8.67/2.57 YES 8.67/2.58 8.67/2.58 Problem: 8.67/2.58 t(o(x1)) -> m(a(x1)) 8.67/2.58 t(e(x1)) -> n(s(x1)) 8.67/2.58 a(l(x1)) -> a(t(x1)) 8.67/2.58 o(m(a(x1))) -> t(e(n(x1))) 8.67/2.58 s(a(x1)) -> l(a(t(o(m(a(t(e(x1)))))))) 8.67/2.58 n(s(x1)) -> a(l(a(t(x1)))) 8.67/2.58 8.67/2.58 Proof: 8.67/2.58 String Reversal Processor: 8.67/2.58 o(t(x1)) -> a(m(x1)) 8.67/2.58 e(t(x1)) -> s(n(x1)) 8.67/2.58 l(a(x1)) -> t(a(x1)) 8.67/2.58 a(m(o(x1))) -> n(e(t(x1))) 8.67/2.58 a(s(x1)) -> e(t(a(m(o(t(a(l(x1)))))))) 8.67/2.58 s(n(x1)) -> t(a(l(a(x1)))) 8.67/2.58 Matrix Interpretation Processor: dim=3 8.67/2.58 8.67/2.58 interpretation: 8.67/2.58 [1 1 0] 8.67/2.58 [l](x0) = [0 0 1]x0 8.67/2.58 [0 0 0] , 8.67/2.58 8.67/2.58 [1 0 0] 8.67/2.58 [n](x0) = [0 0 1]x0 8.67/2.58 [0 0 0] , 8.67/2.58 8.67/2.58 [1 1 0] [1] 8.67/2.58 [s](x0) = [0 0 0]x0 + [0] 8.67/2.58 [0 0 0] [1], 8.67/2.58 8.67/2.58 [1 1 0] [1] 8.67/2.58 [e](x0) = [0 0 0]x0 + [0] 8.67/2.58 [0 0 0] [1], 8.67/2.58 8.67/2.58 [1 0 0] 8.67/2.58 [m](x0) = [1 0 0]x0 8.67/2.58 [0 0 0] , 8.67/2.58 8.67/2.58 [1 0 1] [0] 8.67/2.58 [a](x0) = [0 0 0]x0 + [1] 8.67/2.58 [0 0 1] [0], 8.67/2.58 8.67/2.58 [1 0 0] 8.67/2.58 [t](x0) = [0 0 1]x0 8.67/2.58 [0 0 0] , 8.67/2.58 8.67/2.58 [1 0 1] [1] 8.67/2.58 [o](x0) = [0 0 0]x0 + [1] 8.67/2.58 [0 0 0] [0] 8.67/2.58 orientation: 8.67/2.58 [1 0 0] [1] [1 0 0] [0] 8.67/2.58 o(t(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(m(x1)) 8.67/2.58 [0 0 0] [0] [0 0 0] [0] 8.67/2.58 8.67/2.58 [1 0 1] [1] [1 0 1] [1] 8.67/2.58 e(t(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = s(n(x1)) 8.67/2.58 [0 0 0] [1] [0 0 0] [1] 8.67/2.58 8.67/2.58 [1 0 1] [1] [1 0 1] 8.67/2.58 l(a(x1)) = [0 0 1]x1 + [0] >= [0 0 1]x1 = t(a(x1)) 8.67/2.58 [0 0 0] [0] [0 0 0] 8.67/2.58 8.67/2.58 [1 0 1] [1] [1 0 1] [1] 8.67/2.58 a(m(o(x1))) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = n(e(t(x1))) 8.67/2.58 [0 0 0] [0] [0 0 0] [0] 8.67/2.58 8.67/2.58 [1 1 0] [2] [1 1 0] [2] 8.67/2.58 a(s(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [0] = e(t(a(m(o(t(a(l(x1)))))))) 8.67/2.58 [0 0 0] [1] [0 0 0] [1] 8.67/2.58 8.67/2.58 [1 0 1] [1] [1 0 1] [1] 8.67/2.58 s(n(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = t(a(l(a(x1)))) 8.67/2.58 [0 0 0] [1] [0 0 0] [0] 8.67/2.58 problem: 8.67/2.58 e(t(x1)) -> s(n(x1)) 8.67/2.58 a(m(o(x1))) -> n(e(t(x1))) 8.67/2.58 a(s(x1)) -> e(t(a(m(o(t(a(l(x1)))))))) 8.67/2.58 s(n(x1)) -> t(a(l(a(x1)))) 8.67/2.58 Bounds Processor: 8.67/2.58 bound: 3 8.67/2.58 enrichment: match 8.67/2.58 automaton: 8.67/2.58 final states: {15,7,4,1} 8.67/2.58 transitions: 8.67/2.58 t1(47) -> 48* 8.67/2.58 t1(31) -> 32* 8.67/2.58 a1(44) -> 45* 8.67/2.58 a1(46) -> 47* 8.67/2.58 l1(45) -> 46* 8.67/2.58 n1(19) -> 20* 8.67/2.58 n1(33) -> 34* 8.67/2.58 n1(28) -> 29* 8.67/2.58 e1(32) -> 33* 8.67/2.58 s1(20) -> 21* 8.67/2.58 s1(29) -> 30* 8.67/2.58 t2(68) -> 69* 8.67/2.58 t2(63) -> 64* 8.67/2.58 a2(65) -> 66* 8.67/2.58 a2(60) -> 61* 8.67/2.58 a2(67) -> 68* 8.67/2.58 a2(62) -> 63* 8.67/2.58 l2(66) -> 67* 8.67/2.58 l2(61) -> 62* 8.67/2.58 s2(50) -> 51* 8.67/2.58 f80() -> 2* 8.67/2.58 n2(49) -> 50* 8.67/2.58 s0(3) -> 1* 8.67/2.58 t3(83) -> 84* 8.67/2.58 n0(2) -> 3* 8.67/2.58 n0(6) -> 4* 8.67/2.58 a3(80) -> 81* 8.67/2.58 a3(82) -> 83* 8.67/2.58 e0(5) -> 6* 8.67/2.58 e0(14) -> 7* 8.67/2.58 l3(81) -> 82* 8.67/2.58 t0(2) -> 5* 8.67/2.58 t0(9) -> 10* 8.67/2.58 t0(18) -> 15* 8.67/2.58 t0(13) -> 14* 8.67/2.58 a0(17) -> 18* 8.67/2.58 a0(12) -> 13* 8.67/2.58 a0(2) -> 16* 8.67/2.58 a0(8) -> 9* 8.67/2.58 m0(11) -> 12* 8.67/2.58 o0(10) -> 11* 8.67/2.58 l0(2) -> 8* 8.67/2.58 l0(16) -> 17* 8.67/2.58 2 -> 44,28 8.67/2.58 4 -> 66,16,45 8.67/2.58 7 -> 66,16,45 8.67/2.58 10 -> 31* 8.67/2.58 13 -> 19* 8.67/2.58 19 -> 60* 8.67/2.58 21 -> 7* 8.67/2.58 28 -> 65* 8.67/2.58 30 -> 6* 8.67/2.58 31 -> 49* 8.67/2.58 34 -> 13* 8.67/2.58 48 -> 1* 8.67/2.58 49 -> 80* 8.67/2.58 51 -> 33* 8.67/2.58 64 -> 21,7 8.67/2.58 69 -> 30,6 8.67/2.58 84 -> 51,33 8.67/2.58 problem: 8.67/2.58 8.67/2.58 Qed 8.67/2.59 EOF