58.81/15.26 YES 58.81/15.27 58.81/15.27 Problem: 58.81/15.27 strict: 58.81/15.27 a(a(c(x1))) -> a(c(c(x1))) 58.81/15.27 b(b(c(x1))) -> a(b(b(x1))) 58.81/15.27 weak: 58.81/15.27 c(c(b(x1))) -> a(c(a(x1))) 58.81/15.27 b(a(c(x1))) -> c(a(c(x1))) 58.81/15.27 c(b(c(x1))) -> b(b(b(x1))) 58.81/15.27 b(b(a(x1))) -> b(a(c(x1))) 58.81/15.27 58.81/15.27 Proof: 58.81/15.27 Root-Labeling Processor: 58.81/15.27 strict: 58.81/15.27 a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 58.81/15.27 a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 58.81/15.27 a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 58.81/15.27 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.27 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.27 a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.27 c(b)(b(b)(b(c)(c(a)(x1)))) -> c(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.27 c(b)(b(b)(b(c)(c(c)(x1)))) -> c(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.27 c(b)(b(b)(b(c)(c(b)(x1)))) -> c(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.27 b(b)(b(b)(b(c)(c(a)(x1)))) -> b(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.27 b(b)(b(b)(b(c)(c(c)(x1)))) -> b(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.27 b(b)(b(b)(b(c)(c(b)(x1)))) -> b(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.27 weak: 58.81/15.27 a(c)(c(c)(c(b)(b(a)(x1)))) -> a(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.27 a(c)(c(c)(c(b)(b(c)(x1)))) -> a(a)(a(c)(c(a)(a(c)(x1)))) 58.81/15.27 a(c)(c(c)(c(b)(b(b)(x1)))) -> a(a)(a(c)(c(a)(a(b)(x1)))) 58.81/15.27 c(c)(c(c)(c(b)(b(a)(x1)))) -> c(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.27 c(c)(c(c)(c(b)(b(c)(x1)))) -> c(a)(a(c)(c(a)(a(c)(x1)))) 58.81/15.27 c(c)(c(c)(c(b)(b(b)(x1)))) -> c(a)(a(c)(c(a)(a(b)(x1)))) 58.81/15.27 b(c)(c(c)(c(b)(b(a)(x1)))) -> b(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.27 b(c)(c(c)(c(b)(b(c)(x1)))) -> b(a)(a(c)(c(a)(a(c)(x1)))) 58.81/15.27 b(c)(c(c)(c(b)(b(b)(x1)))) -> b(a)(a(c)(c(a)(a(b)(x1)))) 58.81/15.27 a(b)(b(a)(a(c)(c(a)(x1)))) -> a(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.27 a(b)(b(a)(a(c)(c(c)(x1)))) -> a(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.27 a(b)(b(a)(a(c)(c(b)(x1)))) -> a(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.27 c(b)(b(a)(a(c)(c(a)(x1)))) -> c(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.27 c(b)(b(a)(a(c)(c(c)(x1)))) -> c(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.27 c(b)(b(a)(a(c)(c(b)(x1)))) -> c(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.27 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.27 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.27 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.27 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.27 a(c)(c(b)(b(c)(c(c)(x1)))) -> a(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.27 a(c)(c(b)(b(c)(c(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.27 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.27 c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.27 c(c)(c(b)(b(c)(c(b)(x1)))) -> c(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.27 b(c)(c(b)(b(c)(c(a)(x1)))) -> b(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.27 b(c)(c(b)(b(c)(c(c)(x1)))) -> b(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.27 b(c)(c(b)(b(c)(c(b)(x1)))) -> b(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.27 b(b)(b(a)(a(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 58.81/15.27 b(b)(b(a)(a(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 58.81/15.27 b(b)(b(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 58.81/15.27 RT Transformation Processor: 58.81/15.27 a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 58.81/15.27 a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 58.81/15.27 a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 58.81/15.27 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.27 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.27 a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.27 c(b)(b(b)(b(c)(c(a)(x1)))) -> c(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.27 c(b)(b(b)(b(c)(c(c)(x1)))) -> c(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.27 c(b)(b(b)(b(c)(c(b)(x1)))) -> c(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.27 b(b)(b(b)(b(c)(c(a)(x1)))) -> b(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.27 b(b)(b(b)(b(c)(c(c)(x1)))) -> b(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.27 b(b)(b(b)(b(c)(c(b)(x1)))) -> b(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.27 a(c)(c(c)(c(b)(b(a)(x1)))) -> a(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.27 a(c)(c(c)(c(b)(b(c)(x1)))) -> a(a)(a(c)(c(a)(a(c)(x1)))) 58.81/15.27 a(c)(c(c)(c(b)(b(b)(x1)))) -> a(a)(a(c)(c(a)(a(b)(x1)))) 58.81/15.27 c(c)(c(c)(c(b)(b(a)(x1)))) -> c(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.27 c(c)(c(c)(c(b)(b(c)(x1)))) -> c(a)(a(c)(c(a)(a(c)(x1)))) 58.81/15.27 c(c)(c(c)(c(b)(b(b)(x1)))) -> c(a)(a(c)(c(a)(a(b)(x1)))) 58.81/15.27 b(c)(c(c)(c(b)(b(a)(x1)))) -> b(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.27 b(c)(c(c)(c(b)(b(c)(x1)))) -> b(a)(a(c)(c(a)(a(c)(x1)))) 58.81/15.27 b(c)(c(c)(c(b)(b(b)(x1)))) -> b(a)(a(c)(c(a)(a(b)(x1)))) 58.81/15.27 a(b)(b(a)(a(c)(c(a)(x1)))) -> a(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.27 a(b)(b(a)(a(c)(c(c)(x1)))) -> a(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.27 a(b)(b(a)(a(c)(c(b)(x1)))) -> a(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.28 c(b)(b(a)(a(c)(c(a)(x1)))) -> c(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.28 c(b)(b(a)(a(c)(c(c)(x1)))) -> c(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.28 c(b)(b(a)(a(c)(c(b)(x1)))) -> c(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.28 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.28 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.28 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.28 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.28 a(c)(c(b)(b(c)(c(c)(x1)))) -> a(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.28 a(c)(c(b)(b(c)(c(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.28 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.28 c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.28 c(c)(c(b)(b(c)(c(b)(x1)))) -> c(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.28 b(c)(c(b)(b(c)(c(a)(x1)))) -> b(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.28 b(c)(c(b)(b(c)(c(c)(x1)))) -> b(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.28 b(c)(c(b)(b(c)(c(b)(x1)))) -> b(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.28 b(b)(b(a)(a(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 58.81/15.28 b(b)(b(a)(a(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 58.81/15.28 b(b)(b(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 58.81/15.28 Matrix Interpretation Processor: dim=1 58.81/15.28 58.81/15.28 interpretation: 58.81/15.28 [b(a)](x0) = x0, 58.81/15.28 58.81/15.28 [b(c)](x0) = 2x0 + 1, 58.81/15.28 58.81/15.28 [b(b)](x0) = 2x0 + 1, 58.81/15.28 58.81/15.28 [a(b)](x0) = x0, 58.81/15.28 58.81/15.28 [c(b)](x0) = 2x0 + 1, 58.81/15.28 58.81/15.28 [c(c)](x0) = 2x0 + 1, 58.81/15.28 58.81/15.28 [c(a)](x0) = x0, 58.81/15.28 58.81/15.28 [a(c)](x0) = x0, 58.81/15.28 58.81/15.28 [a(a)](x0) = 2x0 + 1 58.81/15.28 orientation: 58.81/15.28 a(a)(a(c)(c(a)(x1))) = 2x1 + 1 >= 2x1 + 1 = a(c)(c(c)(c(a)(x1))) 58.81/15.28 58.81/15.28 a(a)(a(c)(c(c)(x1))) = 4x1 + 3 >= 4x1 + 3 = a(c)(c(c)(c(c)(x1))) 58.81/15.28 58.81/15.28 a(a)(a(c)(c(b)(x1))) = 4x1 + 3 >= 4x1 + 3 = a(c)(c(c)(c(b)(x1))) 58.81/15.28 58.81/15.28 a(b)(b(b)(b(c)(c(a)(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.28 58.81/15.28 a(b)(b(b)(b(c)(c(c)(x1)))) = 8x1 + 7 >= 8x1 + 7 = a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.28 58.81/15.28 a(b)(b(b)(b(c)(c(b)(x1)))) = 8x1 + 7 >= 8x1 + 7 = a(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.28 58.81/15.28 c(b)(b(b)(b(c)(c(a)(x1)))) = 8x1 + 7 >= 2x1 + 1 = c(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.28 58.81/15.28 c(b)(b(b)(b(c)(c(c)(x1)))) = 16x1 + 15 >= 4x1 + 3 = c(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.28 58.81/15.28 c(b)(b(b)(b(c)(c(b)(x1)))) = 16x1 + 15 >= 4x1 + 3 = c(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.28 58.81/15.28 b(b)(b(b)(b(c)(c(a)(x1)))) = 8x1 + 7 >= 2x1 + 1 = b(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.28 58.81/15.28 b(b)(b(b)(b(c)(c(c)(x1)))) = 16x1 + 15 >= 4x1 + 3 = b(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.28 58.81/15.28 b(b)(b(b)(b(c)(c(b)(x1)))) = 16x1 + 15 >= 4x1 + 3 = b(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.28 58.81/15.28 a(c)(c(c)(c(b)(b(a)(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.28 58.81/15.28 a(c)(c(c)(c(b)(b(c)(x1)))) = 8x1 + 7 >= 2x1 + 1 = a(a)(a(c)(c(a)(a(c)(x1)))) 58.81/15.28 58.81/15.28 a(c)(c(c)(c(b)(b(b)(x1)))) = 8x1 + 7 >= 2x1 + 1 = a(a)(a(c)(c(a)(a(b)(x1)))) 58.81/15.28 58.81/15.28 c(c)(c(c)(c(b)(b(a)(x1)))) = 8x1 + 7 >= 2x1 + 1 = c(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.28 58.81/15.28 c(c)(c(c)(c(b)(b(c)(x1)))) = 16x1 + 15 >= x1 = c(a)(a(c)(c(a)(a(c)(x1)))) 58.81/15.28 58.81/15.28 c(c)(c(c)(c(b)(b(b)(x1)))) = 16x1 + 15 >= x1 = c(a)(a(c)(c(a)(a(b)(x1)))) 58.81/15.28 58.81/15.28 b(c)(c(c)(c(b)(b(a)(x1)))) = 8x1 + 7 >= 2x1 + 1 = b(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.28 58.81/15.28 b(c)(c(c)(c(b)(b(c)(x1)))) = 16x1 + 15 >= x1 = b(a)(a(c)(c(a)(a(c)(x1)))) 58.81/15.28 58.81/15.28 b(c)(c(c)(c(b)(b(b)(x1)))) = 16x1 + 15 >= x1 = b(a)(a(c)(c(a)(a(b)(x1)))) 58.81/15.28 58.81/15.28 a(b)(b(a)(a(c)(c(a)(x1)))) = x1 >= x1 = a(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.28 58.81/15.28 a(b)(b(a)(a(c)(c(c)(x1)))) = 2x1 + 1 >= 2x1 + 1 = a(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.28 58.81/15.28 a(b)(b(a)(a(c)(c(b)(x1)))) = 2x1 + 1 >= 2x1 + 1 = a(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.28 58.81/15.28 c(b)(b(a)(a(c)(c(a)(x1)))) = 2x1 + 1 >= 2x1 + 1 = c(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.28 58.81/15.28 c(b)(b(a)(a(c)(c(c)(x1)))) = 4x1 + 3 >= 4x1 + 3 = c(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.28 58.81/15.28 c(b)(b(a)(a(c)(c(b)(x1)))) = 4x1 + 3 >= 4x1 + 3 = c(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.28 58.81/15.28 b(b)(b(a)(a(c)(c(a)(x1)))) = 2x1 + 1 >= 2x1 + 1 = b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.28 58.81/15.28 b(b)(b(a)(a(c)(c(c)(x1)))) = 4x1 + 3 >= 4x1 + 3 = b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.28 58.81/15.28 b(b)(b(a)(a(c)(c(b)(x1)))) = 4x1 + 3 >= 4x1 + 3 = b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.28 58.81/15.28 a(c)(c(b)(b(c)(c(a)(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.29 58.81/15.29 a(c)(c(b)(b(c)(c(c)(x1)))) = 8x1 + 7 >= 8x1 + 7 = a(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.29 58.81/15.29 a(c)(c(b)(b(c)(c(b)(x1)))) = 8x1 + 7 >= 8x1 + 7 = a(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.29 58.81/15.29 c(c)(c(b)(b(c)(c(a)(x1)))) = 8x1 + 7 >= 8x1 + 7 = c(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.29 58.81/15.29 c(c)(c(b)(b(c)(c(c)(x1)))) = 16x1 + 15 >= 16x1 + 15 = c(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.29 58.81/15.29 c(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 + 15 >= 16x1 + 15 = c(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.29 58.81/15.29 b(c)(c(b)(b(c)(c(a)(x1)))) = 8x1 + 7 >= 8x1 + 7 = b(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.29 58.81/15.29 b(c)(c(b)(b(c)(c(c)(x1)))) = 16x1 + 15 >= 16x1 + 15 = b(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.29 58.81/15.29 b(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 + 15 >= 16x1 + 15 = b(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.29 58.81/15.29 b(b)(b(a)(a(a)(x1))) = 4x1 + 3 >= x1 = b(a)(a(c)(c(a)(x1))) 58.81/15.29 58.81/15.29 b(b)(b(a)(a(c)(x1))) = 2x1 + 1 >= 2x1 + 1 = b(a)(a(c)(c(c)(x1))) 58.81/15.29 58.81/15.29 b(b)(b(a)(a(b)(x1))) = 2x1 + 1 >= 2x1 + 1 = b(a)(a(c)(c(b)(x1))) 58.81/15.29 problem: 58.81/15.29 a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 58.81/15.29 a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 58.81/15.29 a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 58.81/15.29 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.29 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.29 a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.29 a(c)(c(c)(c(b)(b(a)(x1)))) -> a(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.29 a(b)(b(a)(a(c)(c(a)(x1)))) -> a(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.29 a(b)(b(a)(a(c)(c(c)(x1)))) -> a(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.29 a(b)(b(a)(a(c)(c(b)(x1)))) -> a(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.29 c(b)(b(a)(a(c)(c(a)(x1)))) -> c(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.29 c(b)(b(a)(a(c)(c(c)(x1)))) -> c(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.29 c(b)(b(a)(a(c)(c(b)(x1)))) -> c(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.29 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.29 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.29 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.29 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.29 a(c)(c(b)(b(c)(c(c)(x1)))) -> a(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.29 a(c)(c(b)(b(c)(c(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.29 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.29 c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.29 c(c)(c(b)(b(c)(c(b)(x1)))) -> c(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.29 b(c)(c(b)(b(c)(c(a)(x1)))) -> b(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.29 b(c)(c(b)(b(c)(c(c)(x1)))) -> b(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.29 b(c)(c(b)(b(c)(c(b)(x1)))) -> b(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.29 b(b)(b(a)(a(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 58.81/15.29 b(b)(b(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 58.81/15.29 Matrix Interpretation Processor: dim=1 58.81/15.29 58.81/15.29 interpretation: 58.81/15.29 [b(a)](x0) = x0, 58.81/15.29 58.81/15.29 [b(c)](x0) = x0, 58.81/15.29 58.81/15.29 [b(b)](x0) = x0, 58.81/15.29 58.81/15.29 [a(b)](x0) = 4x0 + 4, 58.81/15.29 58.81/15.29 [c(b)](x0) = 4x0, 58.81/15.29 58.81/15.29 [c(c)](x0) = x0, 58.81/15.29 58.81/15.29 [c(a)](x0) = x0, 58.81/15.29 58.81/15.29 [a(c)](x0) = x0 + 4, 58.81/15.29 58.81/15.29 [a(a)](x0) = x0 58.81/15.29 orientation: 58.81/15.29 a(a)(a(c)(c(a)(x1))) = x1 + 4 >= x1 + 4 = a(c)(c(c)(c(a)(x1))) 58.81/15.29 58.81/15.29 a(a)(a(c)(c(c)(x1))) = x1 + 4 >= x1 + 4 = a(c)(c(c)(c(c)(x1))) 58.81/15.29 58.81/15.29 a(a)(a(c)(c(b)(x1))) = 4x1 + 4 >= 4x1 + 4 = a(c)(c(c)(c(b)(x1))) 58.81/15.29 58.81/15.29 a(b)(b(b)(b(c)(c(a)(x1)))) = 4x1 + 4 >= 4x1 + 4 = a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.29 58.81/15.29 a(b)(b(b)(b(c)(c(c)(x1)))) = 4x1 + 4 >= 4x1 + 4 = a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.29 58.81/15.29 a(b)(b(b)(b(c)(c(b)(x1)))) = 16x1 + 4 >= 4x1 + 4 = a(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.29 58.81/15.29 a(c)(c(c)(c(b)(b(a)(x1)))) = 4x1 + 4 >= x1 + 4 = a(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.29 58.81/15.29 a(b)(b(a)(a(c)(c(a)(x1)))) = 4x1 + 20 >= x1 + 8 = a(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.29 58.81/15.29 a(b)(b(a)(a(c)(c(c)(x1)))) = 4x1 + 20 >= x1 + 8 = a(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.29 58.81/15.29 a(b)(b(a)(a(c)(c(b)(x1)))) = 16x1 + 20 >= 4x1 + 8 = a(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.29 58.81/15.29 c(b)(b(a)(a(c)(c(a)(x1)))) = 4x1 + 16 >= x1 + 4 = c(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.29 58.81/15.29 c(b)(b(a)(a(c)(c(c)(x1)))) = 4x1 + 16 >= x1 + 4 = c(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.29 58.81/15.29 c(b)(b(a)(a(c)(c(b)(x1)))) = 16x1 + 16 >= 4x1 + 4 = c(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.29 58.81/15.29 b(b)(b(a)(a(c)(c(a)(x1)))) = x1 + 4 >= x1 + 4 = b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.30 58.81/15.30 b(b)(b(a)(a(c)(c(c)(x1)))) = x1 + 4 >= x1 + 4 = b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.30 58.81/15.30 b(b)(b(a)(a(c)(c(b)(x1)))) = 4x1 + 4 >= 4x1 + 4 = b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.30 58.81/15.30 a(c)(c(b)(b(c)(c(a)(x1)))) = 4x1 + 4 >= 4x1 + 4 = a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.30 58.81/15.30 a(c)(c(b)(b(c)(c(c)(x1)))) = 4x1 + 4 >= 4x1 + 4 = a(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.30 58.81/15.30 a(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 + 4 >= 4x1 + 4 = a(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.30 58.81/15.30 c(c)(c(b)(b(c)(c(a)(x1)))) = 4x1 >= 4x1 = c(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.30 58.81/15.30 c(c)(c(b)(b(c)(c(c)(x1)))) = 4x1 >= 4x1 = c(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.30 58.81/15.30 c(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 >= 4x1 = c(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.30 58.81/15.30 b(c)(c(b)(b(c)(c(a)(x1)))) = 4x1 >= x1 = b(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.30 58.81/15.30 b(c)(c(b)(b(c)(c(c)(x1)))) = 4x1 >= x1 = b(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.30 58.81/15.30 b(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 >= x1 = b(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.30 58.81/15.30 b(b)(b(a)(a(c)(x1))) = x1 + 4 >= x1 + 4 = b(a)(a(c)(c(c)(x1))) 58.81/15.30 58.81/15.30 b(b)(b(a)(a(b)(x1))) = 4x1 + 4 >= 4x1 + 4 = b(a)(a(c)(c(b)(x1))) 58.81/15.30 problem: 58.81/15.30 a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 58.81/15.30 a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 58.81/15.30 a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 58.81/15.30 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.30 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.30 a(b)(b(b)(b(c)(c(b)(x1)))) -> a(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.30 a(c)(c(c)(c(b)(b(a)(x1)))) -> a(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.30 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.30 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.30 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.30 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.30 a(c)(c(b)(b(c)(c(c)(x1)))) -> a(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.30 a(c)(c(b)(b(c)(c(b)(x1)))) -> a(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.30 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.30 c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.30 c(c)(c(b)(b(c)(c(b)(x1)))) -> c(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.30 b(c)(c(b)(b(c)(c(a)(x1)))) -> b(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.30 b(c)(c(b)(b(c)(c(c)(x1)))) -> b(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.30 b(c)(c(b)(b(c)(c(b)(x1)))) -> b(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.30 b(b)(b(a)(a(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 58.81/15.30 b(b)(b(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 58.81/15.30 Matrix Interpretation Processor: dim=1 58.81/15.30 58.81/15.30 interpretation: 58.81/15.30 [b(a)](x0) = 4x0 + 1, 58.81/15.30 58.81/15.30 [b(c)](x0) = 2x0 + 1, 58.81/15.30 58.81/15.30 [b(b)](x0) = x0, 58.81/15.30 58.81/15.30 [a(b)](x0) = 4x0, 58.81/15.30 58.81/15.30 [c(b)](x0) = 2x0, 58.81/15.30 58.81/15.30 [c(c)](x0) = x0, 58.81/15.30 58.81/15.30 [c(a)](x0) = 2x0, 58.81/15.30 58.81/15.30 [a(c)](x0) = 2x0, 58.81/15.30 58.81/15.30 [a(a)](x0) = x0 58.81/15.30 orientation: 58.81/15.30 a(a)(a(c)(c(a)(x1))) = 4x1 >= 4x1 = a(c)(c(c)(c(a)(x1))) 58.81/15.30 58.81/15.30 a(a)(a(c)(c(c)(x1))) = 2x1 >= 2x1 = a(c)(c(c)(c(c)(x1))) 58.81/15.30 58.81/15.30 a(a)(a(c)(c(b)(x1))) = 4x1 >= 4x1 = a(c)(c(c)(c(b)(x1))) 58.81/15.30 58.81/15.30 a(b)(b(b)(b(c)(c(a)(x1)))) = 16x1 + 4 >= 16x1 + 4 = a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.30 58.81/15.30 a(b)(b(b)(b(c)(c(c)(x1)))) = 8x1 + 4 >= 8x1 + 4 = a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.30 58.81/15.30 a(b)(b(b)(b(c)(c(b)(x1)))) = 16x1 + 4 >= 4x1 = a(a)(a(b)(b(b)(b(b)(x1)))) 58.81/15.30 58.81/15.30 a(c)(c(c)(c(b)(b(a)(x1)))) = 16x1 + 4 >= 4x1 = a(a)(a(c)(c(a)(a(a)(x1)))) 58.81/15.30 58.81/15.30 b(b)(b(a)(a(c)(c(a)(x1)))) = 16x1 + 1 >= 16x1 + 1 = b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.30 58.81/15.30 b(b)(b(a)(a(c)(c(c)(x1)))) = 8x1 + 1 >= 8x1 + 1 = b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.30 58.81/15.30 b(b)(b(a)(a(c)(c(b)(x1)))) = 16x1 + 1 >= 16x1 + 1 = b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.30 58.81/15.30 a(c)(c(b)(b(c)(c(a)(x1)))) = 16x1 + 4 >= 16x1 + 4 = a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.30 58.81/15.30 a(c)(c(b)(b(c)(c(c)(x1)))) = 8x1 + 4 >= 8x1 + 4 = a(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.30 58.81/15.30 a(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 + 4 >= 4x1 = a(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.30 58.81/15.30 c(c)(c(b)(b(c)(c(a)(x1)))) = 8x1 + 2 >= 8x1 + 2 = c(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.30 58.81/15.30 c(c)(c(b)(b(c)(c(c)(x1)))) = 4x1 + 2 >= 4x1 + 2 = c(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.31 58.81/15.31 c(c)(c(b)(b(c)(c(b)(x1)))) = 8x1 + 2 >= 2x1 = c(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.31 58.81/15.31 b(c)(c(b)(b(c)(c(a)(x1)))) = 16x1 + 5 >= 4x1 + 1 = b(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.31 58.81/15.31 b(c)(c(b)(b(c)(c(c)(x1)))) = 8x1 + 5 >= 2x1 + 1 = b(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.31 58.81/15.31 b(c)(c(b)(b(c)(c(b)(x1)))) = 16x1 + 5 >= x1 = b(b)(b(b)(b(b)(b(b)(x1)))) 58.81/15.31 58.81/15.31 b(b)(b(a)(a(c)(x1))) = 8x1 + 1 >= 8x1 + 1 = b(a)(a(c)(c(c)(x1))) 58.81/15.31 58.81/15.31 b(b)(b(a)(a(b)(x1))) = 16x1 + 1 >= 16x1 + 1 = b(a)(a(c)(c(b)(x1))) 58.81/15.31 problem: 58.81/15.31 a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 58.81/15.31 a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 58.81/15.31 a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 58.81/15.31 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.31 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.31 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.31 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.31 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.31 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.31 a(c)(c(b)(b(c)(c(c)(x1)))) -> a(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.31 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.31 c(c)(c(b)(b(c)(c(c)(x1)))) -> c(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.31 b(b)(b(a)(a(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 58.81/15.31 b(b)(b(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 58.81/15.31 Matrix Interpretation Processor: dim=3 58.81/15.31 58.81/15.31 interpretation: 58.81/15.31 [1 0 1] 58.81/15.31 [b(a)](x0) = [0 0 0]x0 58.81/15.31 [0 0 0] , 58.81/15.31 58.81/15.31 [1 0 1] 58.81/15.31 [b(c)](x0) = [0 1 0]x0 58.81/15.31 [0 0 0] , 58.81/15.31 58.81/15.31 [1 0 0] 58.81/15.31 [b(b)](x0) = [0 0 0]x0 58.81/15.31 [0 0 0] , 58.81/15.31 58.81/15.31 [1 1 0] 58.81/15.31 [a(b)](x0) = [0 0 0]x0 58.81/15.31 [0 0 1] , 58.81/15.31 58.81/15.31 [1 1 0] 58.81/15.31 [c(b)](x0) = [0 1 0]x0 58.81/15.31 [0 0 1] , 58.81/15.31 58.81/15.31 [1 0 0] [0] 58.81/15.31 [c(c)](x0) = [0 0 0]x0 + [1] 58.81/15.31 [0 0 1] [0], 58.81/15.31 58.81/15.31 58.81/15.31 [c(a)](x0) = x0 58.81/15.31 , 58.81/15.31 58.81/15.31 [1 0 0] 58.81/15.31 [a(c)](x0) = [0 0 0]x0 58.81/15.31 [0 0 1] , 58.81/15.31 58.81/15.31 [1 0 0] 58.81/15.31 [a(a)](x0) = [0 0 1]x0 58.81/15.31 [0 0 1] 58.81/15.31 orientation: 58.81/15.31 [1 0 0] [1 0 0] 58.81/15.31 a(a)(a(c)(c(a)(x1))) = [0 0 1]x1 >= [0 0 0]x1 = a(c)(c(c)(c(a)(x1))) 58.81/15.31 [0 0 1] [0 0 1] 58.81/15.31 58.81/15.31 [1 0 0] [1 0 0] 58.81/15.31 a(a)(a(c)(c(c)(x1))) = [0 0 1]x1 >= [0 0 0]x1 = a(c)(c(c)(c(c)(x1))) 58.81/15.31 [0 0 1] [0 0 1] 58.81/15.31 58.81/15.31 [1 1 0] [1 1 0] 58.81/15.31 a(a)(a(c)(c(b)(x1))) = [0 0 1]x1 >= [0 0 0]x1 = a(c)(c(c)(c(b)(x1))) 58.81/15.31 [0 0 1] [0 0 1] 58.81/15.31 58.81/15.31 [1 0 1] [1 0 1] 58.81/15.31 a(b)(b(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.31 [0 0 0] [0 0 0] 58.81/15.31 58.81/15.31 [1 0 1] [1 0 1] 58.81/15.31 a(b)(b(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.31 [0 0 0] [0 0 0] 58.81/15.31 58.81/15.31 [1 0 1] [1 0 1] 58.81/15.31 b(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.31 [0 0 0] [0 0 0] 58.81/15.31 58.81/15.31 [1 0 1] [1 0 1] 58.81/15.31 b(b)(b(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.32 [0 0 0] [0 0 0] 58.81/15.32 58.81/15.32 [1 1 1] [1 1 1] 58.81/15.32 b(b)(b(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.32 [0 0 0] [0 0 0] 58.81/15.32 58.81/15.32 [1 1 1] [1 0 1] 58.81/15.32 a(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 >= [0 0 0]x1 = a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.32 [0 0 0] [0 0 0] 58.81/15.32 58.81/15.32 [1 0 1] [1] [1 0 1] 58.81/15.32 a(c)(c(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = a(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.32 [0 0 0] [0] [0 0 0] 58.81/15.32 58.81/15.32 [1 1 1] [0] [1 0 1] 58.81/15.32 c(c)(c(b)(b(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = c(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.32 [0 0 0] [0] [0 0 0] 58.81/15.32 58.81/15.32 [1 0 1] [1] [1 0 1] 58.81/15.32 c(c)(c(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 = c(b)(b(b)(b(b)(b(c)(x1)))) 58.81/15.32 [0 0 0] [0] [0 0 0] 58.81/15.32 58.81/15.32 [1 0 1] [1 0 1] 58.81/15.32 b(b)(b(a)(a(c)(x1))) = [0 0 0]x1 >= [0 0 0]x1 = b(a)(a(c)(c(c)(x1))) 58.81/15.32 [0 0 0] [0 0 0] 58.81/15.32 58.81/15.32 [1 1 1] [1 1 1] 58.81/15.32 b(b)(b(a)(a(b)(x1))) = [0 0 0]x1 >= [0 0 0]x1 = b(a)(a(c)(c(b)(x1))) 58.81/15.32 [0 0 0] [0 0 0] 58.81/15.32 problem: 58.81/15.32 a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 58.81/15.32 a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 58.81/15.32 a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 58.81/15.32 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.32 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.32 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.32 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.32 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.32 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.32 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.32 b(b)(b(a)(a(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 58.81/15.32 b(b)(b(a)(a(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 58.81/15.32 Matrix Interpretation Processor: dim=1 58.81/15.32 58.81/15.32 interpretation: 58.81/15.32 [b(a)](x0) = x0 + 1, 58.81/15.32 58.81/15.32 [b(c)](x0) = x0, 58.81/15.32 58.81/15.32 [b(b)](x0) = 2x0, 58.81/15.32 58.81/15.32 [a(b)](x0) = x0, 58.81/15.32 58.81/15.32 [c(b)](x0) = x0, 58.81/15.32 58.81/15.32 [c(c)](x0) = 2x0, 58.81/15.32 58.81/15.32 [c(a)](x0) = 2x0 + 2, 58.81/15.32 58.81/15.32 [a(c)](x0) = 2x0, 58.81/15.32 58.81/15.32 [a(a)](x0) = 2x0 58.81/15.32 orientation: 58.81/15.32 a(a)(a(c)(c(a)(x1))) = 8x1 + 8 >= 8x1 + 8 = a(c)(c(c)(c(a)(x1))) 58.81/15.32 58.81/15.32 a(a)(a(c)(c(c)(x1))) = 8x1 >= 8x1 = a(c)(c(c)(c(c)(x1))) 58.81/15.32 58.81/15.32 a(a)(a(c)(c(b)(x1))) = 4x1 >= 4x1 = a(c)(c(c)(c(b)(x1))) 58.81/15.32 58.81/15.32 a(b)(b(b)(b(c)(c(a)(x1)))) = 4x1 + 4 >= 4x1 + 4 = a(a)(a(b)(b(b)(b(a)(x1)))) 58.81/15.32 58.81/15.32 a(b)(b(b)(b(c)(c(c)(x1)))) = 4x1 >= 4x1 = a(a)(a(b)(b(b)(b(c)(x1)))) 58.81/15.32 58.81/15.32 b(b)(b(a)(a(c)(c(a)(x1)))) = 8x1 + 10 >= 8x1 + 10 = b(c)(c(a)(a(c)(c(a)(x1)))) 58.81/15.32 58.81/15.32 b(b)(b(a)(a(c)(c(c)(x1)))) = 8x1 + 2 >= 8x1 + 2 = b(c)(c(a)(a(c)(c(c)(x1)))) 58.81/15.32 58.81/15.32 b(b)(b(a)(a(c)(c(b)(x1)))) = 4x1 + 2 >= 4x1 + 2 = b(c)(c(a)(a(c)(c(b)(x1)))) 58.81/15.32 58.81/15.32 a(c)(c(b)(b(c)(c(a)(x1)))) = 4x1 + 4 >= 4x1 + 4 = a(b)(b(b)(b(b)(b(a)(x1)))) 58.81/15.32 58.81/15.32 c(c)(c(b)(b(c)(c(a)(x1)))) = 4x1 + 4 >= 4x1 + 4 = c(b)(b(b)(b(b)(b(a)(x1)))) 58.88/15.33 58.88/15.33 b(b)(b(a)(a(c)(x1))) = 4x1 + 2 >= 4x1 + 1 = b(a)(a(c)(c(c)(x1))) 58.88/15.33 58.88/15.33 b(b)(b(a)(a(b)(x1))) = 2x1 + 2 >= 2x1 + 1 = b(a)(a(c)(c(b)(x1))) 58.88/15.33 problem: 58.88/15.33 a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 58.88/15.33 a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 58.88/15.33 a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 58.88/15.33 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) 58.88/15.33 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.88/15.33 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) 58.88/15.33 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) 58.88/15.33 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) 58.88/15.33 a(c)(c(b)(b(c)(c(a)(x1)))) -> a(b)(b(b)(b(b)(b(a)(x1)))) 58.88/15.33 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) 58.88/15.33 Matrix Interpretation Processor: dim=1 58.88/15.33 58.88/15.33 interpretation: 58.88/15.33 [b(a)](x0) = 4x0 + 4, 58.88/15.33 58.88/15.33 [b(c)](x0) = 4x0 + 4, 58.88/15.33 58.88/15.33 [b(b)](x0) = x0, 58.88/15.33 58.88/15.33 [a(b)](x0) = x0 + 1, 58.88/15.33 58.88/15.33 [c(b)](x0) = x0, 58.88/15.33 58.88/15.33 [c(c)](x0) = x0, 58.88/15.33 58.88/15.33 [c(a)](x0) = x0, 58.88/15.33 58.88/15.33 [a(c)](x0) = 4x0, 58.88/15.33 58.88/15.33 [a(a)](x0) = x0 58.88/15.33 orientation: 58.88/15.33 a(a)(a(c)(c(a)(x1))) = 4x1 >= 4x1 = a(c)(c(c)(c(a)(x1))) 58.88/15.33 58.88/15.33 a(a)(a(c)(c(c)(x1))) = 4x1 >= 4x1 = a(c)(c(c)(c(c)(x1))) 58.88/15.33 58.88/15.33 a(a)(a(c)(c(b)(x1))) = 4x1 >= 4x1 = a(c)(c(c)(c(b)(x1))) 58.88/15.33 58.88/15.33 a(b)(b(b)(b(c)(c(a)(x1)))) = 4x1 + 5 >= 4x1 + 5 = a(a)(a(b)(b(b)(b(a)(x1)))) 58.88/15.33 58.88/15.33 a(b)(b(b)(b(c)(c(c)(x1)))) = 4x1 + 5 >= 4x1 + 5 = a(a)(a(b)(b(b)(b(c)(x1)))) 58.88/15.33 58.88/15.33 b(b)(b(a)(a(c)(c(a)(x1)))) = 16x1 + 4 >= 16x1 + 4 = b(c)(c(a)(a(c)(c(a)(x1)))) 58.88/15.33 58.88/15.33 b(b)(b(a)(a(c)(c(c)(x1)))) = 16x1 + 4 >= 16x1 + 4 = b(c)(c(a)(a(c)(c(c)(x1)))) 58.88/15.33 58.88/15.33 b(b)(b(a)(a(c)(c(b)(x1)))) = 16x1 + 4 >= 16x1 + 4 = b(c)(c(a)(a(c)(c(b)(x1)))) 58.88/15.33 58.88/15.33 a(c)(c(b)(b(c)(c(a)(x1)))) = 16x1 + 16 >= 4x1 + 5 = a(b)(b(b)(b(b)(b(a)(x1)))) 58.88/15.33 58.88/15.33 c(c)(c(b)(b(c)(c(a)(x1)))) = 4x1 + 4 >= 4x1 + 4 = c(b)(b(b)(b(b)(b(a)(x1)))) 58.88/15.33 problem: 58.88/15.33 a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 58.88/15.33 a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 58.88/15.33 a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 58.88/15.33 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) 58.88/15.33 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.88/15.33 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) 58.88/15.33 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) 58.88/15.33 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) 58.88/15.33 c(c)(c(b)(b(c)(c(a)(x1)))) -> c(b)(b(b)(b(b)(b(a)(x1)))) 58.88/15.33 Matrix Interpretation Processor: dim=1 58.88/15.33 58.88/15.33 interpretation: 58.88/15.33 [b(a)](x0) = x0 + 2, 58.88/15.33 58.88/15.33 [b(c)](x0) = 2x0, 58.88/15.33 58.88/15.33 [b(b)](x0) = 2x0, 58.88/15.33 58.88/15.33 [a(b)](x0) = 2x0, 58.88/15.33 58.88/15.33 [c(b)](x0) = x0 + 4, 58.88/15.33 58.88/15.33 [c(c)](x0) = 2x0, 58.88/15.33 58.88/15.33 [c(a)](x0) = x0 + 2, 58.88/15.33 58.88/15.33 [a(c)](x0) = 2x0, 58.88/15.33 58.88/15.33 [a(a)](x0) = 2x0 58.88/15.33 orientation: 58.88/15.33 a(a)(a(c)(c(a)(x1))) = 4x1 + 8 >= 4x1 + 8 = a(c)(c(c)(c(a)(x1))) 58.88/15.33 58.88/15.33 a(a)(a(c)(c(c)(x1))) = 8x1 >= 8x1 = a(c)(c(c)(c(c)(x1))) 58.88/15.33 58.88/15.33 a(a)(a(c)(c(b)(x1))) = 4x1 + 16 >= 4x1 + 16 = a(c)(c(c)(c(b)(x1))) 58.88/15.33 58.88/15.33 a(b)(b(b)(b(c)(c(a)(x1)))) = 8x1 + 16 >= 8x1 + 16 = a(a)(a(b)(b(b)(b(a)(x1)))) 58.88/15.33 58.88/15.33 a(b)(b(b)(b(c)(c(c)(x1)))) = 16x1 >= 16x1 = a(a)(a(b)(b(b)(b(c)(x1)))) 58.88/15.33 58.88/15.33 b(b)(b(a)(a(c)(c(a)(x1)))) = 4x1 + 12 >= 4x1 + 12 = b(c)(c(a)(a(c)(c(a)(x1)))) 58.88/15.33 58.88/15.33 b(b)(b(a)(a(c)(c(c)(x1)))) = 8x1 + 4 >= 8x1 + 4 = b(c)(c(a)(a(c)(c(c)(x1)))) 58.88/15.33 58.88/15.33 b(b)(b(a)(a(c)(c(b)(x1)))) = 4x1 + 20 >= 4x1 + 20 = b(c)(c(a)(a(c)(c(b)(x1)))) 58.88/15.33 58.88/15.33 c(c)(c(b)(b(c)(c(a)(x1)))) = 4x1 + 16 >= 4x1 + 12 = c(b)(b(b)(b(b)(b(a)(x1)))) 58.88/15.33 problem: 58.88/15.33 a(a)(a(c)(c(a)(x1))) -> a(c)(c(c)(c(a)(x1))) 58.88/15.33 a(a)(a(c)(c(c)(x1))) -> a(c)(c(c)(c(c)(x1))) 58.88/15.33 a(a)(a(c)(c(b)(x1))) -> a(c)(c(c)(c(b)(x1))) 58.88/15.33 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) 58.88/15.33 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.88/15.33 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) 58.88/15.33 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) 58.88/15.33 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) 58.88/15.33 Matrix Interpretation Processor: dim=3 58.88/15.33 58.88/15.33 interpretation: 58.88/15.33 [1 1 0] 58.88/15.33 [b(a)](x0) = [1 0 0]x0 58.88/15.33 [0 0 0] , 58.88/15.33 58.88/15.33 [1 0 0] 58.88/15.33 [b(c)](x0) = [0 0 0]x0 58.88/15.33 [1 0 0] , 58.88/15.33 58.88/15.33 [1 0 0] [0] 58.88/15.33 [b(b)](x0) = [0 0 0]x0 + [0] 58.88/15.33 [1 0 0] [1], 58.88/15.33 58.88/15.33 [1 0 0] [1] 58.88/15.33 [a(b)](x0) = [0 0 1]x0 + [0] 58.88/15.33 [0 0 0] [0], 58.88/15.33 58.88/15.33 58.88/15.33 [c(b)](x0) = x0 58.88/15.33 , 58.88/15.33 58.88/15.33 [1 0 0] 58.88/15.33 [c(c)](x0) = [0 1 1]x0 58.88/15.33 [0 0 0] , 58.88/15.33 58.88/15.33 [1 1 0] 58.88/15.33 [c(a)](x0) = [0 0 1]x0 58.88/15.33 [0 0 0] , 58.88/15.33 58.88/15.33 [1 1 0] [0] 58.88/15.33 [a(c)](x0) = [0 0 1]x0 + [0] 58.88/15.33 [0 0 1] [1], 58.88/15.33 58.88/15.33 [1 0 1] 58.88/15.33 [a(a)](x0) = [0 0 0]x0 58.88/15.33 [0 0 1] 58.88/15.33 orientation: 58.88/15.33 [1 1 1] [1] [1 1 1] [0] 58.88/15.33 a(a)(a(c)(c(a)(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(c)(c(c)(c(a)(x1))) 58.88/15.33 [0 0 0] [1] [0 0 0] [1] 58.88/15.33 58.88/15.33 [1 1 1] [1] [1 1 1] [0] 58.88/15.33 a(a)(a(c)(c(c)(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(c)(c(c)(c(c)(x1))) 58.88/15.33 [0 0 0] [1] [0 0 0] [1] 58.88/15.33 58.88/15.33 [1 1 1] [1] [1 1 1] [0] 58.88/15.33 a(a)(a(c)(c(b)(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(c)(c(c)(c(b)(x1))) 58.88/15.33 [0 0 1] [1] [0 0 0] [1] 58.88/15.33 58.88/15.33 [1 1 0] [1] [1 1 0] [1] 58.88/15.33 a(b)(b(b)(b(c)(c(a)(x1)))) = [1 1 0]x1 + [1] >= [0 0 0]x1 + [0] = a(a)(a(b)(b(b)(b(a)(x1)))) 58.88/15.33 [0 0 0] [0] [0 0 0] [0] 58.88/15.33 58.88/15.33 [1 0 0] [1] [1 0 0] [1] 58.88/15.33 a(b)(b(b)(b(c)(c(c)(x1)))) = [1 0 0]x1 + [1] >= [0 0 0]x1 + [0] = a(a)(a(b)(b(b)(b(c)(x1)))) 58.88/15.33 [0 0 0] [0] [0 0 0] [0] 58.88/15.33 58.88/15.33 [1 1 1] [0] [1 1 1] 58.88/15.33 b(b)(b(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(a)(x1)))) 58.88/15.33 [1 1 1] [1] [1 1 1] 58.88/15.33 58.88/15.33 [1 1 1] [0] [1 1 1] 58.88/15.33 b(b)(b(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(c)(x1)))) 58.88/15.33 [1 1 1] [1] [1 1 1] 58.88/15.33 58.88/15.33 [1 1 1] [0] [1 1 1] 58.88/15.33 b(b)(b(a)(a(c)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = b(c)(c(a)(a(c)(c(b)(x1)))) 58.88/15.33 [1 1 1] [1] [1 1 1] 58.88/15.34 problem: 58.88/15.34 a(b)(b(b)(b(c)(c(a)(x1)))) -> a(a)(a(b)(b(b)(b(a)(x1)))) 58.88/15.34 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.88/15.34 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(c)(c(a)(a(c)(c(a)(x1)))) 58.88/15.34 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(c)(c(a)(a(c)(c(c)(x1)))) 58.88/15.34 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(c)(c(a)(a(c)(c(b)(x1)))) 58.88/15.34 Matrix Interpretation Processor: dim=1 58.88/15.34 58.88/15.34 interpretation: 58.88/15.34 [b(a)](x0) = 2x0, 58.88/15.34 58.88/15.34 [b(c)](x0) = 4x0 + 3, 58.88/15.34 58.88/15.34 [b(b)](x0) = 4x0 + 5, 58.88/15.34 58.88/15.34 [a(b)](x0) = x0 + 4, 58.88/15.34 58.88/15.34 [c(b)](x0) = x0, 58.88/15.34 58.88/15.34 [c(c)](x0) = x0, 58.88/15.34 58.88/15.34 [c(a)](x0) = x0, 58.88/15.34 58.88/15.34 [a(c)](x0) = 2x0, 58.88/15.34 58.88/15.34 [a(a)](x0) = x0 58.88/15.34 orientation: 58.88/15.34 a(b)(b(b)(b(c)(c(a)(x1)))) = 16x1 + 21 >= 8x1 + 9 = a(a)(a(b)(b(b)(b(a)(x1)))) 58.88/15.34 58.88/15.34 a(b)(b(b)(b(c)(c(c)(x1)))) = 16x1 + 21 >= 16x1 + 21 = a(a)(a(b)(b(b)(b(c)(x1)))) 58.88/15.34 58.88/15.34 b(b)(b(a)(a(c)(c(a)(x1)))) = 16x1 + 5 >= 8x1 + 3 = b(c)(c(a)(a(c)(c(a)(x1)))) 58.88/15.34 58.88/15.34 b(b)(b(a)(a(c)(c(c)(x1)))) = 16x1 + 5 >= 8x1 + 3 = b(c)(c(a)(a(c)(c(c)(x1)))) 58.88/15.34 58.88/15.34 b(b)(b(a)(a(c)(c(b)(x1)))) = 16x1 + 5 >= 8x1 + 3 = b(c)(c(a)(a(c)(c(b)(x1)))) 58.88/15.34 problem: 58.88/15.34 a(b)(b(b)(b(c)(c(c)(x1)))) -> a(a)(a(b)(b(b)(b(c)(x1)))) 58.88/15.34 Matrix Interpretation Processor: dim=3 58.88/15.34 58.88/15.34 interpretation: 58.88/15.34 [1 0 1] [0] 58.88/15.34 [b(c)](x0) = [0 0 0]x0 + [1] 58.88/15.34 [0 1 0] [0], 58.88/15.34 58.88/15.34 [1 0 0] 58.88/15.34 [b(b)](x0) = [1 0 1]x0 58.88/15.34 [0 0 1] , 58.88/15.34 58.88/15.34 [1 0 1] 58.88/15.34 [a(b)](x0) = [0 0 0]x0 58.88/15.34 [0 0 0] , 58.88/15.34 58.88/15.34 [1 0 0] [0] 58.88/15.34 [c(c)](x0) = [0 0 1]x0 + [1] 58.88/15.34 [0 1 0] [0], 58.88/15.34 58.88/15.34 [1 0 0] 58.88/15.34 [a(a)](x0) = [0 0 0]x0 58.88/15.34 [0 0 0] 58.88/15.34 orientation: 58.88/15.34 [1 1 1] [1] [1 1 1] 58.88/15.34 a(b)(b(b)(b(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = a(a)(a(b)(b(b)(b(c)(x1)))) 58.88/15.34 [0 0 0] [0] [0 0 0] 58.88/15.34 problem: 58.88/15.34 58.88/15.34 Qed 58.88/15.34 EOF