7.08/2.22 YES 7.42/2.23 7.42/2.23 Problem: 7.42/2.23 C(x1) -> c(x1) 7.42/2.23 c(c(x1)) -> x1 7.42/2.23 b(b(x1)) -> B(x1) 7.42/2.23 B(B(x1)) -> b(x1) 7.42/2.23 c(B(c(b(c(x1))))) -> B(c(b(c(B(c(b(x1))))))) 7.42/2.23 b(B(x1)) -> x1 7.42/2.23 B(b(x1)) -> x1 7.42/2.23 c(C(x1)) -> x1 7.42/2.23 C(c(x1)) -> x1 7.42/2.23 7.42/2.23 Proof: 7.42/2.23 Matrix Interpretation Processor: dim=3 7.42/2.23 7.42/2.23 interpretation: 7.42/2.23 7.42/2.23 [B](x0) = x0 7.42/2.23 , 7.42/2.23 7.42/2.23 7.42/2.23 [b](x0) = x0 7.42/2.23 , 7.42/2.23 7.42/2.23 [1 0 0] [0] 7.42/2.23 [c](x0) = [0 0 1]x0 + [1] 7.42/2.23 [0 1 0] [1], 7.42/2.23 7.42/2.23 [1 0 0] [1] 7.42/2.23 [C](x0) = [0 0 1]x0 + [1] 7.42/2.23 [0 1 0] [1] 7.42/2.23 orientation: 7.42/2.23 [1 0 0] [1] [1 0 0] [0] 7.42/2.23 C(x1) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = c(x1) 7.42/2.23 [0 1 0] [1] [0 1 0] [1] 7.42/2.23 7.42/2.23 [0] 7.42/2.23 c(c(x1)) = x1 + [2] >= x1 = x1 7.42/2.23 [2] 7.42/2.23 7.42/2.23 7.42/2.23 b(b(x1)) = x1 >= x1 = B(x1) 7.42/2.23 7.42/2.23 7.42/2.23 7.42/2.23 B(B(x1)) = x1 >= x1 = b(x1) 7.42/2.23 7.42/2.23 7.42/2.23 [1 0 0] [0] [1 0 0] [0] 7.42/2.23 c(B(c(b(c(x1))))) = [0 0 1]x1 + [3] >= [0 0 1]x1 + [3] = B(c(b(c(B(c(b(x1))))))) 7.42/2.23 [0 1 0] [3] [0 1 0] [3] 7.42/2.23 7.42/2.23 7.42/2.23 b(B(x1)) = x1 >= x1 = x1 7.42/2.23 7.42/2.23 7.42/2.23 7.42/2.23 B(b(x1)) = x1 >= x1 = x1 7.42/2.23 7.42/2.23 7.42/2.23 [1] 7.42/2.23 c(C(x1)) = x1 + [2] >= x1 = x1 7.42/2.23 [2] 7.42/2.23 7.42/2.23 [1] 7.42/2.23 C(c(x1)) = x1 + [2] >= x1 = x1 7.42/2.23 [2] 7.42/2.23 problem: 7.42/2.23 c(c(x1)) -> x1 7.42/2.23 b(b(x1)) -> B(x1) 7.42/2.23 B(B(x1)) -> b(x1) 7.42/2.23 c(B(c(b(c(x1))))) -> B(c(b(c(B(c(b(x1))))))) 7.42/2.23 b(B(x1)) -> x1 7.42/2.23 B(b(x1)) -> x1 7.42/2.23 String Reversal Processor: 7.42/2.23 c(c(x1)) -> x1 7.42/2.23 b(b(x1)) -> B(x1) 7.42/2.23 B(B(x1)) -> b(x1) 7.42/2.23 c(b(c(B(c(x1))))) -> b(c(B(c(b(c(B(x1))))))) 7.42/2.23 B(b(x1)) -> x1 7.42/2.23 b(B(x1)) -> x1 7.42/2.23 Matrix Interpretation Processor: dim=1 7.42/2.23 7.42/2.23 interpretation: 7.42/2.23 [B](x0) = x0, 7.42/2.23 7.42/2.23 [b](x0) = x0, 7.42/2.23 7.42/2.23 [c](x0) = 2x0 + 2 7.42/2.23 orientation: 7.42/2.23 c(c(x1)) = 4x1 + 6 >= x1 = x1 7.42/2.23 7.42/2.23 b(b(x1)) = x1 >= x1 = B(x1) 7.42/2.23 7.42/2.23 B(B(x1)) = x1 >= x1 = b(x1) 7.42/2.23 7.42/2.23 c(b(c(B(c(x1))))) = 8x1 + 14 >= 8x1 + 14 = b(c(B(c(b(c(B(x1))))))) 7.42/2.23 7.42/2.23 B(b(x1)) = x1 >= x1 = x1 7.42/2.23 7.42/2.23 b(B(x1)) = x1 >= x1 = x1 7.42/2.23 problem: 7.42/2.23 b(b(x1)) -> B(x1) 7.42/2.23 B(B(x1)) -> b(x1) 7.42/2.23 c(b(c(B(c(x1))))) -> b(c(B(c(b(c(B(x1))))))) 7.42/2.23 B(b(x1)) -> x1 7.42/2.23 b(B(x1)) -> x1 7.42/2.23 Bounds Processor: 7.42/2.23 bound: 1 7.42/2.23 enrichment: match 7.42/2.23 automaton: 7.42/2.23 final states: {2,4,3,1} 7.42/2.23 transitions: 7.42/2.23 c0(6) -> 7* 7.42/2.23 c0(1) -> 5* 7.42/2.23 c0(8) -> 9* 7.42/2.23 B1(10) -> 11* 7.42/2.23 f40() -> 2* 7.42/2.23 B0(7) -> 8* 7.42/2.23 B0(2) -> 1* 7.42/2.23 b0(5) -> 6* 7.42/2.23 b0(2) -> 3* 7.42/2.23 b0(9) -> 4* 7.42/2.23 1 -> 3* 7.42/2.23 2 -> 1* 7.42/2.23 3 -> 1* 7.42/2.23 4 -> 5,7 7.42/2.23 9 -> 10,8 7.42/2.23 11 -> 6* 7.42/2.23 problem: 7.42/2.23 7.42/2.23 Qed 7.42/2.23 EOF