45.45/11.97 YES 45.45/11.98 45.45/11.98 Problem: 45.45/11.98 strict: 45.45/11.98 c(c(c(x1))) -> c(a(a(x1))) 45.45/11.98 b(a(b(x1))) -> b(b(c(x1))) 45.45/11.98 c(a(a(x1))) -> c(b(a(x1))) 45.45/11.98 b(a(a(x1))) -> a(b(c(x1))) 45.45/11.98 b(b(c(x1))) -> a(a(c(x1))) 45.45/11.98 weak: 45.45/11.98 a(c(c(x1))) -> b(a(c(x1))) 45.45/11.98 45.45/11.98 Proof: 45.45/11.98 Root-Labeling Processor: 45.45/11.98 strict: 45.45/11.98 c(c)(c(c)(c(c)(x1))) -> c(a)(a(a)(a(c)(x1))) 45.45/11.98 c(c)(c(c)(c(a)(x1))) -> c(a)(a(a)(a(a)(x1))) 45.45/11.98 c(c)(c(c)(c(b)(x1))) -> c(a)(a(a)(a(b)(x1))) 45.45/11.98 b(a)(a(b)(b(c)(x1))) -> b(b)(b(c)(c(c)(x1))) 45.45/11.98 b(a)(a(b)(b(a)(x1))) -> b(b)(b(c)(c(a)(x1))) 45.45/11.98 b(a)(a(b)(b(b)(x1))) -> b(b)(b(c)(c(b)(x1))) 45.45/11.98 c(a)(a(a)(a(c)(x1))) -> c(b)(b(a)(a(c)(x1))) 45.45/11.98 c(a)(a(a)(a(a)(x1))) -> c(b)(b(a)(a(a)(x1))) 45.45/11.98 c(a)(a(a)(a(b)(x1))) -> c(b)(b(a)(a(b)(x1))) 45.45/11.98 c(b)(b(a)(a(a)(a(c)(x1)))) -> c(a)(a(b)(b(c)(c(c)(x1)))) 45.45/11.98 c(b)(b(a)(a(a)(a(a)(x1)))) -> c(a)(a(b)(b(c)(c(a)(x1)))) 45.45/11.98 c(b)(b(a)(a(a)(a(b)(x1)))) -> c(a)(a(b)(b(c)(c(b)(x1)))) 45.45/11.98 a(b)(b(a)(a(a)(a(c)(x1)))) -> a(a)(a(b)(b(c)(c(c)(x1)))) 45.45/11.98 a(b)(b(a)(a(a)(a(a)(x1)))) -> a(a)(a(b)(b(c)(c(a)(x1)))) 45.45/11.98 a(b)(b(a)(a(a)(a(b)(x1)))) -> a(a)(a(b)(b(c)(c(b)(x1)))) 45.45/11.98 b(b)(b(a)(a(a)(a(c)(x1)))) -> b(a)(a(b)(b(c)(c(c)(x1)))) 45.45/11.98 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(a)(a(b)(b(c)(c(a)(x1)))) 45.45/11.98 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(a)(a(b)(b(c)(c(b)(x1)))) 45.45/11.98 c(b)(b(b)(b(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 45.45/11.98 c(b)(b(b)(b(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 45.45/11.98 c(b)(b(b)(b(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) 45.45/11.98 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 45.45/11.98 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 45.45/11.98 a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 45.45/11.98 b(b)(b(b)(b(c)(c(c)(x1)))) -> b(a)(a(a)(a(c)(c(c)(x1)))) 45.45/11.98 b(b)(b(b)(b(c)(c(a)(x1)))) -> b(a)(a(a)(a(c)(c(a)(x1)))) 45.45/11.98 b(b)(b(b)(b(c)(c(b)(x1)))) -> b(a)(a(a)(a(c)(c(b)(x1)))) 45.45/11.98 weak: 45.45/11.98 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(b)(b(a)(a(c)(c(c)(x1)))) 45.45/11.98 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(b)(b(a)(a(c)(c(a)(x1)))) 45.45/11.98 c(a)(a(c)(c(c)(c(b)(x1)))) -> c(b)(b(a)(a(c)(c(b)(x1)))) 45.45/11.98 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(b)(b(a)(a(c)(c(c)(x1)))) 45.45/11.98 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(b)(b(a)(a(c)(c(a)(x1)))) 45.45/11.98 a(a)(a(c)(c(c)(c(b)(x1)))) -> a(b)(b(a)(a(c)(c(b)(x1)))) 45.45/11.98 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(b)(b(a)(a(c)(c(c)(x1)))) 45.45/11.98 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 45.45/11.98 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(b)(b(a)(a(c)(c(b)(x1)))) 45.45/11.98 RT Transformation Processor: 45.45/11.98 c(c)(c(c)(c(c)(x1))) -> c(a)(a(a)(a(c)(x1))) 45.45/11.98 c(c)(c(c)(c(a)(x1))) -> c(a)(a(a)(a(a)(x1))) 45.45/11.98 c(c)(c(c)(c(b)(x1))) -> c(a)(a(a)(a(b)(x1))) 45.45/11.98 b(a)(a(b)(b(c)(x1))) -> b(b)(b(c)(c(c)(x1))) 45.45/11.98 b(a)(a(b)(b(a)(x1))) -> b(b)(b(c)(c(a)(x1))) 45.45/11.98 b(a)(a(b)(b(b)(x1))) -> b(b)(b(c)(c(b)(x1))) 45.45/11.98 c(a)(a(a)(a(c)(x1))) -> c(b)(b(a)(a(c)(x1))) 45.45/11.98 c(a)(a(a)(a(a)(x1))) -> c(b)(b(a)(a(a)(x1))) 45.45/11.98 c(a)(a(a)(a(b)(x1))) -> c(b)(b(a)(a(b)(x1))) 45.45/11.98 c(b)(b(a)(a(a)(a(c)(x1)))) -> c(a)(a(b)(b(c)(c(c)(x1)))) 45.45/11.98 c(b)(b(a)(a(a)(a(a)(x1)))) -> c(a)(a(b)(b(c)(c(a)(x1)))) 45.45/11.98 c(b)(b(a)(a(a)(a(b)(x1)))) -> c(a)(a(b)(b(c)(c(b)(x1)))) 45.45/11.98 a(b)(b(a)(a(a)(a(c)(x1)))) -> a(a)(a(b)(b(c)(c(c)(x1)))) 45.45/11.98 a(b)(b(a)(a(a)(a(a)(x1)))) -> a(a)(a(b)(b(c)(c(a)(x1)))) 45.45/11.98 a(b)(b(a)(a(a)(a(b)(x1)))) -> a(a)(a(b)(b(c)(c(b)(x1)))) 45.45/11.98 b(b)(b(a)(a(a)(a(c)(x1)))) -> b(a)(a(b)(b(c)(c(c)(x1)))) 45.45/11.98 b(b)(b(a)(a(a)(a(a)(x1)))) -> b(a)(a(b)(b(c)(c(a)(x1)))) 45.45/11.98 b(b)(b(a)(a(a)(a(b)(x1)))) -> b(a)(a(b)(b(c)(c(b)(x1)))) 45.45/11.98 c(b)(b(b)(b(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 45.45/11.98 c(b)(b(b)(b(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 45.45/11.98 c(b)(b(b)(b(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) 45.45/11.98 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 45.45/11.98 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 45.45/11.98 a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 45.45/11.98 b(b)(b(b)(b(c)(c(c)(x1)))) -> b(a)(a(a)(a(c)(c(c)(x1)))) 45.45/11.98 b(b)(b(b)(b(c)(c(a)(x1)))) -> b(a)(a(a)(a(c)(c(a)(x1)))) 45.45/11.98 b(b)(b(b)(b(c)(c(b)(x1)))) -> b(a)(a(a)(a(c)(c(b)(x1)))) 45.45/11.98 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(b)(b(a)(a(c)(c(c)(x1)))) 45.45/11.98 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(b)(b(a)(a(c)(c(a)(x1)))) 45.45/11.98 c(a)(a(c)(c(c)(c(b)(x1)))) -> c(b)(b(a)(a(c)(c(b)(x1)))) 45.45/11.98 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(b)(b(a)(a(c)(c(c)(x1)))) 45.45/11.98 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(b)(b(a)(a(c)(c(a)(x1)))) 45.45/11.99 a(a)(a(c)(c(c)(c(b)(x1)))) -> a(b)(b(a)(a(c)(c(b)(x1)))) 45.45/11.99 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(b)(b(a)(a(c)(c(c)(x1)))) 45.45/11.99 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 45.45/11.99 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(b)(b(a)(a(c)(c(b)(x1)))) 45.45/11.99 Matrix Interpretation Processor: dim=1 45.45/11.99 45.45/11.99 interpretation: 45.45/11.99 [b(b)](x0) = 2x0 + 1, 45.45/11.99 45.45/11.99 [b(c)](x0) = x0 + 1, 45.45/11.99 45.45/11.99 [b(a)](x0) = 2x0 + 3, 45.45/11.99 45.45/11.99 [a(b)](x0) = 2x0, 45.45/11.99 45.45/11.99 [c(b)](x0) = 2x0, 45.45/11.99 45.45/11.99 [a(c)](x0) = x0, 45.45/11.99 45.45/11.99 [a(a)](x0) = 2x0 + 2, 45.45/11.99 45.45/11.99 [c(a)](x0) = 2x0 + 2, 45.45/11.99 45.45/11.99 [c(c)](x0) = 2x0 + 2 45.45/11.99 orientation: 45.45/11.99 c(c)(c(c)(c(c)(x1))) = 8x1 + 14 >= 4x1 + 6 = c(a)(a(a)(a(c)(x1))) 45.45/11.99 45.45/11.99 c(c)(c(c)(c(a)(x1))) = 8x1 + 14 >= 8x1 + 14 = c(a)(a(a)(a(a)(x1))) 45.45/11.99 45.45/11.99 c(c)(c(c)(c(b)(x1))) = 8x1 + 6 >= 8x1 + 6 = c(a)(a(a)(a(b)(x1))) 45.45/11.99 45.45/11.99 b(a)(a(b)(b(c)(x1))) = 4x1 + 7 >= 4x1 + 7 = b(b)(b(c)(c(c)(x1))) 45.45/11.99 45.45/11.99 b(a)(a(b)(b(a)(x1))) = 8x1 + 15 >= 4x1 + 7 = b(b)(b(c)(c(a)(x1))) 45.45/11.99 45.45/11.99 b(a)(a(b)(b(b)(x1))) = 8x1 + 7 >= 4x1 + 3 = b(b)(b(c)(c(b)(x1))) 45.45/11.99 45.45/11.99 c(a)(a(a)(a(c)(x1))) = 4x1 + 6 >= 4x1 + 6 = c(b)(b(a)(a(c)(x1))) 45.45/11.99 45.45/11.99 c(a)(a(a)(a(a)(x1))) = 8x1 + 14 >= 8x1 + 14 = c(b)(b(a)(a(a)(x1))) 45.45/11.99 45.45/11.99 c(a)(a(a)(a(b)(x1))) = 8x1 + 6 >= 8x1 + 6 = c(b)(b(a)(a(b)(x1))) 45.45/11.99 45.45/11.99 c(b)(b(a)(a(a)(a(c)(x1)))) = 8x1 + 14 >= 8x1 + 14 = c(a)(a(b)(b(c)(c(c)(x1)))) 45.45/11.99 45.45/11.99 c(b)(b(a)(a(a)(a(a)(x1)))) = 16x1 + 30 >= 8x1 + 14 = c(a)(a(b)(b(c)(c(a)(x1)))) 45.45/11.99 45.45/11.99 c(b)(b(a)(a(a)(a(b)(x1)))) = 16x1 + 14 >= 8x1 + 6 = c(a)(a(b)(b(c)(c(b)(x1)))) 45.45/11.99 45.45/11.99 a(b)(b(a)(a(a)(a(c)(x1)))) = 8x1 + 14 >= 8x1 + 14 = a(a)(a(b)(b(c)(c(c)(x1)))) 45.45/11.99 45.45/11.99 a(b)(b(a)(a(a)(a(a)(x1)))) = 16x1 + 30 >= 8x1 + 14 = a(a)(a(b)(b(c)(c(a)(x1)))) 45.45/11.99 45.45/11.99 a(b)(b(a)(a(a)(a(b)(x1)))) = 16x1 + 14 >= 8x1 + 6 = a(a)(a(b)(b(c)(c(b)(x1)))) 45.45/11.99 45.45/11.99 b(b)(b(a)(a(a)(a(c)(x1)))) = 8x1 + 15 >= 8x1 + 15 = b(a)(a(b)(b(c)(c(c)(x1)))) 45.45/11.99 45.45/11.99 b(b)(b(a)(a(a)(a(a)(x1)))) = 16x1 + 31 >= 8x1 + 15 = b(a)(a(b)(b(c)(c(a)(x1)))) 45.45/11.99 45.45/11.99 b(b)(b(a)(a(a)(a(b)(x1)))) = 16x1 + 15 >= 8x1 + 7 = b(a)(a(b)(b(c)(c(b)(x1)))) 45.45/11.99 45.45/11.99 c(b)(b(b)(b(c)(c(c)(x1)))) = 8x1 + 14 >= 8x1 + 14 = c(a)(a(a)(a(c)(c(c)(x1)))) 45.45/11.99 45.45/11.99 c(b)(b(b)(b(c)(c(a)(x1)))) = 8x1 + 14 >= 8x1 + 14 = c(a)(a(a)(a(c)(c(a)(x1)))) 45.45/11.99 45.45/11.99 c(b)(b(b)(b(c)(c(b)(x1)))) = 8x1 + 6 >= 8x1 + 6 = c(a)(a(a)(a(c)(c(b)(x1)))) 45.45/11.99 45.45/11.99 a(b)(b(b)(b(c)(c(c)(x1)))) = 8x1 + 14 >= 8x1 + 14 = a(a)(a(a)(a(c)(c(c)(x1)))) 45.45/11.99 45.45/11.99 a(b)(b(b)(b(c)(c(a)(x1)))) = 8x1 + 14 >= 8x1 + 14 = a(a)(a(a)(a(c)(c(a)(x1)))) 45.45/11.99 45.45/11.99 a(b)(b(b)(b(c)(c(b)(x1)))) = 8x1 + 6 >= 8x1 + 6 = a(a)(a(a)(a(c)(c(b)(x1)))) 45.45/11.99 45.45/11.99 b(b)(b(b)(b(c)(c(c)(x1)))) = 8x1 + 15 >= 8x1 + 15 = b(a)(a(a)(a(c)(c(c)(x1)))) 45.45/11.99 45.45/11.99 b(b)(b(b)(b(c)(c(a)(x1)))) = 8x1 + 15 >= 8x1 + 15 = b(a)(a(a)(a(c)(c(a)(x1)))) 45.45/11.99 45.45/11.99 b(b)(b(b)(b(c)(c(b)(x1)))) = 8x1 + 7 >= 8x1 + 7 = b(a)(a(a)(a(c)(c(b)(x1)))) 45.45/11.99 45.45/11.99 c(a)(a(c)(c(c)(c(c)(x1)))) = 8x1 + 14 >= 8x1 + 14 = c(b)(b(a)(a(c)(c(c)(x1)))) 45.45/11.99 45.45/11.99 c(a)(a(c)(c(c)(c(a)(x1)))) = 8x1 + 14 >= 8x1 + 14 = c(b)(b(a)(a(c)(c(a)(x1)))) 45.45/11.99 45.45/11.99 c(a)(a(c)(c(c)(c(b)(x1)))) = 8x1 + 6 >= 8x1 + 6 = c(b)(b(a)(a(c)(c(b)(x1)))) 45.45/11.99 45.45/11.99 a(a)(a(c)(c(c)(c(c)(x1)))) = 8x1 + 14 >= 8x1 + 14 = a(b)(b(a)(a(c)(c(c)(x1)))) 45.45/11.99 45.45/11.99 a(a)(a(c)(c(c)(c(a)(x1)))) = 8x1 + 14 >= 8x1 + 14 = a(b)(b(a)(a(c)(c(a)(x1)))) 45.45/11.99 45.45/11.99 a(a)(a(c)(c(c)(c(b)(x1)))) = 8x1 + 6 >= 8x1 + 6 = a(b)(b(a)(a(c)(c(b)(x1)))) 45.45/11.99 45.45/11.99 b(a)(a(c)(c(c)(c(c)(x1)))) = 8x1 + 15 >= 8x1 + 15 = b(b)(b(a)(a(c)(c(c)(x1)))) 45.45/11.99 45.45/11.99 b(a)(a(c)(c(c)(c(a)(x1)))) = 8x1 + 15 >= 8x1 + 15 = b(b)(b(a)(a(c)(c(a)(x1)))) 45.45/11.99 45.45/11.99 b(a)(a(c)(c(c)(c(b)(x1)))) = 8x1 + 7 >= 8x1 + 7 = b(b)(b(a)(a(c)(c(b)(x1)))) 45.45/11.99 problem: 45.45/11.99 c(c)(c(c)(c(a)(x1))) -> c(a)(a(a)(a(a)(x1))) 45.45/11.99 c(c)(c(c)(c(b)(x1))) -> c(a)(a(a)(a(b)(x1))) 45.45/11.99 b(a)(a(b)(b(c)(x1))) -> b(b)(b(c)(c(c)(x1))) 45.45/11.99 c(a)(a(a)(a(c)(x1))) -> c(b)(b(a)(a(c)(x1))) 45.45/11.99 c(a)(a(a)(a(a)(x1))) -> c(b)(b(a)(a(a)(x1))) 45.45/11.99 c(a)(a(a)(a(b)(x1))) -> c(b)(b(a)(a(b)(x1))) 45.45/11.99 c(b)(b(a)(a(a)(a(c)(x1)))) -> c(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.00 a(b)(b(a)(a(a)(a(c)(x1)))) -> a(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.00 b(b)(b(a)(a(a)(a(c)(x1)))) -> b(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.00 c(b)(b(b)(b(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.00 c(b)(b(b)(b(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.00 c(b)(b(b)(b(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.00 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.00 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.00 a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.00 b(b)(b(b)(b(c)(c(c)(x1)))) -> b(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.00 b(b)(b(b)(b(c)(c(a)(x1)))) -> b(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.00 b(b)(b(b)(b(c)(c(b)(x1)))) -> b(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.00 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.00 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.00 c(a)(a(c)(c(c)(c(b)(x1)))) -> c(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.00 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.00 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.00 a(a)(a(c)(c(c)(c(b)(x1)))) -> a(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.00 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.00 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.00 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.00 Matrix Interpretation Processor: dim=1 45.80/12.00 45.80/12.00 interpretation: 45.80/12.00 [b(b)](x0) = 2x0 + 1, 45.80/12.00 45.80/12.00 [b(c)](x0) = x0 + 1, 45.80/12.00 45.80/12.00 [b(a)](x0) = x0, 45.80/12.00 45.80/12.00 [a(b)](x0) = 4x0 + 3, 45.80/12.00 45.80/12.00 [c(b)](x0) = 2x0 + 1, 45.80/12.00 45.80/12.00 [a(c)](x0) = 2x0 + 3, 45.80/12.00 45.80/12.00 [a(a)](x0) = 2x0 + 1, 45.80/12.00 45.80/12.00 [c(a)](x0) = x0, 45.80/12.00 45.80/12.00 [c(c)](x0) = 2x0 + 2 45.80/12.00 orientation: 45.80/12.00 c(c)(c(c)(c(a)(x1))) = 4x1 + 6 >= 4x1 + 3 = c(a)(a(a)(a(a)(x1))) 45.80/12.00 45.80/12.00 c(c)(c(c)(c(b)(x1))) = 8x1 + 10 >= 8x1 + 7 = c(a)(a(a)(a(b)(x1))) 45.80/12.00 45.80/12.00 b(a)(a(b)(b(c)(x1))) = 4x1 + 7 >= 4x1 + 7 = b(b)(b(c)(c(c)(x1))) 45.80/12.00 45.80/12.00 c(a)(a(a)(a(c)(x1))) = 4x1 + 7 >= 4x1 + 7 = c(b)(b(a)(a(c)(x1))) 45.80/12.00 45.80/12.00 c(a)(a(a)(a(a)(x1))) = 4x1 + 3 >= 4x1 + 3 = c(b)(b(a)(a(a)(x1))) 45.80/12.00 45.80/12.00 c(a)(a(a)(a(b)(x1))) = 8x1 + 7 >= 8x1 + 7 = c(b)(b(a)(a(b)(x1))) 45.80/12.00 45.80/12.00 c(b)(b(a)(a(a)(a(c)(x1)))) = 8x1 + 15 >= 8x1 + 15 = c(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.00 45.80/12.00 a(b)(b(a)(a(a)(a(c)(x1)))) = 16x1 + 31 >= 16x1 + 31 = a(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.00 45.80/12.00 b(b)(b(a)(a(a)(a(c)(x1)))) = 8x1 + 15 >= 8x1 + 15 = b(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.00 45.80/12.00 c(b)(b(b)(b(c)(c(c)(x1)))) = 8x1 + 15 >= 8x1 + 15 = c(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.00 45.80/12.00 c(b)(b(b)(b(c)(c(a)(x1)))) = 4x1 + 7 >= 4x1 + 7 = c(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.00 45.80/12.00 c(b)(b(b)(b(c)(c(b)(x1)))) = 8x1 + 11 >= 8x1 + 11 = c(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.00 45.80/12.00 a(b)(b(b)(b(c)(c(c)(x1)))) = 16x1 + 31 >= 16x1 + 31 = a(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.00 45.80/12.00 a(b)(b(b)(b(c)(c(a)(x1)))) = 8x1 + 15 >= 8x1 + 15 = a(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.00 45.80/12.00 a(b)(b(b)(b(c)(c(b)(x1)))) = 16x1 + 23 >= 16x1 + 23 = a(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.00 45.80/12.00 b(b)(b(b)(b(c)(c(c)(x1)))) = 8x1 + 15 >= 8x1 + 15 = b(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.00 45.80/12.00 b(b)(b(b)(b(c)(c(a)(x1)))) = 4x1 + 7 >= 4x1 + 7 = b(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.00 45.80/12.00 b(b)(b(b)(b(c)(c(b)(x1)))) = 8x1 + 11 >= 8x1 + 11 = b(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.00 45.80/12.00 c(a)(a(c)(c(c)(c(c)(x1)))) = 8x1 + 15 >= 8x1 + 15 = c(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.00 45.80/12.00 c(a)(a(c)(c(c)(c(a)(x1)))) = 4x1 + 7 >= 4x1 + 7 = c(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.00 45.80/12.00 c(a)(a(c)(c(c)(c(b)(x1)))) = 8x1 + 11 >= 8x1 + 11 = c(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.00 45.80/12.00 a(a)(a(c)(c(c)(c(c)(x1)))) = 16x1 + 31 >= 16x1 + 31 = a(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.00 45.80/12.00 a(a)(a(c)(c(c)(c(a)(x1)))) = 8x1 + 15 >= 8x1 + 15 = a(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.00 45.80/12.00 a(a)(a(c)(c(c)(c(b)(x1)))) = 16x1 + 23 >= 16x1 + 23 = a(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.00 45.80/12.00 b(a)(a(c)(c(c)(c(c)(x1)))) = 8x1 + 15 >= 8x1 + 15 = b(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.00 45.80/12.00 b(a)(a(c)(c(c)(c(a)(x1)))) = 4x1 + 7 >= 4x1 + 7 = b(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.00 45.80/12.00 b(a)(a(c)(c(c)(c(b)(x1)))) = 8x1 + 11 >= 8x1 + 11 = b(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.00 problem: 45.80/12.00 b(a)(a(b)(b(c)(x1))) -> b(b)(b(c)(c(c)(x1))) 45.80/12.01 c(a)(a(a)(a(c)(x1))) -> c(b)(b(a)(a(c)(x1))) 45.80/12.01 c(a)(a(a)(a(a)(x1))) -> c(b)(b(a)(a(a)(x1))) 45.80/12.01 c(a)(a(a)(a(b)(x1))) -> c(b)(b(a)(a(b)(x1))) 45.80/12.01 c(b)(b(a)(a(a)(a(c)(x1)))) -> c(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.01 a(b)(b(a)(a(a)(a(c)(x1)))) -> a(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.01 b(b)(b(a)(a(a)(a(c)(x1)))) -> b(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.01 c(b)(b(b)(b(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.01 c(b)(b(b)(b(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.01 c(b)(b(b)(b(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.01 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.01 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.01 a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.01 b(b)(b(b)(b(c)(c(c)(x1)))) -> b(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.01 b(b)(b(b)(b(c)(c(a)(x1)))) -> b(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.01 b(b)(b(b)(b(c)(c(b)(x1)))) -> b(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.01 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.01 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 c(a)(a(c)(c(c)(c(b)(x1)))) -> c(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.01 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.01 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 a(a)(a(c)(c(c)(c(b)(x1)))) -> a(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.01 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.01 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.01 Matrix Interpretation Processor: dim=1 45.80/12.01 45.80/12.01 interpretation: 45.80/12.01 [b(b)](x0) = 2x0, 45.80/12.01 45.80/12.01 [b(c)](x0) = 2x0 + 3, 45.80/12.01 45.80/12.01 [b(a)](x0) = 2x0, 45.80/12.01 45.80/12.01 [a(b)](x0) = 2x0, 45.80/12.01 45.80/12.01 [c(b)](x0) = 2x0, 45.80/12.01 45.80/12.01 [a(c)](x0) = 2x0, 45.80/12.01 45.80/12.01 [a(a)](x0) = 2x0 + 4, 45.80/12.01 45.80/12.01 [c(a)](x0) = 2x0 + 1, 45.80/12.01 45.80/12.01 [c(c)](x0) = 2x0 45.80/12.01 orientation: 45.80/12.01 b(a)(a(b)(b(c)(x1))) = 8x1 + 12 >= 8x1 + 6 = b(b)(b(c)(c(c)(x1))) 45.80/12.01 45.80/12.01 c(a)(a(a)(a(c)(x1))) = 8x1 + 9 >= 8x1 = c(b)(b(a)(a(c)(x1))) 45.80/12.01 45.80/12.01 c(a)(a(a)(a(a)(x1))) = 8x1 + 25 >= 8x1 + 16 = c(b)(b(a)(a(a)(x1))) 45.80/12.01 45.80/12.01 c(a)(a(a)(a(b)(x1))) = 8x1 + 9 >= 8x1 = c(b)(b(a)(a(b)(x1))) 45.80/12.01 45.80/12.01 c(b)(b(a)(a(a)(a(c)(x1)))) = 16x1 + 16 >= 16x1 + 13 = c(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 a(b)(b(a)(a(a)(a(c)(x1)))) = 16x1 + 16 >= 16x1 + 16 = a(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 b(b)(b(a)(a(a)(a(c)(x1)))) = 16x1 + 16 >= 16x1 + 12 = b(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 c(b)(b(b)(b(c)(c(c)(x1)))) = 16x1 + 12 >= 16x1 + 9 = c(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 c(b)(b(b)(b(c)(c(a)(x1)))) = 16x1 + 20 >= 16x1 + 17 = c(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.01 45.80/12.01 c(b)(b(b)(b(c)(c(b)(x1)))) = 16x1 + 12 >= 16x1 + 9 = c(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.01 45.80/12.01 a(b)(b(b)(b(c)(c(c)(x1)))) = 16x1 + 12 >= 16x1 + 12 = a(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 a(b)(b(b)(b(c)(c(a)(x1)))) = 16x1 + 20 >= 16x1 + 20 = a(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.01 45.80/12.01 a(b)(b(b)(b(c)(c(b)(x1)))) = 16x1 + 12 >= 16x1 + 12 = a(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.01 45.80/12.01 b(b)(b(b)(b(c)(c(c)(x1)))) = 16x1 + 12 >= 16x1 + 8 = b(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 b(b)(b(b)(b(c)(c(a)(x1)))) = 16x1 + 20 >= 16x1 + 16 = b(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.01 45.80/12.01 b(b)(b(b)(b(c)(c(b)(x1)))) = 16x1 + 12 >= 16x1 + 8 = b(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.01 45.80/12.01 c(a)(a(c)(c(c)(c(c)(x1)))) = 16x1 + 1 >= 16x1 = c(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 c(a)(a(c)(c(c)(c(a)(x1)))) = 16x1 + 9 >= 16x1 + 8 = c(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 45.80/12.01 c(a)(a(c)(c(c)(c(b)(x1)))) = 16x1 + 1 >= 16x1 = c(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.01 45.80/12.01 a(a)(a(c)(c(c)(c(c)(x1)))) = 16x1 + 4 >= 16x1 = a(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 a(a)(a(c)(c(c)(c(a)(x1)))) = 16x1 + 12 >= 16x1 + 8 = a(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 45.80/12.01 a(a)(a(c)(c(c)(c(b)(x1)))) = 16x1 + 4 >= 16x1 = a(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.01 45.80/12.01 b(a)(a(c)(c(c)(c(c)(x1)))) = 16x1 >= 16x1 = b(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 b(a)(a(c)(c(c)(c(a)(x1)))) = 16x1 + 8 >= 16x1 + 8 = b(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 45.80/12.01 b(a)(a(c)(c(c)(c(b)(x1)))) = 16x1 >= 16x1 = b(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.01 problem: 45.80/12.01 a(b)(b(a)(a(a)(a(c)(x1)))) -> a(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.01 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.01 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.01 a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.01 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.01 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.01 Matrix Interpretation Processor: dim=1 45.80/12.01 45.80/12.01 interpretation: 45.80/12.01 [b(b)](x0) = x0, 45.80/12.01 45.80/12.01 [b(c)](x0) = 4x0 + 7, 45.80/12.01 45.80/12.01 [b(a)](x0) = 4x0 + 3, 45.80/12.01 45.80/12.01 [a(b)](x0) = x0 + 4, 45.80/12.01 45.80/12.01 [c(b)](x0) = x0 + 1, 45.80/12.01 45.80/12.01 [a(c)](x0) = 4x0, 45.80/12.01 45.80/12.01 [a(a)](x0) = x0 + 5, 45.80/12.01 45.80/12.01 [c(a)](x0) = x0, 45.80/12.01 45.80/12.01 [c(c)](x0) = x0 45.80/12.01 orientation: 45.80/12.01 a(b)(b(a)(a(a)(a(c)(x1)))) = 16x1 + 27 >= 4x1 + 16 = a(a)(a(b)(b(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 a(b)(b(b)(b(c)(c(c)(x1)))) = 4x1 + 11 >= 4x1 + 10 = a(a)(a(a)(a(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 a(b)(b(b)(b(c)(c(a)(x1)))) = 4x1 + 11 >= 4x1 + 10 = a(a)(a(a)(a(c)(c(a)(x1)))) 45.80/12.01 45.80/12.01 a(b)(b(b)(b(c)(c(b)(x1)))) = 4x1 + 15 >= 4x1 + 14 = a(a)(a(a)(a(c)(c(b)(x1)))) 45.80/12.01 45.80/12.01 b(a)(a(c)(c(c)(c(c)(x1)))) = 16x1 + 3 >= 16x1 + 3 = b(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.01 45.80/12.01 b(a)(a(c)(c(c)(c(a)(x1)))) = 16x1 + 3 >= 16x1 + 3 = b(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 45.80/12.01 b(a)(a(c)(c(c)(c(b)(x1)))) = 16x1 + 19 >= 16x1 + 19 = b(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.01 problem: 45.80/12.01 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.01 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.01 Matrix Interpretation Processor: dim=3 45.80/12.01 45.80/12.01 interpretation: 45.80/12.01 [1 0 0] 45.80/12.01 [b(b)](x0) = [1 0 0]x0 45.80/12.01 [1 0 0] , 45.80/12.01 45.80/12.01 [1 0 0] 45.80/12.01 [b(a)](x0) = [0 1 0]x0 45.80/12.01 [1 0 0] , 45.80/12.01 45.80/12.01 [1 1 1] [0] 45.80/12.01 [c(b)](x0) = [0 0 0]x0 + [1] 45.80/12.01 [1 1 1] [0], 45.80/12.01 45.80/12.01 [1 0 0] 45.80/12.01 [a(c)](x0) = [0 1 0]x0 45.80/12.01 [0 0 0] , 45.80/12.01 45.80/12.01 [1 0 0] 45.80/12.01 [c(a)](x0) = [0 0 1]x0 45.80/12.01 [1 0 0] , 45.80/12.01 45.80/12.01 [1 1 0] [0] 45.80/12.01 [c(c)](x0) = [0 0 1]x0 + [1] 45.80/12.01 [1 1 0] [0] 45.80/12.01 orientation: 45.80/12.01 [1 1 1] [1] [1 1 0] 45.80/12.01 b(a)(a(c)(c(c)(c(c)(x1)))) = [1 1 0]x1 + [1] >= [1 1 0]x1 = b(b)(b(a)(a(c)(c(c)(x1)))) 45.80/12.01 [1 1 1] [1] [1 1 0] 45.80/12.01 45.80/12.01 [1 0 1] [0] [1 0 0] 45.80/12.01 b(a)(a(c)(c(c)(c(a)(x1)))) = [1 0 0]x1 + [1] >= [1 0 0]x1 = b(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 [1 0 1] [0] [1 0 0] 45.80/12.01 45.80/12.01 [1 1 1] [1] [1 1 1] 45.80/12.01 b(a)(a(c)(c(c)(c(b)(x1)))) = [1 1 1]x1 + [1] >= [1 1 1]x1 = b(b)(b(a)(a(c)(c(b)(x1)))) 45.80/12.01 [1 1 1] [1] [1 1 1] 45.80/12.01 problem: 45.80/12.01 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 Matrix Interpretation Processor: dim=3 45.80/12.01 45.80/12.01 interpretation: 45.80/12.01 [1 0 0] [0] 45.80/12.01 [b(b)](x0) = [0 0 0]x0 + [1] 45.80/12.01 [0 0 0] [0], 45.80/12.01 45.80/12.01 [1 0 1] 45.80/12.01 [b(a)](x0) = [0 1 0]x0 45.80/12.01 [0 0 0] , 45.80/12.01 45.80/12.01 [1 0 0] [0] 45.80/12.01 [a(c)](x0) = [0 0 0]x0 + [1] 45.80/12.01 [0 0 1] [0], 45.80/12.01 45.80/12.01 [1 0 0] 45.80/12.01 [c(a)](x0) = [0 1 0]x0 45.80/12.01 [0 1 0] , 45.80/12.01 45.80/12.01 [1 0 0] [0] 45.80/12.01 [c(c)](x0) = [0 0 0]x0 + [0] 45.80/12.01 [0 1 0] [1] 45.80/12.01 orientation: 45.80/12.01 [1 1 0] [1] [1 1 0] [0] 45.80/12.01 b(a)(a(c)(c(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(b)(b(a)(a(c)(c(a)(x1)))) 45.80/12.01 [0 0 0] [0] [0 0 0] [0] 45.80/12.01 problem: 45.80/12.01 45.80/12.01 Qed 45.80/12.02 EOF