21.88/6.08 YES 21.88/6.08 21.88/6.08 Problem: 21.88/6.08 r(r(x1)) -> s(r(x1)) 21.88/6.08 r(s(x1)) -> s(r(x1)) 21.88/6.08 r(n(x1)) -> s(r(x1)) 21.88/6.08 r(b(x1)) -> u(s(b(x1))) 21.88/6.08 r(u(x1)) -> u(r(x1)) 21.88/6.08 s(u(x1)) -> u(s(x1)) 21.88/6.08 n(u(x1)) -> u(n(x1)) 21.88/6.08 t(r(u(x1))) -> t(c(r(x1))) 21.88/6.08 t(s(u(x1))) -> t(c(r(x1))) 21.88/6.08 t(n(u(x1))) -> t(c(r(x1))) 21.88/6.08 c(u(x1)) -> u(c(x1)) 21.88/6.08 c(s(x1)) -> s(c(x1)) 21.88/6.08 c(r(x1)) -> r(c(x1)) 21.88/6.08 c(n(x1)) -> n(c(x1)) 21.88/6.08 c(n(x1)) -> n(x1) 21.88/6.08 21.88/6.08 Proof: 21.88/6.08 Matrix Interpretation Processor: dim=1 21.88/6.08 21.88/6.08 interpretation: 21.88/6.08 [c](x0) = x0, 21.88/6.08 21.88/6.08 [t](x0) = 2x0, 21.88/6.08 21.88/6.08 [u](x0) = x0 + 4, 21.88/6.08 21.88/6.08 [b](x0) = 8x0 + 4, 21.88/6.08 21.88/6.08 [n](x0) = x0 + 4, 21.88/6.08 21.88/6.08 [s](x0) = x0 + 4, 21.88/6.08 21.88/6.08 [r](x0) = x0 + 8 21.88/6.08 orientation: 21.88/6.08 r(r(x1)) = x1 + 16 >= x1 + 12 = s(r(x1)) 21.88/6.08 21.88/6.08 r(s(x1)) = x1 + 12 >= x1 + 12 = s(r(x1)) 21.88/6.08 21.88/6.08 r(n(x1)) = x1 + 12 >= x1 + 12 = s(r(x1)) 21.88/6.08 21.88/6.08 r(b(x1)) = 8x1 + 12 >= 8x1 + 12 = u(s(b(x1))) 21.88/6.08 21.88/6.08 r(u(x1)) = x1 + 12 >= x1 + 12 = u(r(x1)) 21.88/6.08 21.88/6.08 s(u(x1)) = x1 + 8 >= x1 + 8 = u(s(x1)) 21.88/6.08 21.88/6.08 n(u(x1)) = x1 + 8 >= x1 + 8 = u(n(x1)) 21.88/6.08 21.88/6.08 t(r(u(x1))) = 2x1 + 24 >= 2x1 + 16 = t(c(r(x1))) 21.88/6.08 21.88/6.08 t(s(u(x1))) = 2x1 + 16 >= 2x1 + 16 = t(c(r(x1))) 21.88/6.08 21.88/6.08 t(n(u(x1))) = 2x1 + 16 >= 2x1 + 16 = t(c(r(x1))) 21.88/6.08 21.88/6.08 c(u(x1)) = x1 + 4 >= x1 + 4 = u(c(x1)) 21.88/6.08 21.88/6.08 c(s(x1)) = x1 + 4 >= x1 + 4 = s(c(x1)) 21.88/6.08 21.88/6.08 c(r(x1)) = x1 + 8 >= x1 + 8 = r(c(x1)) 21.88/6.08 21.88/6.08 c(n(x1)) = x1 + 4 >= x1 + 4 = n(c(x1)) 21.88/6.08 21.88/6.08 c(n(x1)) = x1 + 4 >= x1 + 4 = n(x1) 21.88/6.08 problem: 21.88/6.08 r(s(x1)) -> s(r(x1)) 21.88/6.08 r(n(x1)) -> s(r(x1)) 21.88/6.08 r(b(x1)) -> u(s(b(x1))) 21.88/6.08 r(u(x1)) -> u(r(x1)) 21.88/6.08 s(u(x1)) -> u(s(x1)) 21.88/6.08 n(u(x1)) -> u(n(x1)) 21.88/6.08 t(s(u(x1))) -> t(c(r(x1))) 21.88/6.08 t(n(u(x1))) -> t(c(r(x1))) 21.88/6.08 c(u(x1)) -> u(c(x1)) 21.88/6.08 c(s(x1)) -> s(c(x1)) 21.88/6.08 c(r(x1)) -> r(c(x1)) 21.88/6.08 c(n(x1)) -> n(c(x1)) 21.88/6.08 c(n(x1)) -> n(x1) 21.88/6.08 String Reversal Processor: 21.88/6.08 s(r(x1)) -> r(s(x1)) 21.88/6.08 n(r(x1)) -> r(s(x1)) 21.88/6.08 b(r(x1)) -> b(s(u(x1))) 21.88/6.08 u(r(x1)) -> r(u(x1)) 21.88/6.08 u(s(x1)) -> s(u(x1)) 21.88/6.08 u(n(x1)) -> n(u(x1)) 21.88/6.08 u(s(t(x1))) -> r(c(t(x1))) 21.88/6.08 u(n(t(x1))) -> r(c(t(x1))) 21.88/6.08 u(c(x1)) -> c(u(x1)) 21.88/6.08 s(c(x1)) -> c(s(x1)) 21.88/6.08 r(c(x1)) -> c(r(x1)) 21.88/6.08 n(c(x1)) -> c(n(x1)) 21.88/6.08 n(c(x1)) -> n(x1) 21.88/6.08 Matrix Interpretation Processor: dim=1 21.88/6.08 21.88/6.08 interpretation: 21.88/6.08 [c](x0) = x0, 21.88/6.08 21.88/6.08 [t](x0) = 4x0, 21.88/6.08 21.88/6.08 [u](x0) = x0, 21.88/6.08 21.88/6.08 [b](x0) = x0, 21.88/6.08 21.88/6.08 [n](x0) = 4x0 + 1, 21.88/6.08 21.88/6.08 [s](x0) = x0, 21.88/6.08 21.88/6.08 [r](x0) = x0 21.88/6.08 orientation: 21.88/6.08 s(r(x1)) = x1 >= x1 = r(s(x1)) 21.88/6.08 21.88/6.08 n(r(x1)) = 4x1 + 1 >= x1 = r(s(x1)) 21.88/6.08 21.88/6.08 b(r(x1)) = x1 >= x1 = b(s(u(x1))) 21.88/6.08 21.88/6.08 u(r(x1)) = x1 >= x1 = r(u(x1)) 21.88/6.08 21.88/6.08 u(s(x1)) = x1 >= x1 = s(u(x1)) 21.88/6.08 21.88/6.08 u(n(x1)) = 4x1 + 1 >= 4x1 + 1 = n(u(x1)) 21.88/6.08 21.88/6.08 u(s(t(x1))) = 4x1 >= 4x1 = r(c(t(x1))) 21.88/6.08 21.88/6.08 u(n(t(x1))) = 16x1 + 1 >= 4x1 = r(c(t(x1))) 21.88/6.08 21.88/6.08 u(c(x1)) = x1 >= x1 = c(u(x1)) 21.88/6.08 21.88/6.08 s(c(x1)) = x1 >= x1 = c(s(x1)) 21.88/6.08 21.88/6.08 r(c(x1)) = x1 >= x1 = c(r(x1)) 21.88/6.08 21.88/6.08 n(c(x1)) = 4x1 + 1 >= 4x1 + 1 = c(n(x1)) 21.88/6.08 21.88/6.08 n(c(x1)) = 4x1 + 1 >= 4x1 + 1 = n(x1) 21.88/6.08 problem: 21.88/6.08 s(r(x1)) -> r(s(x1)) 21.88/6.08 b(r(x1)) -> b(s(u(x1))) 21.88/6.08 u(r(x1)) -> r(u(x1)) 21.88/6.08 u(s(x1)) -> s(u(x1)) 21.88/6.08 u(n(x1)) -> n(u(x1)) 21.88/6.08 u(s(t(x1))) -> r(c(t(x1))) 21.88/6.08 u(c(x1)) -> c(u(x1)) 21.88/6.08 s(c(x1)) -> c(s(x1)) 21.88/6.08 r(c(x1)) -> c(r(x1)) 21.88/6.08 n(c(x1)) -> c(n(x1)) 21.88/6.08 n(c(x1)) -> n(x1) 21.88/6.08 Matrix Interpretation Processor: dim=3 21.88/6.08 21.88/6.08 interpretation: 21.88/6.08 [1 0 0] [0] 21.88/6.08 [c](x0) = [0 0 1]x0 + [1] 21.88/6.08 [0 1 0] [1], 21.88/6.08 21.88/6.08 [1 0 0] [1] 21.88/6.08 [t](x0) = [0 0 0]x0 + [1] 21.88/6.08 [0 0 0] [0], 21.88/6.08 21.88/6.08 [1 0 0] 21.88/6.08 [u](x0) = [0 0 1]x0 21.88/6.08 [0 1 0] , 21.88/6.08 21.88/6.08 [1 0 0] 21.88/6.08 [b](x0) = [0 0 0]x0 21.88/6.08 [0 0 0] , 21.88/6.08 21.88/6.08 [1 1 1] 21.88/6.08 [n](x0) = [0 1 1]x0 21.88/6.08 [0 1 1] , 21.88/6.08 21.88/6.08 [1 0 0] 21.88/6.08 [s](x0) = [1 0 1]x0 21.88/6.08 [1 1 0] , 21.88/6.08 21.88/6.08 [1 0 0] 21.88/6.08 [r](x0) = [0 0 1]x0 21.88/6.08 [0 1 0] 21.88/6.08 orientation: 21.88/6.08 [1 0 0] [1 0 0] 21.88/6.08 s(r(x1)) = [1 1 0]x1 >= [1 1 0]x1 = r(s(x1)) 21.88/6.08 [1 0 1] [1 0 1] 21.88/6.08 21.88/6.08 [1 0 0] [1 0 0] 21.88/6.09 b(r(x1)) = [0 0 0]x1 >= [0 0 0]x1 = b(s(u(x1))) 21.88/6.09 [0 0 0] [0 0 0] 21.88/6.09 21.88/6.09 21.88/6.09 u(r(x1)) = x1 >= x1 = r(u(x1)) 21.88/6.09 21.88/6.09 21.88/6.09 [1 0 0] [1 0 0] 21.88/6.09 u(s(x1)) = [1 1 0]x1 >= [1 1 0]x1 = s(u(x1)) 21.88/6.09 [1 0 1] [1 0 1] 21.88/6.09 21.88/6.09 [1 1 1] [1 1 1] 21.88/6.09 u(n(x1)) = [0 1 1]x1 >= [0 1 1]x1 = n(u(x1)) 21.88/6.09 [0 1 1] [0 1 1] 21.88/6.09 21.88/6.09 [1 0 0] [1] [1 0 0] [1] 21.88/6.09 u(s(t(x1))) = [1 0 0]x1 + [2] >= [0 0 0]x1 + [2] = r(c(t(x1))) 21.88/6.09 [1 0 0] [1] [0 0 0] [1] 21.88/6.09 21.88/6.09 [0] [0] 21.88/6.09 u(c(x1)) = x1 + [1] >= x1 + [1] = c(u(x1)) 21.88/6.09 [1] [1] 21.88/6.09 21.88/6.09 [1 0 0] [0] [1 0 0] [0] 21.88/6.09 s(c(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = c(s(x1)) 21.88/6.09 [1 0 1] [1] [1 0 1] [1] 21.88/6.09 21.88/6.09 [0] [0] 21.88/6.09 r(c(x1)) = x1 + [1] >= x1 + [1] = c(r(x1)) 21.88/6.09 [1] [1] 21.88/6.09 21.88/6.09 [1 1 1] [2] [1 1 1] [0] 21.88/6.09 n(c(x1)) = [0 1 1]x1 + [2] >= [0 1 1]x1 + [1] = c(n(x1)) 21.88/6.09 [0 1 1] [2] [0 1 1] [1] 21.88/6.09 21.88/6.09 [1 1 1] [2] [1 1 1] 21.88/6.09 n(c(x1)) = [0 1 1]x1 + [2] >= [0 1 1]x1 = n(x1) 21.88/6.09 [0 1 1] [2] [0 1 1] 21.88/6.09 problem: 21.88/6.09 s(r(x1)) -> r(s(x1)) 21.88/6.09 b(r(x1)) -> b(s(u(x1))) 21.88/6.09 u(r(x1)) -> r(u(x1)) 21.88/6.09 u(s(x1)) -> s(u(x1)) 21.88/6.09 u(n(x1)) -> n(u(x1)) 21.88/6.09 u(s(t(x1))) -> r(c(t(x1))) 21.88/6.09 u(c(x1)) -> c(u(x1)) 21.88/6.09 s(c(x1)) -> c(s(x1)) 21.88/6.09 r(c(x1)) -> c(r(x1)) 21.88/6.09 Matrix Interpretation Processor: dim=1 21.88/6.09 21.88/6.09 interpretation: 21.88/6.09 [c](x0) = x0, 21.88/6.09 21.88/6.09 [t](x0) = x0, 21.88/6.09 21.88/6.09 [u](x0) = 4x0, 21.88/6.09 21.88/6.09 [b](x0) = 2x0 + 4, 21.88/6.09 21.88/6.09 [n](x0) = x0 + 2, 21.88/6.09 21.88/6.09 [s](x0) = x0, 21.88/6.09 21.88/6.09 [r](x0) = 4x0 21.88/6.09 orientation: 21.88/6.09 s(r(x1)) = 4x1 >= 4x1 = r(s(x1)) 21.88/6.09 21.88/6.09 b(r(x1)) = 8x1 + 4 >= 8x1 + 4 = b(s(u(x1))) 21.88/6.09 21.88/6.09 u(r(x1)) = 16x1 >= 16x1 = r(u(x1)) 21.88/6.09 21.88/6.09 u(s(x1)) = 4x1 >= 4x1 = s(u(x1)) 21.88/6.09 21.88/6.09 u(n(x1)) = 4x1 + 8 >= 4x1 + 2 = n(u(x1)) 21.88/6.09 21.88/6.09 u(s(t(x1))) = 4x1 >= 4x1 = r(c(t(x1))) 21.88/6.09 21.88/6.09 u(c(x1)) = 4x1 >= 4x1 = c(u(x1)) 21.88/6.09 21.88/6.09 s(c(x1)) = x1 >= x1 = c(s(x1)) 21.88/6.09 21.88/6.09 r(c(x1)) = 4x1 >= 4x1 = c(r(x1)) 21.88/6.09 problem: 21.88/6.09 s(r(x1)) -> r(s(x1)) 21.88/6.09 b(r(x1)) -> b(s(u(x1))) 21.88/6.09 u(r(x1)) -> r(u(x1)) 21.88/6.09 u(s(x1)) -> s(u(x1)) 21.88/6.09 u(s(t(x1))) -> r(c(t(x1))) 21.88/6.09 u(c(x1)) -> c(u(x1)) 21.88/6.09 s(c(x1)) -> c(s(x1)) 21.88/6.09 r(c(x1)) -> c(r(x1)) 21.88/6.09 Matrix Interpretation Processor: dim=3 21.88/6.09 21.88/6.09 interpretation: 21.88/6.09 [1 0 0] 21.88/6.09 [c](x0) = [0 0 0]x0 21.88/6.09 [0 0 0] , 21.88/6.09 21.88/6.09 [1 0 0] [0] 21.88/6.09 [t](x0) = [1 0 0]x0 + [1] 21.88/6.09 [0 0 0] [0], 21.88/6.09 21.88/6.09 [1 0 0] 21.88/6.09 [u](x0) = [0 1 0]x0 21.88/6.09 [0 1 0] , 21.88/6.09 21.88/6.09 [1 1 0] [0] 21.88/6.09 [b](x0) = [0 0 0]x0 + [1] 21.88/6.09 [0 1 0] [0], 21.88/6.09 21.88/6.09 [1 0 0] 21.88/6.09 [s](x0) = [0 1 0]x0 21.88/6.09 [0 1 0] , 21.88/6.09 21.88/6.09 [1 0 0] [0] 21.88/6.09 [r](x0) = [1 1 0]x0 + [1] 21.88/6.09 [0 0 0] [0] 21.88/6.09 orientation: 21.88/6.09 [1 0 0] [0] [1 0 0] [0] 21.88/6.09 s(r(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = r(s(x1)) 21.88/6.09 [1 1 0] [1] [0 0 0] [0] 21.88/6.09 21.88/6.09 [2 1 0] [1] [1 1 0] [0] 21.88/6.09 b(r(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = b(s(u(x1))) 21.88/6.09 [1 1 0] [1] [0 1 0] [0] 21.88/6.09 21.88/6.09 [1 0 0] [0] [1 0 0] [0] 21.88/6.09 u(r(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = r(u(x1)) 21.88/6.09 [1 1 0] [1] [0 0 0] [0] 21.88/6.09 21.88/6.09 [1 0 0] [1 0 0] 21.88/6.09 u(s(x1)) = [0 1 0]x1 >= [0 1 0]x1 = s(u(x1)) 21.88/6.09 [0 1 0] [0 1 0] 21.88/6.09 21.88/6.09 [1 0 0] [0] [1 0 0] [0] 21.88/6.09 u(s(t(x1))) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = r(c(t(x1))) 21.88/6.09 [1 0 0] [1] [0 0 0] [0] 21.88/6.09 21.88/6.09 [1 0 0] [1 0 0] 21.88/6.09 u(c(x1)) = [0 0 0]x1 >= [0 0 0]x1 = c(u(x1)) 21.88/6.09 [0 0 0] [0 0 0] 21.88/6.09 21.88/6.09 [1 0 0] [1 0 0] 21.88/6.09 s(c(x1)) = [0 0 0]x1 >= [0 0 0]x1 = c(s(x1)) 21.88/6.09 [0 0 0] [0 0 0] 21.88/6.09 21.88/6.09 [1 0 0] [0] [1 0 0] 21.88/6.09 r(c(x1)) = [1 0 0]x1 + [1] >= [0 0 0]x1 = c(r(x1)) 21.88/6.09 [0 0 0] [0] [0 0 0] 21.88/6.09 problem: 21.88/6.09 s(r(x1)) -> r(s(x1)) 21.88/6.09 u(r(x1)) -> r(u(x1)) 21.88/6.09 u(s(x1)) -> s(u(x1)) 21.88/6.09 u(s(t(x1))) -> r(c(t(x1))) 21.88/6.09 u(c(x1)) -> c(u(x1)) 21.88/6.09 s(c(x1)) -> c(s(x1)) 21.88/6.09 r(c(x1)) -> c(r(x1)) 21.88/6.09 String Reversal Processor: 21.88/6.09 r(s(x1)) -> s(r(x1)) 21.88/6.09 r(u(x1)) -> u(r(x1)) 21.88/6.09 s(u(x1)) -> u(s(x1)) 21.88/6.09 t(s(u(x1))) -> t(c(r(x1))) 21.88/6.09 c(u(x1)) -> u(c(x1)) 21.88/6.09 c(s(x1)) -> s(c(x1)) 21.88/6.09 c(r(x1)) -> r(c(x1)) 21.88/6.09 KBO Processor: 21.88/6.09 weight function: 21.88/6.09 w0 = 1 21.88/6.09 w(t) = w(u) = w(s) = w(r) = 1 21.88/6.09 w(c) = 0 21.88/6.09 precedence: 21.88/6.09 c > r > s > t ~ u 21.88/6.09 problem: 21.88/6.09 21.88/6.09 Qed 21.88/6.10 EOF