13.51/3.74 YES 13.51/3.75 13.51/3.75 Problem: 13.51/3.75 strict: 13.51/3.75 b(c(a(x1))) -> d(d(x1)) 13.51/3.75 b(x1) -> c(c(x1)) 13.51/3.75 a(a(x1)) -> a(x1) 13.51/3.75 weak: 13.51/3.75 a(b(x1)) -> d(x1) 13.51/3.75 d(x1) -> a(b(x1)) 13.51/3.75 13.51/3.75 Proof: 13.51/3.75 String Reversal Processor: 13.51/3.75 strict: 13.51/3.75 a(c(b(x1))) -> d(d(x1)) 13.51/3.75 b(x1) -> c(c(x1)) 13.51/3.75 a(a(x1)) -> a(x1) 13.51/3.75 weak: 13.51/3.75 b(a(x1)) -> d(x1) 13.51/3.75 d(x1) -> b(a(x1)) 13.51/3.75 Matrix Interpretation Processor: dim=3 13.51/3.75 13.51/3.75 interpretation: 13.51/3.75 [1 0 1] [0] 13.51/3.75 [d](x0) = [0 0 0]x0 + [2] 13.51/3.75 [0 0 0] [0], 13.51/3.75 13.51/3.75 [1 0 0] [0] 13.51/3.75 [b](x0) = [0 0 1]x0 + [2] 13.51/3.75 [0 0 0] [0], 13.51/3.75 13.51/3.75 [1 0 0] 13.51/3.75 [c](x0) = [0 0 0]x0 13.51/3.75 [0 1 0] , 13.51/3.75 13.51/3.75 [1 0 1] [0] 13.51/3.75 [a](x0) = [0 0 0]x0 + [3] 13.51/3.75 [0 0 0] [0] 13.51/3.75 orientation: 13.51/3.75 [1 0 1] [2] [1 0 1] [0] 13.51/3.75 a(c(b(x1))) = [0 0 0]x1 + [3] >= [0 0 0]x1 + [2] = d(d(x1)) 13.51/3.75 [0 0 0] [0] [0 0 0] [0] 13.51/3.75 13.51/3.75 [1 0 0] [0] [1 0 0] 13.51/3.75 b(x1) = [0 0 1]x1 + [2] >= [0 0 0]x1 = c(c(x1)) 13.51/3.75 [0 0 0] [0] [0 0 0] 13.51/3.75 13.51/3.75 [1 0 1] [0] [1 0 1] [0] 13.51/3.75 a(a(x1)) = [0 0 0]x1 + [3] >= [0 0 0]x1 + [3] = a(x1) 13.51/3.75 [0 0 0] [0] [0 0 0] [0] 13.51/3.75 13.51/3.75 [1 0 1] [0] [1 0 1] [0] 13.51/3.75 b(a(x1)) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = d(x1) 13.51/3.75 [0 0 0] [0] [0 0 0] [0] 13.51/3.75 13.51/3.75 [1 0 1] [0] [1 0 1] [0] 13.51/3.75 d(x1) = [0 0 0]x1 + [2] >= [0 0 0]x1 + [2] = b(a(x1)) 13.51/3.75 [0 0 0] [0] [0 0 0] [0] 13.51/3.75 problem: 13.51/3.75 strict: 13.51/3.75 b(x1) -> c(c(x1)) 13.51/3.75 a(a(x1)) -> a(x1) 13.51/3.75 weak: 13.51/3.75 b(a(x1)) -> d(x1) 13.51/3.75 d(x1) -> b(a(x1)) 13.51/3.75 Arctic Interpretation Processor: 13.51/3.75 dimension: 2 13.51/3.75 interpretation: 13.51/3.75 [5 5] 13.51/3.75 [d](x0) = [6 5]x0, 13.51/3.75 13.51/3.75 [5 2] 13.51/3.75 [b](x0) = [4 4]x0, 13.51/3.75 13.51/3.75 [1 0] 13.51/3.75 [c](x0) = [2 2]x0, 13.51/3.75 13.51/3.75 [0 0] 13.51/3.75 [a](x0) = [2 1]x0 13.51/3.75 orientation: 13.51/3.75 [5 2] [2 2] 13.51/3.75 b(x1) = [4 4]x1 >= [4 4]x1 = c(c(x1)) 13.51/3.75 13.51/3.75 [2 1] [0 0] 13.51/3.75 a(a(x1)) = [3 2]x1 >= [2 1]x1 = a(x1) 13.51/3.75 13.51/3.75 [5 5] [5 5] 13.51/3.75 b(a(x1)) = [6 5]x1 >= [6 5]x1 = d(x1) 13.51/3.75 13.51/3.75 [5 5] [5 5] 13.51/3.75 d(x1) = [6 5]x1 >= [6 5]x1 = b(a(x1)) 13.51/3.75 problem: 13.51/3.75 strict: 13.51/3.75 b(x1) -> c(c(x1)) 13.51/3.75 weak: 13.51/3.75 b(a(x1)) -> d(x1) 13.51/3.75 d(x1) -> b(a(x1)) 13.51/3.75 String Reversal Processor: 13.51/3.75 strict: 13.51/3.75 b(x1) -> c(c(x1)) 13.51/3.75 weak: 13.51/3.75 a(b(x1)) -> d(x1) 13.51/3.75 d(x1) -> a(b(x1)) 13.51/3.75 Arctic Interpretation Processor: 13.51/3.75 dimension: 2 13.51/3.75 interpretation: 13.51/3.75 [7 5] 13.51/3.75 [d](x0) = [4 2]x0, 13.51/3.75 13.51/3.75 [3 2] 13.51/3.75 [b](x0) = [4 2]x0, 13.51/3.75 13.51/3.75 [0 0] 13.51/3.75 [c](x0) = [0 0]x0, 13.51/3.75 13.51/3.75 [0 3 ] 13.51/3.75 [a](x0) = [-& 0 ]x0 13.51/3.75 orientation: 13.51/3.75 [3 2] [0 0] 13.51/3.75 b(x1) = [4 2]x1 >= [0 0]x1 = c(c(x1)) 13.51/3.75 13.51/3.75 [7 5] [7 5] 13.51/3.75 a(b(x1)) = [4 2]x1 >= [4 2]x1 = d(x1) 13.51/3.75 13.51/3.75 [7 5] [7 5] 13.51/3.75 d(x1) = [4 2]x1 >= [4 2]x1 = a(b(x1)) 13.51/3.75 problem: 13.51/3.75 strict: 13.51/3.75 13.51/3.75 weak: 13.51/3.75 a(b(x1)) -> d(x1) 13.51/3.75 d(x1) -> a(b(x1)) 13.51/3.75 Qed 13.51/3.75 EOF