14.27/4.06 YES 14.27/4.07 14.27/4.07 Problem: 14.27/4.07 r0(0(x1)) -> 0(r0(x1)) 14.27/4.07 r0(1(x1)) -> 1(r0(x1)) 14.27/4.07 r0(m(x1)) -> m(r0(x1)) 14.27/4.07 r1(0(x1)) -> 0(r1(x1)) 14.27/4.07 r1(1(x1)) -> 1(r1(x1)) 14.27/4.07 r1(m(x1)) -> m(r1(x1)) 14.27/4.07 r0(b(x1)) -> qr(0(b(x1))) 14.27/4.07 r1(b(x1)) -> qr(1(b(x1))) 14.27/4.07 0(qr(x1)) -> qr(0(x1)) 14.27/4.07 1(qr(x1)) -> qr(1(x1)) 14.27/4.07 m(qr(x1)) -> ql(m(x1)) 14.27/4.07 0(ql(x1)) -> ql(0(x1)) 14.27/4.07 1(ql(x1)) -> ql(1(x1)) 14.27/4.07 b(ql(0(x1))) -> 0(b(r0(x1))) 14.27/4.07 b(ql(1(x1))) -> 1(b(r1(x1))) 14.27/4.07 14.27/4.07 Proof: 14.27/4.07 String Reversal Processor: 14.27/4.07 0(r0(x1)) -> r0(0(x1)) 14.27/4.07 1(r0(x1)) -> r0(1(x1)) 14.27/4.07 m(r0(x1)) -> r0(m(x1)) 14.27/4.07 0(r1(x1)) -> r1(0(x1)) 14.27/4.07 1(r1(x1)) -> r1(1(x1)) 14.27/4.07 m(r1(x1)) -> r1(m(x1)) 14.27/4.07 b(r0(x1)) -> b(0(qr(x1))) 14.27/4.07 b(r1(x1)) -> b(1(qr(x1))) 14.27/4.07 qr(0(x1)) -> 0(qr(x1)) 14.27/4.07 qr(1(x1)) -> 1(qr(x1)) 14.27/4.07 qr(m(x1)) -> m(ql(x1)) 14.27/4.07 ql(0(x1)) -> 0(ql(x1)) 14.27/4.07 ql(1(x1)) -> 1(ql(x1)) 14.27/4.07 0(ql(b(x1))) -> r0(b(0(x1))) 14.27/4.07 1(ql(b(x1))) -> r1(b(1(x1))) 14.27/4.07 Matrix Interpretation Processor: dim=2 14.27/4.07 14.27/4.07 interpretation: 14.27/4.07 14.27/4.07 [ql](x0) = x0, 14.27/4.07 14.27/4.07 [1 0] [0] 14.27/4.07 [qr](x0) = [0 2]x0 + [1], 14.27/4.07 14.27/4.07 [1 0] 14.27/4.07 [b](x0) = [0 0]x0, 14.27/4.07 14.27/4.07 [0] 14.27/4.07 [r1](x0) = x0 + [1], 14.27/4.07 14.27/4.07 [2 2] 14.27/4.07 [m](x0) = [2 2]x0, 14.27/4.07 14.27/4.07 [1 0] [0] 14.27/4.07 [1](x0) = [1 1]x0 + [1], 14.27/4.07 14.27/4.07 14.27/4.07 [r0](x0) = x0, 14.27/4.07 14.27/4.07 14.27/4.07 [0](x0) = x0 14.27/4.07 orientation: 14.27/4.07 14.27/4.07 0(r0(x1)) = x1 >= x1 = r0(0(x1)) 14.27/4.07 14.27/4.07 [1 0] [0] [1 0] [0] 14.27/4.07 1(r0(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = r0(1(x1)) 14.27/4.07 14.27/4.07 [2 2] [2 2] 14.27/4.07 m(r0(x1)) = [2 2]x1 >= [2 2]x1 = r0(m(x1)) 14.27/4.07 14.27/4.07 [0] [0] 14.27/4.07 0(r1(x1)) = x1 + [1] >= x1 + [1] = r1(0(x1)) 14.27/4.07 14.27/4.07 [1 0] [0] [1 0] [0] 14.27/4.07 1(r1(x1)) = [1 1]x1 + [2] >= [1 1]x1 + [2] = r1(1(x1)) 14.27/4.07 14.27/4.07 [2 2] [2] [2 2] [0] 14.27/4.07 m(r1(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [1] = r1(m(x1)) 14.27/4.07 14.27/4.07 [1 0] [1 0] 14.27/4.07 b(r0(x1)) = [0 0]x1 >= [0 0]x1 = b(0(qr(x1))) 14.27/4.07 14.27/4.07 [1 0] [1 0] 14.27/4.07 b(r1(x1)) = [0 0]x1 >= [0 0]x1 = b(1(qr(x1))) 14.27/4.07 14.27/4.07 [1 0] [0] [1 0] [0] 14.27/4.07 qr(0(x1)) = [0 2]x1 + [1] >= [0 2]x1 + [1] = 0(qr(x1)) 14.27/4.07 14.27/4.07 [1 0] [0] [1 0] [0] 14.27/4.07 qr(1(x1)) = [2 2]x1 + [3] >= [1 2]x1 + [2] = 1(qr(x1)) 14.27/4.07 14.27/4.07 [2 2] [0] [2 2] 14.27/4.07 qr(m(x1)) = [4 4]x1 + [1] >= [2 2]x1 = m(ql(x1)) 14.27/4.07 14.27/4.07 14.27/4.07 ql(0(x1)) = x1 >= x1 = 0(ql(x1)) 14.27/4.07 14.27/4.07 [1 0] [0] [1 0] [0] 14.27/4.07 ql(1(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = 1(ql(x1)) 14.27/4.07 14.27/4.07 [1 0] [1 0] 14.27/4.07 0(ql(b(x1))) = [0 0]x1 >= [0 0]x1 = r0(b(0(x1))) 14.27/4.07 14.27/4.07 [1 0] [0] [1 0] [0] 14.27/4.07 1(ql(b(x1))) = [1 0]x1 + [1] >= [0 0]x1 + [1] = r1(b(1(x1))) 14.27/4.07 problem: 14.27/4.07 0(r0(x1)) -> r0(0(x1)) 14.27/4.07 1(r0(x1)) -> r0(1(x1)) 14.27/4.07 m(r0(x1)) -> r0(m(x1)) 14.27/4.07 0(r1(x1)) -> r1(0(x1)) 14.27/4.07 1(r1(x1)) -> r1(1(x1)) 14.27/4.07 b(r0(x1)) -> b(0(qr(x1))) 14.27/4.07 b(r1(x1)) -> b(1(qr(x1))) 14.27/4.07 qr(0(x1)) -> 0(qr(x1)) 14.27/4.07 qr(1(x1)) -> 1(qr(x1)) 14.27/4.07 qr(m(x1)) -> m(ql(x1)) 14.27/4.07 ql(0(x1)) -> 0(ql(x1)) 14.27/4.07 ql(1(x1)) -> 1(ql(x1)) 14.27/4.07 0(ql(b(x1))) -> r0(b(0(x1))) 14.27/4.07 1(ql(b(x1))) -> r1(b(1(x1))) 14.27/4.07 Matrix Interpretation Processor: dim=3 14.27/4.07 14.27/4.07 interpretation: 14.27/4.07 [1 1 0] [1] 14.27/4.07 [ql](x0) = [0 1 0]x0 + [0] 14.27/4.07 [0 0 1] [0], 14.27/4.07 14.27/4.07 [1 1 0] 14.27/4.07 [qr](x0) = [0 1 0]x0 14.27/4.07 [0 0 1] , 14.27/4.07 14.27/4.07 [1 0 0] [1] 14.27/4.07 [b](x0) = [0 1 0]x0 + [0] 14.27/4.07 [0 0 0] [1], 14.27/4.07 14.27/4.07 [1 1 0] [1] 14.27/4.07 [r1](x0) = [0 1 0]x0 + [0] 14.27/4.07 [0 0 0] [0], 14.27/4.07 14.27/4.07 [1 0 1] [0] 14.27/4.07 [m](x0) = [0 1 0]x0 + [1] 14.27/4.07 [0 0 1] [0], 14.27/4.07 14.27/4.07 14.27/4.07 [1](x0) = x0 14.27/4.07 , 14.27/4.07 14.27/4.07 [1 1 0] [1] 14.27/4.07 [r0](x0) = [0 1 0]x0 + [0] 14.27/4.07 [0 0 1] [1], 14.27/4.07 14.27/4.07 [0] 14.27/4.08 [0](x0) = x0 + [0] 14.27/4.08 [1] 14.27/4.08 orientation: 14.27/4.08 [1 1 0] [1] [1 1 0] [1] 14.27/4.08 0(r0(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = r0(0(x1)) 14.27/4.08 [0 0 1] [2] [0 0 1] [2] 14.27/4.08 14.27/4.08 [1 1 0] [1] [1 1 0] [1] 14.27/4.08 1(r0(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = r0(1(x1)) 14.27/4.08 [0 0 1] [1] [0 0 1] [1] 14.27/4.08 14.27/4.08 [1 1 1] [2] [1 1 1] [2] 14.27/4.08 m(r0(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = r0(m(x1)) 14.27/4.08 [0 0 1] [1] [0 0 1] [1] 14.27/4.08 14.27/4.08 [1 1 0] [1] [1 1 0] [1] 14.27/4.08 0(r1(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = r1(0(x1)) 14.27/4.08 [0 0 0] [1] [0 0 0] [0] 14.27/4.08 14.27/4.08 [1 1 0] [1] [1 1 0] [1] 14.27/4.08 1(r1(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = r1(1(x1)) 14.27/4.08 [0 0 0] [0] [0 0 0] [0] 14.27/4.08 14.27/4.08 [1 1 0] [2] [1 1 0] [1] 14.27/4.08 b(r0(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = b(0(qr(x1))) 14.27/4.08 [0 0 0] [1] [0 0 0] [1] 14.27/4.08 14.27/4.08 [1 1 0] [2] [1 1 0] [1] 14.27/4.08 b(r1(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = b(1(qr(x1))) 14.27/4.08 [0 0 0] [1] [0 0 0] [1] 14.27/4.08 14.27/4.08 [1 1 0] [0] [1 1 0] [0] 14.27/4.08 qr(0(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = 0(qr(x1)) 14.27/4.08 [0 0 1] [1] [0 0 1] [1] 14.27/4.08 14.27/4.08 [1 1 0] [1 1 0] 14.27/4.08 qr(1(x1)) = [0 1 0]x1 >= [0 1 0]x1 = 1(qr(x1)) 14.27/4.08 [0 0 1] [0 0 1] 14.27/4.08 14.27/4.08 [1 1 1] [1] [1 1 1] [1] 14.27/4.08 qr(m(x1)) = [0 1 0]x1 + [1] >= [0 1 0]x1 + [1] = m(ql(x1)) 14.27/4.08 [0 0 1] [0] [0 0 1] [0] 14.27/4.08 14.27/4.08 [1 1 0] [1] [1 1 0] [1] 14.27/4.08 ql(0(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = 0(ql(x1)) 14.27/4.08 [0 0 1] [1] [0 0 1] [1] 14.27/4.08 14.27/4.08 [1 1 0] [1] [1 1 0] [1] 14.27/4.08 ql(1(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = 1(ql(x1)) 14.27/4.08 [0 0 1] [0] [0 0 1] [0] 14.27/4.08 14.27/4.08 [1 1 0] [2] [1 1 0] [2] 14.27/4.08 0(ql(b(x1))) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = r0(b(0(x1))) 14.27/4.08 [0 0 0] [2] [0 0 0] [2] 14.27/4.08 14.27/4.08 [1 1 0] [2] [1 1 0] [2] 14.27/4.08 1(ql(b(x1))) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = r1(b(1(x1))) 14.27/4.08 [0 0 0] [1] [0 0 0] [0] 14.27/4.08 problem: 14.27/4.08 0(r0(x1)) -> r0(0(x1)) 14.27/4.08 1(r0(x1)) -> r0(1(x1)) 14.27/4.08 m(r0(x1)) -> r0(m(x1)) 14.27/4.08 0(r1(x1)) -> r1(0(x1)) 14.27/4.08 1(r1(x1)) -> r1(1(x1)) 14.27/4.08 qr(0(x1)) -> 0(qr(x1)) 14.27/4.08 qr(1(x1)) -> 1(qr(x1)) 14.27/4.08 qr(m(x1)) -> m(ql(x1)) 14.27/4.08 ql(0(x1)) -> 0(ql(x1)) 14.27/4.08 ql(1(x1)) -> 1(ql(x1)) 14.27/4.08 0(ql(b(x1))) -> r0(b(0(x1))) 14.27/4.08 1(ql(b(x1))) -> r1(b(1(x1))) 14.27/4.08 KBO Processor: 14.27/4.08 weight function: 14.27/4.08 w0 = 1 14.27/4.08 w(ql) = w(qr) = w(b) = w(r1) = w(m) = w(1) = w(r0) = w(0) = 1 14.27/4.08 precedence: 14.27/4.08 ql ~ qr > m ~ 1 ~ 0 > b ~ r1 ~ r0 14.27/4.08 problem: 14.27/4.08 14.27/4.08 Qed 14.27/4.08 EOF