b)(x1)))) = 8x1 + 16 >= 2x1 + 4 = c(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.86 41.41/10.86 a(c)(c(c)(c(c)(c(c)(x1)))) = 8x1 >= 2x1 = a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.86 41.41/10.86 a(c)(c(c)(c(c)(c(a)(x1)))) = 8x1 >= 2x1 = a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.86 41.41/10.86 a(c)(c(c)(c(c)(c(b)(x1)))) = 4x1 + 8 >= x1 + 2 = a(a)(a(a)(a(c)(c(b)(x1)))) 41.41/10.86 41.41/10.86 c(c)(c(a)(a(c)(c(c)(x1)))) = 8x1 >= 8x1 = c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.86 41.41/10.86 c(c)(c(a)(a(c)(c(a)(x1)))) = 8x1 >= 8x1 = c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.86 41.41/10.86 c(c)(c(a)(a(c)(c(b)(x1)))) = 4x1 + 8 >= 4x1 + 8 = c(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.87 41.41/10.87 a(c)(c(a)(a(c)(c(c)(x1)))) = 4x1 >= 4x1 = a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.87 41.41/10.87 a(c)(c(a)(a(c)(c(a)(x1)))) = 4x1 >= 4x1 = a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.87 41.41/10.87 a(c)(c(a)(a(c)(c(b)(x1)))) = 2x1 + 4 >= 2x1 + 4 = a(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.87 problem: 41.41/10.87 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.87 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.87 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.87 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.87 c(c)(c(a)(a(c)(c(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.87 c(c)(c(a)(a(c)(c(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.87 c(c)(c(a)(a(c)(c(b)(x1)))) -> c(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.87 a(c)(c(a)(a(c)(c(c)(x1)))) -> a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.87 a(c)(c(a)(a(c)(c(a)(x1)))) -> a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.87 a(c)(c(a)(a(c)(c(b)(x1)))) -> a(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.87 Matrix Interpretation Processor: dim=3 41.41/10.87 41.41/10.87 interpretation: 41.41/10.87 [1 0 0] [0] 41.41/10.87 [c(b)](x0) = [0 0 0]x0 + [1] 41.41/10.87 [0 0 0] [0], 41.41/10.87 41.41/10.87 [1 1 0] 41.41/10.87 [a(c)](x0) = [0 0 1]x0 41.41/10.87 [0 0 1] , 41.41/10.87 41.41/10.87 [1 0 0] 41.41/10.87 [a(a)](x0) = [0 0 0]x0 41.41/10.87 [0 0 0] , 41.41/10.87 41.41/10.87 [1 0 0] 41.41/10.87 [c(a)](x0) = [0 0 0]x0 41.41/10.87 [0 0 0] , 41.41/10.87 41.41/10.87 [1 0 0] 41.41/10.87 [c(c)](x0) = [0 0 0]x0 41.41/10.87 [1 0 0] 41.41/10.87 orientation: 41.41/10.87 [1 0 0] [1 0 0] 41.41/10.87 c(c)(c(c)(c(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.87 [1 0 0] [0 0 0] 41.41/10.87 41.41/10.87 [1 0 0] [1 0 0] 41.41/10.87 c(c)(c(c)(c(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.87 [1 0 0] [0 0 0] 41.41/10.87 41.41/10.87 [1 0 0] [1 0 0] 41.41/10.87 a(c)(c(c)(c(c)(c(c)(x1)))) = [1 0 0]x1 >= [0 0 0]x1 = a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.87 [1 0 0] [0 0 0] 41.41/10.87 41.41/10.87 [1 0 0] [1 0 0] 41.41/10.87 a(c)(c(c)(c(c)(c(a)(x1)))) = [1 0 0]x1 >= [0 0 0]x1 = a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.87 [1 0 0] [0 0 0] 41.41/10.87 41.41/10.87 [1 0 0] [1 0 0] 41.41/10.87 c(c)(c(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.87 [1 0 0] [0 0 0] 41.41/10.87 41.41/10.87 [1 0 0] [1 0 0] 41.41/10.87 c(c)(c(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.87 [1 0 0] [0 0 0] 41.41/10.87 41.41/10.87 [1 0 0] [1] [1 0 0] 41.41/10.87 c(c)(c(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.87 [1 0 0] [1] [0 0 0] 41.41/10.87 41.41/10.87 [1 0 0] [1 0 0] 41.41/10.87 a(c)(c(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.87 [0 0 0] [0 0 0] 41.41/10.87 41.41/10.87 [1 0 0] [1 0 0] 41.41/10.87 a(c)(c(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.87 [0 0 0] [0 0 0] 41.41/10.87 41.41/10.88 [1 0 0] [1] [1 0 0] 41.41/10.88 a(c)(c(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = a(a)(a(c)(c(c)(c(b)(x1)))) 41.41/10.88 [0 0 0] [0] [0 0 0] 41.41/10.88 problem: 41.41/10.88 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.88 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.88 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.88 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.88 c(c)(c(a)(a(c)(c(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.88 c(c)(c(a)(a(c)(c(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.88 a(c)(c(a)(a(c)(c(c)(x1)))) -> a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.88 a(c)(c(a)(a(c)(c(a)(x1)))) -> a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.88 Matrix Interpretation Processor: dim=3 41.41/10.88 41.41/10.88 interpretation: 41.41/10.88 [1 0 0] [0] 41.41/10.88 [a(c)](x0) = [0 0 0]x0 + [1] 41.41/10.88 [1 0 0] [0], 41.41/10.88 41.41/10.88 [1 0 0] 41.41/10.88 [a(a)](x0) = [0 0 0]x0 41.41/10.88 [1 0 0] , 41.41/10.88 41.41/10.88 [1 1 0] 41.41/10.88 [c(a)](x0) = [0 0 0]x0 41.41/10.88 [1 1 0] , 41.41/10.88 41.41/10.88 [1 0 0] 41.41/10.88 [c(c)](x0) = [1 0 0]x0 41.41/10.88 [1 0 0] 41.41/10.88 orientation: 41.41/10.88 [1 0 0] [1 0 0] 41.41/10.88 c(c)(c(c)(c(c)(c(c)(x1)))) = [1 0 0]x1 >= [0 0 0]x1 = c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.88 [1 0 0] [1 0 0] 41.41/10.88 41.41/10.88 [1 1 0] [1 1 0] 41.41/10.88 c(c)(c(c)(c(c)(c(a)(x1)))) = [1 1 0]x1 >= [0 0 0]x1 = c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.88 [1 1 0] [1 1 0] 41.41/10.88 41.41/10.88 [1 0 0] [0] [1 0 0] 41.41/10.88 a(c)(c(c)(c(c)(c(c)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.88 [1 0 0] [0] [1 0 0] 41.41/10.88 41.41/10.88 [1 1 0] [0] [1 1 0] 41.41/10.88 a(c)(c(c)(c(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.88 [1 1 0] [0] [1 1 0] 41.41/10.88 41.41/10.88 [1 0 0] [1] [1 0 0] [1] 41.41/10.88 c(c)(c(a)(a(c)(c(c)(x1)))) = [1 0 0]x1 + [1] >= [0 0 0]x1 + [0] = c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.88 [1 0 0] [1] [1 0 0] [1] 41.41/10.88 41.41/10.88 [1 1 0] [1] [1 1 0] [1] 41.41/10.88 c(c)(c(a)(a(c)(c(a)(x1)))) = [1 1 0]x1 + [1] >= [0 0 0]x1 + [0] = c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.88 [1 1 0] [1] [1 1 0] [1] 41.41/10.88 41.41/10.88 [1 0 0] [1] [1 0 0] 41.41/10.88 a(c)(c(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = a(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.88 [1 0 0] [1] [1 0 0] 41.41/10.88 41.41/10.88 [1 1 0] [1] [1 1 0] 41.41/10.88 a(c)(c(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = a(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.88 [1 1 0] [1] [1 1 0] 41.41/10.88 problem: 41.41/10.88 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.88 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.88 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.88 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.88 c(c)(c(a)(a(c)(c(c)(x1)))) -> c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.88 c(c)(c(a)(a(c)(c(a)(x1)))) -> c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.88 Matrix Interpretation Processor: dim=1 41.41/10.88 41.41/10.88 interpretation: 41.41/10.88 [a(c)](x0) = 2x0 + 2, 41.41/10.88 41.41/10.88 [a(a)](x0) = x0, 41.41/10.88 41.41/10.88 [c(a)](x0) = 2x0 + 2, 41.41/10.88 41.41/10.88 [c(c)](x0) = 2x0 + 1 41.41/10.88 orientation: 41.41/10.88 c(c)(c(c)(c(c)(c(c)(x1)))) = 16x1 + 15 >= 8x1 + 10 = c(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.88 41.41/10.88 c(c)(c(c)(c(c)(c(a)(x1)))) = 16x1 + 23 >= 8x1 + 14 = c(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.88 41.41/10.88 a(c)(c(c)(c(c)(c(c)(x1)))) = 16x1 + 16 >= 4x1 + 4 = a(a)(a(a)(a(c)(c(c)(x1)))) 41.41/10.88 41.41/10.88 a(c)(c(c)(c(c)(c(a)(x1)))) = 16x1 + 24 >= 4x1 + 6 = a(a)(a(a)(a(c)(c(a)(x1)))) 41.41/10.88 41.41/10.88 c(c)(c(a)(a(c)(c(c)(x1)))) = 16x1 + 21 >= 16x1 + 18 = c(a)(a(c)(c(c)(c(c)(x1)))) 41.41/10.88 41.41/10.88 c(c)(c(a)(a(c)(c(a)(x1)))) = 16x1 + 29 >= 16x1 + 26 = c(a)(a(c)(c(c)(c(a)(x1)))) 41.41/10.88 problem: 41.41/10.88 41.41/10.88 Qed 41.41/10.89 EOF