57.58/14.96 YES 57.58/14.97 57.58/14.97 Problem: 57.58/14.97 strict: 57.58/14.97 b(c(b(x1))) -> b(a(c(x1))) 57.58/14.97 b(a(c(x1))) -> b(c(a(x1))) 57.58/14.97 weak: 57.58/14.97 a(c(c(x1))) -> c(c(b(x1))) 57.58/14.97 a(c(a(x1))) -> a(b(b(x1))) 57.58/14.97 b(b(b(x1))) -> c(c(a(x1))) 57.58/14.97 57.58/14.97 Proof: 57.58/14.97 Root-Labeling Processor: 57.58/14.97 strict: 57.58/14.97 b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 57.58/14.97 b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 57.58/14.97 b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 57.58/14.97 b(a)(a(c)(c(b)(x1))) -> b(c)(c(a)(a(b)(x1))) 57.58/14.97 b(a)(a(c)(c(c)(x1))) -> b(c)(c(a)(a(c)(x1))) 57.58/14.97 b(a)(a(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(x1))) 57.58/14.97 weak: 57.58/14.97 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.97 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.97 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.97 c(a)(a(c)(c(c)(c(b)(x1)))) -> c(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.97 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.97 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.97 a(a)(a(c)(c(c)(c(b)(x1)))) -> a(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.97 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.97 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.97 a(c)(c(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) 57.58/14.97 a(c)(c(a)(a(c)(x1))) -> a(b)(b(b)(b(c)(x1))) 57.58/14.97 a(c)(c(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) 57.58/14.97 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(c)(c(a)(a(b)(x1)))) 57.58/14.97 b(b)(b(b)(b(b)(b(c)(x1)))) -> b(c)(c(c)(c(a)(a(c)(x1)))) 57.58/14.97 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(c)(c(c)(c(a)(a(a)(x1)))) 57.58/14.97 c(b)(b(b)(b(b)(b(b)(x1)))) -> c(c)(c(c)(c(a)(a(b)(x1)))) 57.58/14.97 c(b)(b(b)(b(b)(b(c)(x1)))) -> c(c)(c(c)(c(a)(a(c)(x1)))) 57.58/14.97 c(b)(b(b)(b(b)(b(a)(x1)))) -> c(c)(c(c)(c(a)(a(a)(x1)))) 57.58/14.97 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(c)(c(c)(c(a)(a(b)(x1)))) 57.58/14.97 a(b)(b(b)(b(b)(b(c)(x1)))) -> a(c)(c(c)(c(a)(a(c)(x1)))) 57.58/14.97 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(c)(c(c)(c(a)(a(a)(x1)))) 57.58/14.97 RT Transformation Processor: 57.58/14.97 b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 57.58/14.97 b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 57.58/14.97 b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 57.58/14.97 b(a)(a(c)(c(b)(x1))) -> b(c)(c(a)(a(b)(x1))) 57.58/14.97 b(a)(a(c)(c(c)(x1))) -> b(c)(c(a)(a(c)(x1))) 57.58/14.97 b(a)(a(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(x1))) 57.58/14.97 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.97 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.97 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.97 c(a)(a(c)(c(c)(c(b)(x1)))) -> c(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.97 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.97 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.97 a(a)(a(c)(c(c)(c(b)(x1)))) -> a(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.97 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.97 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.97 a(c)(c(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) 57.58/14.97 a(c)(c(a)(a(c)(x1))) -> a(b)(b(b)(b(c)(x1))) 57.58/14.97 a(c)(c(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) 57.58/14.97 b(b)(b(b)(b(b)(b(b)(x1)))) -> b(c)(c(c)(c(a)(a(b)(x1)))) 57.58/14.97 b(b)(b(b)(b(b)(b(c)(x1)))) -> b(c)(c(c)(c(a)(a(c)(x1)))) 57.58/14.97 b(b)(b(b)(b(b)(b(a)(x1)))) -> b(c)(c(c)(c(a)(a(a)(x1)))) 57.58/14.97 c(b)(b(b)(b(b)(b(b)(x1)))) -> c(c)(c(c)(c(a)(a(b)(x1)))) 57.58/14.97 c(b)(b(b)(b(b)(b(c)(x1)))) -> c(c)(c(c)(c(a)(a(c)(x1)))) 57.58/14.97 c(b)(b(b)(b(b)(b(a)(x1)))) -> c(c)(c(c)(c(a)(a(a)(x1)))) 57.58/14.97 a(b)(b(b)(b(b)(b(b)(x1)))) -> a(c)(c(c)(c(a)(a(b)(x1)))) 57.58/14.97 a(b)(b(b)(b(b)(b(c)(x1)))) -> a(c)(c(c)(c(a)(a(c)(x1)))) 57.58/14.97 a(b)(b(b)(b(b)(b(a)(x1)))) -> a(c)(c(c)(c(a)(a(a)(x1)))) 57.58/14.97 Matrix Interpretation Processor: dim=2 57.58/14.97 57.58/14.97 interpretation: 57.58/14.97 [1 0] [2] 57.58/14.97 [a(a)](x0) = [1 0]x0 + [1], 57.58/14.97 57.58/14.97 [1 0] [2] 57.58/14.97 [a(b)](x0) = [0 0]x0 + [0], 57.58/14.97 57.58/14.97 [1 0] [1] 57.58/14.97 [c(a)](x0) = [2 0]x0 + [0], 57.58/14.97 57.58/14.97 [1 0] 57.58/14.97 [c(c)](x0) = [0 0]x0, 57.58/14.97 57.58/14.97 [1 0] [1] 57.58/14.97 [a(c)](x0) = [0 0]x0 + [0], 57.58/14.97 57.58/14.97 [1 0] [1] 57.58/14.97 [b(a)](x0) = [0 0]x0 + [1], 57.58/14.97 57.58/14.97 [1] 57.58/14.97 [b(b)](x0) = x0 + [1], 57.58/14.97 57.58/14.97 [1 1] [1] 57.58/14.97 [c(b)](x0) = [0 0]x0 + [0], 57.58/14.97 57.58/14.97 [1 0] [0] 57.58/14.97 [b(c)](x0) = [0 0]x0 + [1] 57.58/14.97 orientation: 57.58/14.97 [1 1] [3] [1 1] [3] 57.58/14.97 b(c)(c(b)(b(b)(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a)(a(c)(c(b)(x1))) 57.58/14.97 57.58/14.97 [1 0] [2] [1 0] [2] 57.58/14.97 b(c)(c(b)(b(c)(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a)(a(c)(c(c)(x1))) 57.58/14.97 57.58/14.97 [1 0] [3] [1 0] [3] 57.58/14.97 b(c)(c(b)(b(a)(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a)(a(c)(c(a)(x1))) 57.58/14.97 57.58/14.97 [1 1] [3] [1 0] [3] 57.58/14.97 b(a)(a(c)(c(b)(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c)(c(a)(a(b)(x1))) 57.58/14.97 57.58/14.97 [1 0] [2] [1 0] [2] 57.58/14.97 b(a)(a(c)(c(c)(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c)(c(a)(a(c)(x1))) 57.58/14.97 57.58/14.97 [1 0] [3] [1 0] [3] 57.58/14.97 b(a)(a(c)(c(a)(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c)(c(a)(a(a)(x1))) 57.58/14.97 57.58/14.97 [1 1] [3] [1 1] [3] 57.58/14.97 b(a)(a(c)(c(c)(c(b)(x1)))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.97 57.58/14.97 [1 0] [2] [1 0] [2] 57.58/14.97 b(a)(a(c)(c(c)(c(c)(x1)))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.97 57.58/14.97 [1 0] [3] [1 0] [3] 57.58/14.97 b(a)(a(c)(c(c)(c(a)(x1)))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.97 57.58/14.97 [1 1] [3] [1 1] [3] 57.58/14.97 c(a)(a(c)(c(c)(c(b)(x1)))) = [2 2]x1 + [4] >= [0 0]x1 + [0] = c(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.97 57.58/14.97 [1 0] [2] [1 0] [2] 57.58/14.97 c(a)(a(c)(c(c)(c(c)(x1)))) = [2 0]x1 + [2] >= [0 0]x1 + [0] = c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.97 57.58/14.97 [1 0] [3] [1 0] [3] 57.58/14.97 c(a)(a(c)(c(c)(c(a)(x1)))) = [2 0]x1 + [4] >= [0 0]x1 + [0] = c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.97 57.58/14.97 [1 1] [4] [1 1] [4] 57.58/14.97 a(a)(a(c)(c(c)(c(b)(x1)))) = [1 1]x1 + [3] >= [0 0]x1 + [0] = a(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.97 57.58/14.97 [1 0] [3] [1 0] [3] 57.58/14.97 a(a)(a(c)(c(c)(c(c)(x1)))) = [1 0]x1 + [2] >= [0 0]x1 + [0] = a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.97 57.58/14.97 [1 0] [4] [1 0] [4] 57.58/14.97 a(a)(a(c)(c(c)(c(a)(x1)))) = [1 0]x1 + [3] >= [0 0]x1 + [0] = a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.97 57.58/14.97 [1 0] [4] [1 0] [4] 57.58/14.97 a(c)(c(a)(a(b)(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(b)(b(b)(b(b)(x1))) 57.58/14.97 57.58/14.97 [1 0] [3] [1 0] [3] 57.58/14.97 a(c)(c(a)(a(c)(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(b)(b(b)(b(c)(x1))) 57.58/14.97 57.58/14.97 [1 0] [4] [1 0] [4] 57.58/14.97 a(c)(c(a)(a(a)(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(b)(b(b)(b(a)(x1))) 57.58/14.97 57.58/14.97 [4] [1 0] [3] 57.58/14.97 b(b)(b(b)(b(b)(b(b)(x1)))) = x1 + [4] >= [0 0]x1 + [1] = b(c)(c(c)(c(a)(a(b)(x1)))) 57.58/14.97 57.58/14.97 [1 0] [3] [1 0] [2] 57.58/14.97 b(b)(b(b)(b(b)(b(c)(x1)))) = [0 0]x1 + [4] >= [0 0]x1 + [1] = b(c)(c(c)(c(a)(a(c)(x1)))) 57.58/14.97 57.58/14.97 [1 0] [4] [1 0] [3] 57.58/14.97 b(b)(b(b)(b(b)(b(a)(x1)))) = [0 0]x1 + [4] >= [0 0]x1 + [1] = b(c)(c(c)(c(a)(a(a)(x1)))) 57.58/14.97 57.58/14.97 [1 1] [7] [1 0] [3] 57.58/14.97 c(b)(b(b)(b(b)(b(b)(x1)))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(c)(c(c)(c(a)(a(b)(x1)))) 57.58/14.97 57.58/14.97 [1 0] [6] [1 0] [2] 57.58/14.97 c(b)(b(b)(b(b)(b(c)(x1)))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(c)(c(c)(c(a)(a(c)(x1)))) 57.58/14.98 57.58/14.98 [1 0] [7] [1 0] [3] 57.58/14.98 c(b)(b(b)(b(b)(b(a)(x1)))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(c)(c(c)(c(a)(a(a)(x1)))) 57.58/14.98 57.58/14.98 [1 0] [5] [1 0] [4] 57.58/14.98 a(b)(b(b)(b(b)(b(b)(x1)))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(c)(c(c)(c(a)(a(b)(x1)))) 57.58/14.98 57.58/14.98 [1 0] [4] [1 0] [3] 57.58/14.98 a(b)(b(b)(b(b)(b(c)(x1)))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(c)(c(c)(c(a)(a(c)(x1)))) 57.58/14.98 57.58/14.98 [1 0] [5] [1 0] [4] 57.58/14.98 a(b)(b(b)(b(b)(b(a)(x1)))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(c)(c(c)(c(a)(a(a)(x1)))) 57.58/14.98 problem: 57.58/14.98 b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 57.58/14.98 b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 57.58/14.98 b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 57.58/14.98 b(a)(a(c)(c(b)(x1))) -> b(c)(c(a)(a(b)(x1))) 57.58/14.98 b(a)(a(c)(c(c)(x1))) -> b(c)(c(a)(a(c)(x1))) 57.58/14.98 b(a)(a(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(x1))) 57.58/14.98 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.98 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.98 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.98 c(a)(a(c)(c(c)(c(b)(x1)))) -> c(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.98 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.98 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.98 a(a)(a(c)(c(c)(c(b)(x1)))) -> a(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.98 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.98 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.98 a(c)(c(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) 57.58/14.98 a(c)(c(a)(a(c)(x1))) -> a(b)(b(b)(b(c)(x1))) 57.58/14.98 a(c)(c(a)(a(a)(x1))) -> a(b)(b(b)(b(a)(x1))) 57.58/14.98 Matrix Interpretation Processor: dim=3 57.58/14.98 57.58/14.98 interpretation: 57.58/14.98 [1 1 0] [0] 57.58/14.98 [a(a)](x0) = [0 0 0]x0 + [1] 57.58/14.98 [1 0 1] [0], 57.58/14.98 57.58/14.98 [1 0 0] 57.58/14.98 [a(b)](x0) = [0 0 1]x0 57.58/14.98 [0 0 0] , 57.58/14.98 57.58/14.98 [1 1 0] 57.58/14.98 [c(a)](x0) = [0 0 0]x0 57.58/14.98 [0 0 1] , 57.58/14.98 57.58/14.98 [1 0 0] [0] 57.58/14.98 [c(c)](x0) = [0 0 0]x0 + [0] 57.58/14.98 [0 0 0] [1], 57.58/14.98 57.58/14.98 [1 0 0] [0] 57.58/14.98 [a(c)](x0) = [0 0 0]x0 + [1] 57.58/14.98 [0 0 1] [0], 57.58/14.98 57.58/14.98 [1 1 0] [0] 57.58/14.98 [b(a)](x0) = [0 0 0]x0 + [1] 57.58/14.98 [0 0 0] [0], 57.58/14.98 57.58/14.98 [1 0 0] [0] 57.58/14.98 [b(b)](x0) = [0 1 1]x0 + [0] 57.58/14.98 [0 0 0] [1], 57.58/14.98 57.58/14.98 [1 1 1] 57.58/14.98 [c(b)](x0) = [0 0 0]x0 57.58/14.98 [0 0 0] , 57.58/14.98 57.58/14.98 [1 0 0] [0] 57.58/14.98 [b(c)](x0) = [0 0 0]x0 + [1] 57.58/14.98 [0 0 0] [0] 57.58/14.98 orientation: 57.58/14.98 [1 1 1] [1] [1 1 1] [1] 57.58/14.98 b(c)(c(b)(b(b)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a)(a(c)(c(b)(x1))) 57.58/14.98 [0 0 0] [0] [0 0 0] [0] 57.58/14.98 57.58/14.98 [1 0 0] [1] [1 0 0] [1] 57.58/14.98 b(c)(c(b)(b(c)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a)(a(c)(c(c)(x1))) 57.58/14.98 [0 0 0] [0] [0 0 0] [0] 57.58/14.98 57.58/14.98 [1 1 0] [1] [1 1 0] [1] 57.58/14.98 b(c)(c(b)(b(a)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a)(a(c)(c(a)(x1))) 57.58/14.98 [0 0 0] [0] [0 0 0] [0] 57.58/14.98 57.58/14.98 [1 1 1] [1] [1 0 1] [0] 57.58/14.98 b(a)(a(c)(c(b)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(c)(c(a)(a(b)(x1))) 57.58/14.98 [0 0 0] [0] [0 0 0] [0] 57.58/14.98 57.58/14.98 [1 0 0] [1] [1 0 0] [1] 57.58/14.98 b(a)(a(c)(c(c)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(c)(c(a)(a(c)(x1))) 57.58/14.99 [0 0 0] [0] [0 0 0] [0] 57.58/14.99 57.58/14.99 [1 1 0] [1] [1 1 0] [1] 57.58/14.99 b(a)(a(c)(c(a)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(c)(c(a)(a(a)(x1))) 57.58/14.99 [0 0 0] [0] [0 0 0] [0] 57.58/14.99 57.58/14.99 [1 1 1] [1] [1 1 1] [1] 57.58/14.99 b(a)(a(c)(c(c)(c(b)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.99 [0 0 0] [0] [0 0 0] [0] 57.58/14.99 57.58/14.99 [1 0 0] [1] [1 0 0] [1] 57.58/14.99 b(a)(a(c)(c(c)(c(c)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.99 [0 0 0] [0] [0 0 0] [0] 57.58/14.99 57.58/14.99 [1 1 0] [1] [1 1 0] [1] 57.58/14.99 b(a)(a(c)(c(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.99 [0 0 0] [0] [0 0 0] [0] 57.58/14.99 57.58/14.99 [1 1 1] [1] [1 1 1] [1] 57.58/14.99 c(a)(a(c)(c(c)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.99 [0 0 0] [1] [0 0 0] [1] 57.58/14.99 57.58/14.99 [1 0 0] [1] [1 0 0] [1] 57.58/14.99 c(a)(a(c)(c(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.99 [0 0 0] [1] [0 0 0] [1] 57.58/14.99 57.58/14.99 [1 1 0] [1] [1 1 0] [1] 57.58/14.99 c(a)(a(c)(c(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.99 [0 0 0] [1] [0 0 0] [1] 57.58/14.99 57.58/14.99 [1 1 1] [1] [1 1 1] [1] 57.58/14.99 a(a)(a(c)(c(c)(c(b)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(c)(c(c)(c(b)(b(b)(x1)))) 57.58/14.99 [1 1 1] [1] [0 0 0] [1] 57.58/14.99 57.58/14.99 [1 0 0] [1] [1 0 0] [1] 57.58/14.99 a(a)(a(c)(c(c)(c(c)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/14.99 [1 0 0] [1] [0 0 0] [1] 57.58/14.99 57.58/14.99 [1 1 0] [1] [1 1 0] [1] 57.58/14.99 a(a)(a(c)(c(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/14.99 [1 1 0] [1] [0 0 0] [1] 57.58/14.99 57.58/14.99 [1 0 1] [0] [1 0 0] [0] 57.58/14.99 a(c)(c(a)(a(b)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b)(b(b)(b(b)(x1))) 57.58/14.99 [0 0 0] [0] [0 0 0] [0] 57.58/14.99 57.58/14.99 [1 0 0] [1] [1 0 0] [0] 57.58/14.99 a(c)(c(a)(a(c)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b)(b(b)(b(c)(x1))) 57.58/14.99 [0 0 1] [0] [0 0 0] [0] 57.58/14.99 57.58/14.99 [1 1 0] [1] [1 1 0] [0] 57.58/14.99 a(c)(c(a)(a(a)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(b)(b(b)(b(a)(x1))) 57.58/14.99 [1 0 1] [0] [0 0 0] [0] 57.58/14.99 problem: 57.58/14.99 b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 57.58/14.99 b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 57.58/14.99 b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 57.58/14.99 b(a)(a(c)(c(c)(x1))) -> b(c)(c(a)(a(c)(x1))) 57.58/15.00 b(a)(a(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(x1))) 57.58/15.00 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.00 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.00 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.00 c(a)(a(c)(c(c)(c(b)(x1)))) -> c(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.00 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.00 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.00 a(a)(a(c)(c(c)(c(b)(x1)))) -> a(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.00 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.00 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.00 a(c)(c(a)(a(b)(x1))) -> a(b)(b(b)(b(b)(x1))) 57.58/15.00 Matrix Interpretation Processor: dim=1 57.58/15.00 57.58/15.00 interpretation: 57.58/15.00 [a(a)](x0) = x0, 57.58/15.00 57.58/15.00 [a(b)](x0) = 4x0 + 4, 57.58/15.00 57.58/15.00 [c(a)](x0) = 2x0, 57.58/15.00 57.58/15.00 [c(c)](x0) = 2x0, 57.58/15.00 57.58/15.00 [a(c)](x0) = x0, 57.58/15.00 57.58/15.00 [b(a)](x0) = x0, 57.58/15.00 57.58/15.00 [b(b)](x0) = x0, 57.58/15.00 57.58/15.00 [c(b)](x0) = 2x0, 57.58/15.00 57.58/15.00 [b(c)](x0) = x0 57.58/15.00 orientation: 57.58/15.00 b(c)(c(b)(b(b)(x1))) = 2x1 >= 2x1 = b(a)(a(c)(c(b)(x1))) 57.58/15.00 57.58/15.00 b(c)(c(b)(b(c)(x1))) = 2x1 >= 2x1 = b(a)(a(c)(c(c)(x1))) 57.58/15.00 57.58/15.00 b(c)(c(b)(b(a)(x1))) = 2x1 >= 2x1 = b(a)(a(c)(c(a)(x1))) 57.58/15.00 57.58/15.00 b(a)(a(c)(c(c)(x1))) = 2x1 >= 2x1 = b(c)(c(a)(a(c)(x1))) 57.58/15.00 57.58/15.00 b(a)(a(c)(c(a)(x1))) = 2x1 >= 2x1 = b(c)(c(a)(a(a)(x1))) 57.58/15.00 57.58/15.00 b(a)(a(c)(c(c)(c(b)(x1)))) = 4x1 >= 4x1 = b(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.00 57.58/15.00 b(a)(a(c)(c(c)(c(c)(x1)))) = 4x1 >= 4x1 = b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.00 57.58/15.00 b(a)(a(c)(c(c)(c(a)(x1)))) = 4x1 >= 4x1 = b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.00 57.58/15.00 c(a)(a(c)(c(c)(c(b)(x1)))) = 8x1 >= 8x1 = c(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.00 57.58/15.00 c(a)(a(c)(c(c)(c(c)(x1)))) = 8x1 >= 8x1 = c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.00 57.58/15.00 c(a)(a(c)(c(c)(c(a)(x1)))) = 8x1 >= 8x1 = c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.00 57.58/15.00 a(a)(a(c)(c(c)(c(b)(x1)))) = 4x1 >= 4x1 = a(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.00 57.58/15.00 a(a)(a(c)(c(c)(c(c)(x1)))) = 4x1 >= 4x1 = a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.00 57.58/15.00 a(a)(a(c)(c(c)(c(a)(x1)))) = 4x1 >= 4x1 = a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.00 57.58/15.00 a(c)(c(a)(a(b)(x1))) = 8x1 + 8 >= 4x1 + 4 = a(b)(b(b)(b(b)(x1))) 57.58/15.00 problem: 57.58/15.00 b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 57.58/15.00 b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 57.58/15.00 b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 57.58/15.00 b(a)(a(c)(c(c)(x1))) -> b(c)(c(a)(a(c)(x1))) 57.58/15.00 b(a)(a(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(x1))) 57.58/15.00 b(a)(a(c)(c(c)(c(b)(x1)))) -> b(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.00 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.00 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.00 c(a)(a(c)(c(c)(c(b)(x1)))) -> c(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.00 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.00 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.00 a(a)(a(c)(c(c)(c(b)(x1)))) -> a(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.00 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.00 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.00 Matrix Interpretation Processor: dim=3 57.58/15.00 57.58/15.00 interpretation: 57.58/15.00 [1 1 1] [0] 57.58/15.00 [a(a)](x0) = [0 0 0]x0 + [1] 57.58/15.00 [0 0 0] [0], 57.58/15.00 57.58/15.00 [1 1 0] [0] 57.58/15.00 [c(a)](x0) = [0 0 1]x0 + [1] 57.58/15.00 [0 0 0] [0], 57.58/15.00 57.58/15.00 [1 0 0] 57.58/15.00 [c(c)](x0) = [0 1 1]x0 57.58/15.00 [0 0 0] , 57.58/15.00 57.58/15.00 [1 0 0] 57.58/15.00 [a(c)](x0) = [0 1 0]x0 57.58/15.00 [0 0 0] , 57.58/15.00 57.58/15.00 [1 1 0] [0] 57.58/15.00 [b(a)](x0) = [0 0 0]x0 + [0] 57.58/15.00 [0 0 1] [1], 57.58/15.00 57.58/15.00 [1 0 1] 57.58/15.00 [b(b)](x0) = [0 0 0]x0 57.58/15.00 [0 0 0] , 57.58/15.00 57.58/15.00 [1 0 1] [0] 57.58/15.00 [c(b)](x0) = [0 0 0]x0 + [0] 57.58/15.00 [0 0 0] [1], 57.58/15.00 57.58/15.00 [1 0 0] 57.58/15.00 [b(c)](x0) = [0 0 0]x0 57.58/15.00 [0 1 1] 57.58/15.00 orientation: 57.58/15.00 [1 0 1] [0] [1 0 1] [0] 57.58/15.01 b(c)(c(b)(b(b)(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a)(a(c)(c(b)(x1))) 57.58/15.01 [0 0 0] [1] [0 0 0] [1] 57.58/15.01 57.58/15.01 [1 1 1] [0] [1 1 1] [0] 57.58/15.01 b(c)(c(b)(b(c)(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a)(a(c)(c(c)(x1))) 57.58/15.01 [0 0 0] [1] [0 0 0] [1] 57.58/15.01 57.58/15.01 [1 1 1] [1] [1 1 1] [1] 57.58/15.01 b(c)(c(b)(b(a)(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(a)(a(c)(c(a)(x1))) 57.58/15.01 [0 0 0] [1] [0 0 0] [1] 57.58/15.01 57.58/15.01 [1 1 1] [0] [1 1 0] [0] 57.58/15.01 b(a)(a(c)(c(c)(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(c)(x1))) 57.58/15.01 [0 0 0] [1] [0 0 0] [1] 57.58/15.01 57.58/15.01 [1 1 1] [1] [1 1 1] [1] 57.58/15.01 b(a)(a(c)(c(a)(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(a)(a(a)(x1))) 57.58/15.01 [0 0 0] [1] [0 0 0] [1] 57.58/15.01 57.58/15.01 [1 0 1] [1] [1 0 1] [0] 57.58/15.01 b(a)(a(c)(c(c)(c(b)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.01 [0 0 0] [1] [0 0 0] [1] 57.58/15.01 57.58/15.01 [1 1 1] [0] [1 1 1] [0] 57.58/15.01 b(a)(a(c)(c(c)(c(c)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 [0 0 0] [1] [0 0 0] [1] 57.58/15.01 57.58/15.01 [1 1 1] [1] [1 1 1] [1] 57.58/15.01 b(a)(a(c)(c(c)(c(a)(x1)))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 [0 0 0] [1] [0 0 0] [1] 57.58/15.01 57.58/15.01 [1 0 1] [1] [1 0 1] [0] 57.58/15.01 c(a)(a(c)(c(c)(c(b)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.01 [0 0 0] [0] [0 0 0] [0] 57.58/15.01 57.58/15.01 [1 1 1] [0] [1 1 1] [0] 57.58/15.01 c(a)(a(c)(c(c)(c(c)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 [0 0 0] [0] [0 0 0] [0] 57.58/15.01 57.58/15.01 [1 1 1] [1] [1 1 1] [1] 57.58/15.01 c(a)(a(c)(c(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 [0 0 0] [0] [0 0 0] [0] 57.58/15.01 57.58/15.01 [1 0 1] [1] [1 0 1] [0] 57.58/15.01 a(a)(a(c)(c(c)(c(b)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(c)(c(c)(c(b)(b(b)(x1)))) 57.58/15.01 [0 0 0] [0] [0 0 0] [0] 57.58/15.01 57.58/15.01 [1 1 1] [0] [1 1 1] [0] 57.58/15.01 a(a)(a(c)(c(c)(c(c)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 [0 0 0] [0] [0 0 0] [0] 57.58/15.01 57.58/15.01 [1 1 1] [1] [1 1 1] [1] 57.58/15.01 a(a)(a(c)(c(c)(c(a)(x1)))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 [0 0 0] [0] [0 0 0] [0] 57.58/15.01 problem: 57.58/15.01 b(c)(c(b)(b(b)(x1))) -> b(a)(a(c)(c(b)(x1))) 57.58/15.01 b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 57.58/15.01 b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 57.58/15.01 b(a)(a(c)(c(c)(x1))) -> b(c)(c(a)(a(c)(x1))) 57.58/15.01 b(a)(a(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(x1))) 57.58/15.01 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 Matrix Interpretation Processor: dim=1 57.58/15.01 57.58/15.01 interpretation: 57.58/15.01 [a(a)](x0) = 2x0, 57.58/15.01 57.58/15.01 [c(a)](x0) = 2x0, 57.58/15.01 57.58/15.01 [c(c)](x0) = 2x0, 57.58/15.01 57.58/15.01 [a(c)](x0) = 2x0, 57.58/15.01 57.58/15.01 [b(a)](x0) = x0, 57.58/15.01 57.58/15.01 [b(b)](x0) = 4x0 + 2, 57.58/15.01 57.58/15.01 [c(b)](x0) = 4x0, 57.58/15.01 57.58/15.01 [b(c)](x0) = x0 57.58/15.01 orientation: 57.58/15.01 b(c)(c(b)(b(b)(x1))) = 16x1 + 8 >= 8x1 = b(a)(a(c)(c(b)(x1))) 57.58/15.01 57.58/15.01 b(c)(c(b)(b(c)(x1))) = 4x1 >= 4x1 = b(a)(a(c)(c(c)(x1))) 57.58/15.01 57.58/15.01 b(c)(c(b)(b(a)(x1))) = 4x1 >= 4x1 = b(a)(a(c)(c(a)(x1))) 57.58/15.01 57.58/15.01 b(a)(a(c)(c(c)(x1))) = 4x1 >= 4x1 = b(c)(c(a)(a(c)(x1))) 57.58/15.01 57.58/15.01 b(a)(a(c)(c(a)(x1))) = 4x1 >= 4x1 = b(c)(c(a)(a(a)(x1))) 57.58/15.01 57.58/15.01 b(a)(a(c)(c(c)(c(c)(x1)))) = 8x1 >= 8x1 = b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 57.58/15.01 b(a)(a(c)(c(c)(c(a)(x1)))) = 8x1 >= 8x1 = b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 57.58/15.01 c(a)(a(c)(c(c)(c(c)(x1)))) = 16x1 >= 16x1 = c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 57.58/15.01 c(a)(a(c)(c(c)(c(a)(x1)))) = 16x1 >= 16x1 = c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 57.58/15.01 a(a)(a(c)(c(c)(c(c)(x1)))) = 16x1 >= 16x1 = a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 57.58/15.01 a(a)(a(c)(c(c)(c(a)(x1)))) = 16x1 >= 16x1 = a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 problem: 57.58/15.01 b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 57.58/15.01 b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 57.58/15.01 b(a)(a(c)(c(c)(x1))) -> b(c)(c(a)(a(c)(x1))) 57.58/15.01 b(a)(a(c)(c(a)(x1))) -> b(c)(c(a)(a(a)(x1))) 57.58/15.01 b(a)(a(c)(c(c)(c(c)(x1)))) -> b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 b(a)(a(c)(c(c)(c(a)(x1)))) -> b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 c(a)(a(c)(c(c)(c(c)(x1)))) -> c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 c(a)(a(c)(c(c)(c(a)(x1)))) -> c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 a(a)(a(c)(c(c)(c(c)(x1)))) -> a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 a(a)(a(c)(c(c)(c(a)(x1)))) -> a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 Matrix Interpretation Processor: dim=1 57.58/15.01 57.58/15.01 interpretation: 57.58/15.01 [a(a)](x0) = 2x0, 57.58/15.01 57.58/15.01 [c(a)](x0) = 2x0 + 1, 57.58/15.01 57.58/15.01 [c(c)](x0) = 2x0 + 1, 57.58/15.01 57.58/15.01 [a(c)](x0) = 2x0, 57.58/15.01 57.58/15.01 [b(a)](x0) = 2x0, 57.58/15.01 57.58/15.01 [c(b)](x0) = 2x0 + 2, 57.58/15.01 57.58/15.01 [b(c)](x0) = 2x0 57.58/15.01 orientation: 57.58/15.01 b(c)(c(b)(b(c)(x1))) = 8x1 + 4 >= 8x1 + 4 = b(a)(a(c)(c(c)(x1))) 57.58/15.01 57.58/15.01 b(c)(c(b)(b(a)(x1))) = 8x1 + 4 >= 8x1 + 4 = b(a)(a(c)(c(a)(x1))) 57.58/15.01 57.58/15.01 b(a)(a(c)(c(c)(x1))) = 8x1 + 4 >= 8x1 + 2 = b(c)(c(a)(a(c)(x1))) 57.58/15.01 57.58/15.01 b(a)(a(c)(c(a)(x1))) = 8x1 + 4 >= 8x1 + 2 = b(c)(c(a)(a(a)(x1))) 57.58/15.01 57.58/15.01 b(a)(a(c)(c(c)(c(c)(x1)))) = 16x1 + 12 >= 16x1 + 10 = b(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 57.58/15.01 b(a)(a(c)(c(c)(c(a)(x1)))) = 16x1 + 12 >= 16x1 + 10 = b(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 57.58/15.01 c(a)(a(c)(c(c)(c(c)(x1)))) = 16x1 + 13 >= 16x1 + 11 = c(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 57.58/15.01 c(a)(a(c)(c(c)(c(a)(x1)))) = 16x1 + 13 >= 16x1 + 11 = c(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 57.58/15.01 a(a)(a(c)(c(c)(c(c)(x1)))) = 16x1 + 12 >= 16x1 + 10 = a(c)(c(c)(c(b)(b(c)(x1)))) 57.58/15.01 57.58/15.01 a(a)(a(c)(c(c)(c(a)(x1)))) = 16x1 + 12 >= 16x1 + 10 = a(c)(c(c)(c(b)(b(a)(x1)))) 57.58/15.01 problem: 57.58/15.01 b(c)(c(b)(b(c)(x1))) -> b(a)(a(c)(c(c)(x1))) 57.58/15.01 b(c)(c(b)(b(a)(x1))) -> b(a)(a(c)(c(a)(x1))) 57.58/15.02 Matrix Interpretation Processor: dim=3 57.58/15.02 57.58/15.02 interpretation: 57.58/15.02 [1 0 0] 57.58/15.02 [c(a)](x0) = [0 1 0]x0 57.58/15.02 [0 0 0] , 57.58/15.02 57.58/15.02 [1 0 0] 57.58/15.02 [c(c)](x0) = [0 0 0]x0 57.58/15.02 [0 1 0] , 57.58/15.02 57.58/15.02 [1 1 0] 57.58/15.02 [a(c)](x0) = [0 0 1]x0 57.58/15.02 [0 0 0] , 57.58/15.02 57.58/15.02 [1 1 0] [0] 57.58/15.02 [b(a)](x0) = [0 0 0]x0 + [1] 57.58/15.02 [0 0 0] [0], 57.58/15.02 57.58/15.02 [1 1 0] 57.58/15.02 [c(b)](x0) = [0 0 0]x0 57.58/15.02 [0 0 0] , 57.58/15.02 57.58/15.02 [1 1 0] [0] 57.58/15.02 [b(c)](x0) = [0 0 0]x0 + [1] 57.58/15.02 [0 0 0] [0] 57.58/15.02 orientation: 57.58/15.02 [1 1 0] [1] [1 1 0] [0] 57.58/15.02 b(c)(c(b)(b(c)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a)(a(c)(c(c)(x1))) 57.58/15.02 [0 0 0] [0] [0 0 0] [0] 57.58/15.02 57.58/15.02 [1 1 0] [1] [1 1 0] [0] 57.58/15.02 b(c)(c(b)(b(a)(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(a)(a(c)(c(a)(x1))) 57.58/15.02 [0 0 0] [0] [0 0 0] [0] 57.58/15.02 problem: 57.58/15.02 57.58/15.02 Qed 57.58/15.02 EOF