40.54/10.85 YES 40.54/10.86 40.54/10.86 Problem: 40.54/10.86 strict: 40.54/10.86 a(a(c(x1))) -> b(b(c(x1))) 40.54/10.86 b(a(c(x1))) -> a(a(b(x1))) 40.54/10.86 weak: 40.54/10.86 a(c(a(x1))) -> a(b(b(x1))) 40.54/10.86 b(b(b(x1))) -> c(c(b(x1))) 40.54/10.86 b(a(c(x1))) -> a(a(c(x1))) 40.54/10.86 c(a(a(x1))) -> a(a(a(x1))) 40.54/10.86 40.54/10.86 Proof: 40.54/10.86 Root-Labeling Processor: 40.54/10.86 strict: 40.54/10.86 a(a)(a(a)(a(c)(c(a)(x1)))) -> a(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.86 a(a)(a(a)(a(c)(c(c)(x1)))) -> a(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.86 a(a)(a(a)(a(c)(c(b)(x1)))) -> a(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.86 c(a)(a(a)(a(c)(c(a)(x1)))) -> c(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.86 c(a)(a(a)(a(c)(c(c)(x1)))) -> c(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.86 c(a)(a(a)(a(c)(c(b)(x1)))) -> c(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.86 b(a)(a(a)(a(c)(c(a)(x1)))) -> b(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.86 b(a)(a(a)(a(c)(c(c)(x1)))) -> b(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.86 b(a)(a(a)(a(c)(c(b)(x1)))) -> b(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.86 a(b)(b(a)(a(c)(c(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 40.54/10.86 a(b)(b(a)(a(c)(c(c)(x1)))) -> a(a)(a(a)(a(b)(b(c)(x1)))) 40.54/10.86 a(b)(b(a)(a(c)(c(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 40.54/10.86 c(b)(b(a)(a(c)(c(a)(x1)))) -> c(a)(a(a)(a(b)(b(a)(x1)))) 40.54/10.86 c(b)(b(a)(a(c)(c(c)(x1)))) -> c(a)(a(a)(a(b)(b(c)(x1)))) 40.54/10.86 c(b)(b(a)(a(c)(c(b)(x1)))) -> c(a)(a(a)(a(b)(b(b)(x1)))) 40.54/10.86 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(a)(a(a)(a(b)(b(a)(x1)))) 40.54/10.86 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(a)(a(a)(a(b)(b(c)(x1)))) 40.54/10.86 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(a)(a(a)(a(b)(b(b)(x1)))) 40.54/10.86 weak: 40.54/10.86 a(c)(c(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) 40.54/10.86 a(c)(c(a)(a(c)(x1))) -> a(b)(b(b)(b(c)(x1))) 40.54/10.86 a(c)(c(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) 40.54/10.86 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 40.54/10.86 a(b)(b(b)(b(b)(b(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 40.54/10.86 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(c)(c(c)(c(b)(b(b)(x1)))) 40.54/10.86 c(b)(b(b)(b(b)(b(a)(x1)))) -> c(c)(c(c)(c(b)(b(a)(x1)))) 40.54/10.86 c(b)(b(b)(b(b)(b(c)(x1)))) -> c(c)(c(c)(c(b)(b(c)(x1)))) 40.54/10.86 c(b)(b(b)(b(b)(b(b)(x1)))) -> c(c)(c(c)(c(b)(b(b)(x1)))) 40.54/10.86 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(c)(c(c)(c(b)(b(a)(x1)))) 40.54/10.86 b(b)(b(b)(b(b)(b(c)(x1)))) -> b(c)(c(c)(c(b)(b(c)(x1)))) 40.54/10.86 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(c)(c(b)(b(b)(x1)))) 40.54/10.86 a(b)(b(a)(a(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 40.54/10.86 a(b)(b(a)(a(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 40.54/10.86 a(b)(b(a)(a(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 40.54/10.86 c(b)(b(a)(a(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 40.54/10.86 c(b)(b(a)(a(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 40.54/10.86 c(b)(b(a)(a(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) 40.54/10.86 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(a)(a(a)(a(c)(c(a)(x1)))) 40.54/10.86 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(a)(a(a)(a(c)(c(c)(x1)))) 40.54/10.86 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(a)(a(a)(a(c)(c(b)(x1)))) 40.54/10.86 a(c)(c(a)(a(a)(a(a)(x1)))) -> a(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.86 a(c)(c(a)(a(a)(a(c)(x1)))) -> a(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.86 a(c)(c(a)(a(a)(a(b)(x1)))) -> a(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.86 c(c)(c(a)(a(a)(a(a)(x1)))) -> c(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.86 c(c)(c(a)(a(a)(a(c)(x1)))) -> c(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.86 c(c)(c(a)(a(a)(a(b)(x1)))) -> c(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.86 b(c)(c(a)(a(a)(a(a)(x1)))) -> b(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.86 b(c)(c(a)(a(a)(a(c)(x1)))) -> b(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.86 b(c)(c(a)(a(a)(a(b)(x1)))) -> b(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.86 RT Transformation Processor: 40.54/10.86 a(a)(a(a)(a(c)(c(a)(x1)))) -> a(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.86 a(a)(a(a)(a(c)(c(c)(x1)))) -> a(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.86 a(a)(a(a)(a(c)(c(b)(x1)))) -> a(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.86 c(a)(a(a)(a(c)(c(a)(x1)))) -> c(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.86 c(a)(a(a)(a(c)(c(c)(x1)))) -> c(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.86 c(a)(a(a)(a(c)(c(b)(x1)))) -> c(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.86 b(a)(a(a)(a(c)(c(a)(x1)))) -> b(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.86 b(a)(a(a)(a(c)(c(c)(x1)))) -> b(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.86 b(a)(a(a)(a(c)(c(b)(x1)))) -> b(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.86 a(b)(b(a)(a(c)(c(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) 40.54/10.86 a(b)(b(a)(a(c)(c(c)(x1)))) -> a(a)(a(a)(a(b)(b(c)(x1)))) 40.54/10.86 a(b)(b(a)(a(c)(c(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) 40.54/10.86 c(b)(b(a)(a(c)(c(a)(x1)))) -> c(a)(a(a)(a(b)(b(a)(x1)))) 40.54/10.86 c(b)(b(a)(a(c)(c(c)(x1)))) -> c(a)(a(a)(a(b)(b(c)(x1)))) 40.54/10.86 c(b)(b(a)(a(c)(c(b)(x1)))) -> c(a)(a(a)(a(b)(b(b)(x1)))) 40.54/10.86 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(a)(a(a)(a(b)(b(a)(x1)))) 40.54/10.86 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(a)(a(a)(a(b)(b(c)(x1)))) 40.54/10.87 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(a)(a(a)(a(b)(b(b)(x1)))) 40.54/10.87 a(c)(c(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) 40.54/10.87 a(c)(c(a)(a(c)(x1))) -> a(b)(b(b)(b(c)(x1))) 40.54/10.87 a(c)(c(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) 40.54/10.87 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 40.54/10.87 a(b)(b(b)(b(b)(b(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 40.54/10.87 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(c)(c(c)(c(b)(b(b)(x1)))) 40.54/10.87 c(b)(b(b)(b(b)(b(a)(x1)))) -> c(c)(c(c)(c(b)(b(a)(x1)))) 40.54/10.87 c(b)(b(b)(b(b)(b(c)(x1)))) -> c(c)(c(c)(c(b)(b(c)(x1)))) 40.54/10.87 c(b)(b(b)(b(b)(b(b)(x1)))) -> c(c)(c(c)(c(b)(b(b)(x1)))) 40.54/10.87 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(c)(c(c)(c(b)(b(a)(x1)))) 40.54/10.87 b(b)(b(b)(b(b)(b(c)(x1)))) -> b(c)(c(c)(c(b)(b(c)(x1)))) 40.54/10.87 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(c)(c(b)(b(b)(x1)))) 40.54/10.87 a(b)(b(a)(a(c)(c(a)(x1)))) -> a(a)(a(a)(a(c)(c(a)(x1)))) 40.54/10.87 a(b)(b(a)(a(c)(c(c)(x1)))) -> a(a)(a(a)(a(c)(c(c)(x1)))) 40.54/10.87 a(b)(b(a)(a(c)(c(b)(x1)))) -> a(a)(a(a)(a(c)(c(b)(x1)))) 40.54/10.87 c(b)(b(a)(a(c)(c(a)(x1)))) -> c(a)(a(a)(a(c)(c(a)(x1)))) 40.54/10.87 c(b)(b(a)(a(c)(c(c)(x1)))) -> c(a)(a(a)(a(c)(c(c)(x1)))) 40.54/10.87 c(b)(b(a)(a(c)(c(b)(x1)))) -> c(a)(a(a)(a(c)(c(b)(x1)))) 40.54/10.87 b(b)(b(a)(a(c)(c(a)(x1)))) -> b(a)(a(a)(a(c)(c(a)(x1)))) 40.54/10.87 b(b)(b(a)(a(c)(c(c)(x1)))) -> b(a)(a(a)(a(c)(c(c)(x1)))) 40.54/10.87 b(b)(b(a)(a(c)(c(b)(x1)))) -> b(a)(a(a)(a(c)(c(b)(x1)))) 40.54/10.87 a(c)(c(a)(a(a)(a(a)(x1)))) -> a(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.87 a(c)(c(a)(a(a)(a(c)(x1)))) -> a(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.87 a(c)(c(a)(a(a)(a(b)(x1)))) -> a(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.87 c(c)(c(a)(a(a)(a(a)(x1)))) -> c(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.87 c(c)(c(a)(a(a)(a(c)(x1)))) -> c(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.87 c(c)(c(a)(a(a)(a(b)(x1)))) -> c(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.87 b(c)(c(a)(a(a)(a(a)(x1)))) -> b(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.87 b(c)(c(a)(a(a)(a(c)(x1)))) -> b(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.87 b(c)(c(a)(a(a)(a(b)(x1)))) -> b(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.87 Matrix Interpretation Processor: dim=1 40.54/10.87 40.54/10.87 interpretation: 40.54/10.87 [b(a)](x0) = 2x0 + 1, 40.54/10.87 40.54/10.87 [c(b)](x0) = x0, 40.54/10.87 40.54/10.87 [c(c)](x0) = x0, 40.54/10.87 40.54/10.87 [b(c)](x0) = 2x0 + 1, 40.54/10.87 40.54/10.87 [b(b)](x0) = 2x0 + 1, 40.54/10.87 40.54/10.87 [a(b)](x0) = x0, 40.54/10.87 40.54/10.87 [c(a)](x0) = x0, 40.54/10.87 40.54/10.87 [a(c)](x0) = 4x0 + 3, 40.54/10.87 40.54/10.87 [a(a)](x0) = x0 40.54/10.87 orientation: 40.54/10.87 a(a)(a(a)(a(c)(c(a)(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.87 40.54/10.87 a(a)(a(a)(a(c)(c(c)(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.87 40.54/10.87 a(a)(a(a)(a(c)(c(b)(x1)))) = 4x1 + 3 >= 4x1 + 3 = a(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.87 40.54/10.87 c(a)(a(a)(a(c)(c(a)(x1)))) = 4x1 + 3 >= 4x1 + 3 = c(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.87 40.54/10.87 c(a)(a(a)(a(c)(c(c)(x1)))) = 4x1 + 3 >= 4x1 + 3 = c(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.87 40.54/10.87 c(a)(a(a)(a(c)(c(b)(x1)))) = 4x1 + 3 >= 4x1 + 3 = c(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.87 40.54/10.87 b(a)(a(a)(a(c)(c(a)(x1)))) = 8x1 + 7 >= 8x1 + 7 = b(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.87 40.54/10.87 b(a)(a(a)(a(c)(c(c)(x1)))) = 8x1 + 7 >= 8x1 + 7 = b(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.87 40.54/10.87 b(a)(a(a)(a(c)(c(b)(x1)))) = 8x1 + 7 >= 8x1 + 7 = b(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.87 40.54/10.87 a(b)(b(a)(a(c)(c(a)(x1)))) = 8x1 + 7 >= 2x1 + 1 = a(a)(a(a)(a(b)(b(a)(x1)))) 40.54/10.87 40.54/10.87 a(b)(b(a)(a(c)(c(c)(x1)))) = 8x1 + 7 >= 2x1 + 1 = a(a)(a(a)(a(b)(b(c)(x1)))) 40.54/10.87 40.54/10.87 a(b)(b(a)(a(c)(c(b)(x1)))) = 8x1 + 7 >= 2x1 + 1 = a(a)(a(a)(a(b)(b(b)(x1)))) 40.54/10.87 40.54/10.87 c(b)(b(a)(a(c)(c(a)(x1)))) = 8x1 + 7 >= 2x1 + 1 = c(a)(a(a)(a(b)(b(a)(x1)))) 40.54/10.87 40.54/10.87 c(b)(b(a)(a(c)(c(c)(x1)))) = 8x1 + 7 >= 2x1 + 1 = c(a)(a(a)(a(b)(b(c)(x1)))) 40.54/10.87 40.54/10.87 c(b)(b(a)(a(c)(c(b)(x1)))) = 8x1 + 7 >= 2x1 + 1 = c(a)(a(a)(a(b)(b(b)(x1)))) 40.54/10.87 40.54/10.87 b(b)(b(a)(a(c)(c(a)(x1)))) = 16x1 + 15 >= 4x1 + 3 = b(a)(a(a)(a(b)(b(a)(x1)))) 40.54/10.87 40.54/10.87 b(b)(b(a)(a(c)(c(c)(x1)))) = 16x1 + 15 >= 4x1 + 3 = b(a)(a(a)(a(b)(b(c)(x1)))) 40.54/10.87 40.54/10.87 b(b)(b(a)(a(c)(c(b)(x1)))) = 16x1 + 15 >= 4x1 + 3 = b(a)(a(a)(a(b)(b(b)(x1)))) 40.54/10.87 40.54/10.87 a(c)(c(a)(a(a)(x1))) = 4x1 + 3 >= 4x1 + 3 = a(b)(b(b)(b(a)(x1))) 40.54/10.87 40.54/10.87 a(c)(c(a)(a(c)(x1))) = 16x1 + 15 >= 4x1 + 3 = a(b)(b(b)(b(c)(x1))) 40.54/10.87 40.54/10.87 a(c)(c(a)(a(b)(x1))) = 4x1 + 3 >= 4x1 + 3 = a(b)(b(b)(b(b)(x1))) 40.54/10.87 40.54/10.87 a(b)(b(b)(b(b)(b(a)(x1)))) = 8x1 + 7 >= 8x1 + 7 = a(c)(c(c)(c(b)(b(a)(x1)))) 40.54/10.88 40.54/10.88 a(b)(b(b)(b(b)(b(c)(x1)))) = 8x1 + 7 >= 8x1 + 7 = a(c)(c(c)(c(b)(b(c)(x1)))) 40.54/10.88 40.54/10.88 a(b)(b(b)(b(b)(b(b)(x1)))) = 8x1 + 7 >= 8x1 + 7 = a(c)(c(c)(c(b)(b(b)(x1)))) 40.54/10.88 40.54/10.88 c(b)(b(b)(b(b)(b(a)(x1)))) = 8x1 + 7 >= 2x1 + 1 = c(c)(c(c)(c(b)(b(a)(x1)))) 40.54/10.88 40.54/10.88 c(b)(b(b)(b(b)(b(c)(x1)))) = 8x1 + 7 >= 2x1 + 1 = c(c)(c(c)(c(b)(b(c)(x1)))) 40.54/10.88 40.54/10.88 c(b)(b(b)(b(b)(b(b)(x1)))) = 8x1 + 7 >= 2x1 + 1 = c(c)(c(c)(c(b)(b(b)(x1)))) 40.54/10.88 40.54/10.88 b(b)(b(b)(b(b)(b(a)(x1)))) = 16x1 + 15 >= 4x1 + 3 = b(c)(c(c)(c(b)(b(a)(x1)))) 40.54/10.88 40.54/10.88 b(b)(b(b)(b(b)(b(c)(x1)))) = 16x1 + 15 >= 4x1 + 3 = b(c)(c(c)(c(b)(b(c)(x1)))) 40.54/10.88 40.54/10.88 b(b)(b(b)(b(b)(b(b)(x1)))) = 16x1 + 15 >= 4x1 + 3 = b(c)(c(c)(c(b)(b(b)(x1)))) 40.54/10.88 40.54/10.88 a(b)(b(a)(a(c)(c(a)(x1)))) = 8x1 + 7 >= 4x1 + 3 = a(a)(a(a)(a(c)(c(a)(x1)))) 40.54/10.88 40.54/10.88 a(b)(b(a)(a(c)(c(c)(x1)))) = 8x1 + 7 >= 4x1 + 3 = a(a)(a(a)(a(c)(c(c)(x1)))) 40.54/10.88 40.54/10.88 a(b)(b(a)(a(c)(c(b)(x1)))) = 8x1 + 7 >= 4x1 + 3 = a(a)(a(a)(a(c)(c(b)(x1)))) 40.54/10.88 40.54/10.88 c(b)(b(a)(a(c)(c(a)(x1)))) = 8x1 + 7 >= 4x1 + 3 = c(a)(a(a)(a(c)(c(a)(x1)))) 40.54/10.88 40.54/10.88 c(b)(b(a)(a(c)(c(c)(x1)))) = 8x1 + 7 >= 4x1 + 3 = c(a)(a(a)(a(c)(c(c)(x1)))) 40.54/10.88 40.54/10.88 c(b)(b(a)(a(c)(c(b)(x1)))) = 8x1 + 7 >= 4x1 + 3 = c(a)(a(a)(a(c)(c(b)(x1)))) 40.54/10.88 40.54/10.88 b(b)(b(a)(a(c)(c(a)(x1)))) = 16x1 + 15 >= 8x1 + 7 = b(a)(a(a)(a(c)(c(a)(x1)))) 40.54/10.88 40.54/10.88 b(b)(b(a)(a(c)(c(c)(x1)))) = 16x1 + 15 >= 8x1 + 7 = b(a)(a(a)(a(c)(c(c)(x1)))) 40.54/10.88 40.54/10.88 b(b)(b(a)(a(c)(c(b)(x1)))) = 16x1 + 15 >= 8x1 + 7 = b(a)(a(a)(a(c)(c(b)(x1)))) 40.54/10.88 40.54/10.88 a(c)(c(a)(a(a)(a(a)(x1)))) = 4x1 + 3 >= x1 = a(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.88 40.54/10.88 a(c)(c(a)(a(a)(a(c)(x1)))) = 16x1 + 15 >= 4x1 + 3 = a(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.88 40.54/10.88 a(c)(c(a)(a(a)(a(b)(x1)))) = 4x1 + 3 >= x1 = a(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.88 40.54/10.88 c(c)(c(a)(a(a)(a(a)(x1)))) = x1 >= x1 = c(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.88 40.54/10.88 c(c)(c(a)(a(a)(a(c)(x1)))) = 4x1 + 3 >= 4x1 + 3 = c(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.88 40.54/10.88 c(c)(c(a)(a(a)(a(b)(x1)))) = x1 >= x1 = c(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.88 40.54/10.88 b(c)(c(a)(a(a)(a(a)(x1)))) = 2x1 + 1 >= 2x1 + 1 = b(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.88 40.54/10.88 b(c)(c(a)(a(a)(a(c)(x1)))) = 8x1 + 7 >= 8x1 + 7 = b(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.88 40.54/10.88 b(c)(c(a)(a(a)(a(b)(x1)))) = 2x1 + 1 >= 2x1 + 1 = b(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.88 problem: 40.54/10.88 a(a)(a(a)(a(c)(c(a)(x1)))) -> a(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.88 a(a)(a(a)(a(c)(c(c)(x1)))) -> a(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.88 a(a)(a(a)(a(c)(c(b)(x1)))) -> a(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.88 c(a)(a(a)(a(c)(c(a)(x1)))) -> c(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.88 c(a)(a(a)(a(c)(c(c)(x1)))) -> c(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.88 c(a)(a(a)(a(c)(c(b)(x1)))) -> c(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.88 b(a)(a(a)(a(c)(c(a)(x1)))) -> b(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.88 b(a)(a(a)(a(c)(c(c)(x1)))) -> b(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.88 b(a)(a(a)(a(c)(c(b)(x1)))) -> b(b)(b(b)(b(c)(c(b)(x1)))) 40.54/10.88 a(c)(c(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) 40.54/10.88 a(c)(c(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) 40.54/10.88 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 40.54/10.88 a(b)(b(b)(b(b)(b(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 40.54/10.88 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(c)(c(c)(c(b)(b(b)(x1)))) 40.54/10.88 c(c)(c(a)(a(a)(a(a)(x1)))) -> c(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.88 c(c)(c(a)(a(a)(a(c)(x1)))) -> c(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.88 c(c)(c(a)(a(a)(a(b)(x1)))) -> c(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.88 b(c)(c(a)(a(a)(a(a)(x1)))) -> b(a)(a(a)(a(a)(a(a)(x1)))) 40.54/10.88 b(c)(c(a)(a(a)(a(c)(x1)))) -> b(a)(a(a)(a(a)(a(c)(x1)))) 40.54/10.88 b(c)(c(a)(a(a)(a(b)(x1)))) -> b(a)(a(a)(a(a)(a(b)(x1)))) 40.54/10.88 Matrix Interpretation Processor: dim=1 40.54/10.88 40.54/10.88 interpretation: 40.54/10.88 [b(a)](x0) = 2x0, 40.54/10.88 40.54/10.88 [c(b)](x0) = x0, 40.54/10.88 40.54/10.88 [c(c)](x0) = 2x0, 40.54/10.88 40.54/10.88 [b(c)](x0) = x0 + 2, 40.54/10.88 40.54/10.88 [b(b)](x0) = 2x0, 40.54/10.88 40.54/10.88 [a(b)](x0) = x0 + 2, 40.54/10.88 40.54/10.88 [c(a)](x0) = 2x0 + 2, 40.54/10.88 40.54/10.88 [a(c)](x0) = 2x0 + 2, 40.54/10.88 40.54/10.88 [a(a)](x0) = x0 + 2 40.54/10.88 orientation: 40.54/10.88 a(a)(a(a)(a(c)(c(a)(x1)))) = 4x1 + 10 >= 4x1 + 10 = a(b)(b(b)(b(c)(c(a)(x1)))) 40.54/10.88 40.54/10.88 a(a)(a(a)(a(c)(c(c)(x1)))) = 4x1 + 6 >= 4x1 + 6 = a(b)(b(b)(b(c)(c(c)(x1)))) 40.54/10.88 40.54/10.88 a(a)(a(a)(a(c)(c(b)(x1)))) = 2x1 + 6 >= 2x1 + 6 = a(b)(b(b)(b(c)(c(b)(x1)))) 41.50/10.89 41.50/10.89 c(a)(a(a)(a(c)(c(a)(x1)))) = 8x1 + 18 >= 4x1 + 8 = c(b)(b(b)(b(c)(c(a)(x1)))) 41.50/10.89 41.50/10.89 c(a)(a(a)(a(c)(c(c)(x1)))) = 8x1 + 10 >= 4x1 + 4 = c(b)(b(b)(b(c)(c(c)(x1)))) 41.50/10.89 41.50/10.89 c(a)(a(a)(a(c)(c(b)(x1)))) = 4x1 + 10 >= 2x1 + 4 = c(b)(b(b)(b(c)(c(b)(x1)))) 41.50/10.89 41.50/10.89 b(a)(a(a)(a(c)(c(a)(x1)))) = 8x1 + 16 >= 8x1 + 16 = b(b)(b(b)(b(c)(c(a)(x1)))) 41.50/10.89 41.50/10.89 b(a)(a(a)(a(c)(c(c)(x1)))) = 8x1 + 8 >= 8x1 + 8 = b(b)(b(b)(b(c)(c(c)(x1)))) 41.50/10.89 41.50/10.89 b(a)(a(a)(a(c)(c(b)(x1)))) = 4x1 + 8 >= 4x1 + 8 = b(b)(b(b)(b(c)(c(b)(x1)))) 41.50/10.89 41.50/10.89 a(c)(c(a)(a(a)(x1))) = 4x1 + 14 >= 4x1 + 2 = a(b)(b(b)(b(a)(x1))) 41.50/10.89 41.50/10.89 a(c)(c(a)(a(b)(x1))) = 4x1 + 14 >= 4x1 + 2 = a(b)(b(b)(b(b)(x1))) 41.50/10.89 41.50/10.89 a(b)(b(b)(b(b)(b(a)(x1)))) = 8x1 + 2 >= 8x1 + 2 = a(c)(c(c)(c(b)(b(a)(x1)))) 41.50/10.89 41.50/10.89 a(b)(b(b)(b(b)(b(c)(x1)))) = 4x1 + 10 >= 4x1 + 10 = a(c)(c(c)(c(b)(b(c)(x1)))) 41.50/10.89 41.50/10.89 a(b)(b(b)(b(b)(b(b)(x1)))) = 8x1 + 2 >= 8x1 + 2 = a(c)(c(c)(c(b)(b(b)(x1)))) 41.50/10.89 41.50/10.89 c(c)(c(a)(a(a)(a(a)(x1)))) = 4x1 + 20 >= 2x1 + 14 = c(a)(a(a)(a(a)(a(a)(x1)))) 41.50/10.89 41.50/10.89 c(c)(c(a)(a(a)(a(c)(x1)))) = 8x1 + 20 >= 4x1 + 14 = c(a)(a(a)(a(a)(a(c)(x1)))) 41.50/10.89 41.50/10.89 c(c)(c(a)(a(a)(a(b)(x1)))) = 4x1 + 20 >= 2x1 + 14 = c(a)(a(a)(a(a)(a(b)(x1)))) 41.50/10.89 41.50/10.89 b(c)(c(a)(a(a)(a(a)(x1)))) = 2x1 + 12 >= 2x1 + 12 = b(a)(a(a)(a(a)(a(a)(x1)))) 41.50/10.89 41.50/10.89 b(c)(c(a)(a(a)(a(c)(x1)))) = 4x1 + 12 >= 4x1 + 12 = b(a)(a(a)(a(a)(a(c)(x1)))) 41.50/10.89 41.50/10.89 b(c)(c(a)(a(a)(a(b)(x1)))) = 2x1 + 12 >= 2x1 + 12 = b(a)(a(a)(a(a)(a(b)(x1)))) 41.50/10.89 problem: 41.50/10.89 a(a)(a(a)(a(c)(c(a)(x1)))) -> a(b)(b(b)(b(c)(c(a)(x1)))) 41.50/10.89 a(a)(a(a)(a(c)(c(c)(x1)))) -> a(b)(b(b)(b(c)(c(c)(x1)))) 41.50/10.89 a(a)(a(a)(a(c)(c(b)(x1)))) -> a(b)(b(b)(b(c)(c(b)(x1)))) 41.50/10.89 b(a)(a(a)(a(c)(c(a)(x1)))) -> b(b)(b(b)(b(c)(c(a)(x1)))) 41.50/10.89 b(a)(a(a)(a(c)(c(c)(x1)))) -> b(b)(b(b)(b(c)(c(c)(x1)))) 41.50/10.89 b(a)(a(a)(a(c)(c(b)(x1)))) -> b(b)(b(b)(b(c)(c(b)(x1)))) 41.50/10.89 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 41.50/10.89 a(b)(b(b)(b(b)(b(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 41.50/10.89 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(c)(c(c)(c(b)(b(b)(x1)))) 41.50/10.89 b(c)(c(a)(a(a)(a(a)(x1)))) -> b(a)(a(a)(a(a)(a(a)(x1)))) 41.50/10.89 b(c)(c(a)(a(a)(a(c)(x1)))) -> b(a)(a(a)(a(a)(a(c)(x1)))) 41.50/10.89 b(c)(c(a)(a(a)(a(b)(x1)))) -> b(a)(a(a)(a(a)(a(b)(x1)))) 41.50/10.89 Matrix Interpretation Processor: dim=1 41.50/10.89 41.50/10.89 interpretation: 41.50/10.89 [b(a)](x0) = 2x0 + 1, 41.50/10.89 41.50/10.89 [c(b)](x0) = 4x0 + 2, 41.50/10.89 41.50/10.89 [c(c)](x0) = 2x0, 41.50/10.89 41.50/10.89 [b(c)](x0) = x0, 41.50/10.89 41.50/10.89 [b(b)](x0) = 2x0 + 1, 41.50/10.89 41.50/10.89 [a(b)](x0) = 2x0 + 2, 41.50/10.89 41.50/10.89 [c(a)](x0) = 4x0 + 3, 41.50/10.89 41.50/10.89 [a(c)](x0) = x0 + 1, 41.50/10.89 41.50/10.89 [a(a)](x0) = 2x0 41.50/10.89 orientation: 41.50/10.89 a(a)(a(a)(a(c)(c(a)(x1)))) = 16x1 + 16 >= 16x1 + 16 = a(b)(b(b)(b(c)(c(a)(x1)))) 41.50/10.89 41.50/10.89 a(a)(a(a)(a(c)(c(c)(x1)))) = 8x1 + 4 >= 8x1 + 4 = a(b)(b(b)(b(c)(c(c)(x1)))) 41.50/10.89 41.50/10.89 a(a)(a(a)(a(c)(c(b)(x1)))) = 16x1 + 12 >= 16x1 + 12 = a(b)(b(b)(b(c)(c(b)(x1)))) 41.50/10.89 41.50/10.89 b(a)(a(a)(a(c)(c(a)(x1)))) = 16x1 + 17 >= 16x1 + 15 = b(b)(b(b)(b(c)(c(a)(x1)))) 41.50/10.89 41.50/10.89 b(a)(a(a)(a(c)(c(c)(x1)))) = 8x1 + 5 >= 8x1 + 3 = b(b)(b(b)(b(c)(c(c)(x1)))) 41.50/10.89 41.50/10.89 b(a)(a(a)(a(c)(c(b)(x1)))) = 16x1 + 13 >= 16x1 + 11 = b(b)(b(b)(b(c)(c(b)(x1)))) 41.50/10.89 41.50/10.89 a(b)(b(b)(b(b)(b(a)(x1)))) = 16x1 + 16 >= 16x1 + 13 = a(c)(c(c)(c(b)(b(a)(x1)))) 41.50/10.89 41.50/10.89 a(b)(b(b)(b(b)(b(c)(x1)))) = 8x1 + 8 >= 8x1 + 5 = a(c)(c(c)(c(b)(b(c)(x1)))) 41.50/10.89 41.50/10.89 a(b)(b(b)(b(b)(b(b)(x1)))) = 16x1 + 16 >= 16x1 + 13 = a(c)(c(c)(c(b)(b(b)(x1)))) 41.50/10.89 41.50/10.89 b(c)(c(a)(a(a)(a(a)(x1)))) = 16x1 + 3 >= 16x1 + 1 = b(a)(a(a)(a(a)(a(a)(x1)))) 41.50/10.89 41.50/10.89 b(c)(c(a)(a(a)(a(c)(x1)))) = 8x1 + 11 >= 8x1 + 9 = b(a)(a(a)(a(a)(a(c)(x1)))) 41.50/10.89 41.50/10.89 b(c)(c(a)(a(a)(a(b)(x1)))) = 16x1 + 19 >= 16x1 + 17 = b(a)(a(a)(a(a)(a(b)(x1)))) 41.50/10.89 problem: 41.50/10.89 a(a)(a(a)(a(c)(c(a)(x1)))) -> a(b)(b(b)(b(c)(c(a)(x1)))) 41.50/10.89 a(a)(a(a)(a(c)(c(c)(x1)))) -> a(b)(b(b)(b(c)(c(c)(x1)))) 41.50/10.89 a(a)(a(a)(a(c)(c(b)(x1)))) -> a(b)(b(b)(b(c)(c(b)(x1)))) 41.50/10.90 Matrix Interpretation Processor: dim=3 41.50/10.90 41.50/10.90 interpretation: 41.50/10.90 [1 0 0] 41.50/10.90 [c(b)](x0) = [0 0 1]x0 41.50/10.90 [0 0 1] , 41.50/10.90 41.50/10.90 [1 0 1] 41.50/10.90 [c(c)](x0) = [0 0 0]x0 41.50/10.90 [0 0 0] , 41.50/10.90 41.50/10.90 [1 0 0] [0] 41.50/10.90 [b(c)](x0) = [1 0 0]x0 + [0] 41.50/10.90 [0 0 0] [1], 41.50/10.90 41.50/10.90 [1 0 0] 41.50/10.90 [b(b)](x0) = [0 0 0]x0 41.50/10.90 [0 0 0] , 41.50/10.90 41.50/10.90 [1 0 0] [0] 41.50/10.90 [a(b)](x0) = [0 0 0]x0 + [0] 41.50/10.90 [0 0 0] [1], 41.50/10.90 41.50/10.90 [1 0 0] 41.50/10.90 [c(a)](x0) = [0 0 0]x0 41.50/10.90 [0 0 0] , 41.50/10.90 41.50/10.90 [1 0 0] 41.50/10.90 [a(c)](x0) = [0 0 1]x0 41.50/10.90 [0 1 0] , 41.50/10.90 41.50/10.90 [1 0 1] [0] 41.50/10.90 [a(a)](x0) = [0 1 0]x0 + [0] 41.50/10.90 [0 0 0] [1] 41.50/10.90 orientation: 41.50/10.90 [1 0 0] [1] [1 0 0] [0] 41.50/10.90 a(a)(a(a)(a(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(b)(b(b)(b(c)(c(a)(x1)))) 41.50/10.90 [0 0 0] [1] [0 0 0] [1] 41.50/10.90 41.50/10.90 [1 0 1] [1] [1 0 1] [0] 41.50/10.90 a(a)(a(a)(a(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(b)(b(b)(b(c)(c(c)(x1)))) 41.50/10.90 [0 0 0] [1] [0 0 0] [1] 41.50/10.90 41.50/10.90 [1 0 1] [1] [1 0 0] [0] 41.50/10.90 a(a)(a(a)(a(c)(c(b)(x1)))) = [0 0 1]x1 + [0] >= [0 0 0]x1 + [0] = a(b)(b(b)(b(c)(c(b)(x1)))) 41.50/10.90 [0 0 0] [1] [0 0 0] [1] 41.50/10.90 problem: 41.50/10.90 41.50/10.90 Qed 41.50/10.90 EOF