YES Problem: t(o(x1)) -> m(a(x1)) t(e(x1)) -> n(s(x1)) a(l(x1)) -> a(t(x1)) o(m(a(x1))) -> t(e(n(x1))) s(a(x1)) -> l(a(t(o(m(a(t(e(x1)))))))) n(s(x1)) -> a(l(a(t(x1)))) Proof: String Reversal Processor: o(t(x1)) -> a(m(x1)) e(t(x1)) -> s(n(x1)) l(a(x1)) -> t(a(x1)) a(m(o(x1))) -> n(e(t(x1))) a(s(x1)) -> e(t(a(m(o(t(a(l(x1)))))))) s(n(x1)) -> t(a(l(a(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [0] [l](x0) = [0 0 0]x0 + [0] [1 1 0] [1], [1 1 0] [n](x0) = [0 0 0]x0 [0 1 0] , [1 1 1] [0] [s](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 1] [0] [e](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [0] [m](x0) = [0 1 0]x0 + [0] [1 0 0] [1], [1 1 0] [a](x0) = [0 1 0]x0 [0 0 1] , [1 1 0] [t](x0) = [0 0 0]x0 [0 1 0] , [1 1 0] [1] [o](x0) = [0 1 1]x0 + [0] [1 0 0] [1] orientation: [1 1 0] [1] [1 1 0] [0] o(t(x1)) = [0 1 0]x1 + [0] >= [0 1 0]x1 + [0] = a(m(x1)) [1 1 0] [1] [1 0 0] [1] [1 2 0] [0] [1 2 0] [0] e(t(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = s(n(x1)) [0 0 0] [0] [0 0 0] [0] [1 2 0] [0] [1 2 0] l(a(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = t(a(x1)) [1 2 0] [1] [0 1 0] [1 2 1] [1] [1 2 0] [1] a(m(o(x1))) = [0 1 1]x1 + [0] >= [0 0 0]x1 + [0] = n(e(t(x1))) [1 1 0] [2] [0 0 0] [1] [1 1 1] [1] [1 1 0] [1] a(s(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = e(t(a(m(o(t(a(l(x1)))))))) [0 0 0] [0] [0 0 0] [0] [1 2 0] [0] [1 2 0] s(n(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 = t(a(l(a(x1)))) [0 0 0] [0] [0 0 0] problem: e(t(x1)) -> s(n(x1)) l(a(x1)) -> t(a(x1)) a(m(o(x1))) -> n(e(t(x1))) a(s(x1)) -> e(t(a(m(o(t(a(l(x1)))))))) s(n(x1)) -> t(a(l(a(x1)))) String Reversal Processor: t(e(x1)) -> n(s(x1)) a(l(x1)) -> a(t(x1)) o(m(a(x1))) -> t(e(n(x1))) s(a(x1)) -> l(a(t(o(m(a(t(e(x1)))))))) n(s(x1)) -> a(l(a(t(x1)))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [l](x0) = [0 0 1]x0 [0 0 0] , [1 0 0] [n](x0) = [0 0 1]x0 [0 0 0] , [1 1 0] [1] [s](x0) = [1 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [1] [e](x0) = [0 0 0]x0 + [0] [1 0 0] [1], [1 0 0] [1] [m](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 1] [0] [a](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 0] [t](x0) = [0 0 1]x0 [0 0 0] , [1 0 0] [0] [o](x0) = [1 0 0]x0 + [0] [0 0 1] [1] orientation: [1 1 0] [1] [1 1 0] [1] t(e(x1)) = [1 0 0]x1 + [1] >= [0 0 0]x1 + [1] = n(s(x1)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] a(l(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = a(t(x1)) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [1] o(m(a(x1))) = [1 0 1]x1 + [1] >= [1 0 0]x1 + [1] = t(e(n(x1))) [0 0 0] [2] [0 0 0] [0] [1 1 1] [2] [1 1 0] [2] s(a(x1)) = [1 0 1]x1 + [0] >= [0 0 0]x1 + [0] = l(a(t(o(m(a(t(e(x1)))))))) [0 0 0] [1] [0 0 0] [0] [1 1 0] [1] [1 0 0] [0] n(s(x1)) = [0 0 0]x1 + [1] >= [0 0 0]x1 + [1] = a(l(a(t(x1)))) [0 0 0] [0] [0 0 0] [0] problem: t(e(x1)) -> n(s(x1)) a(l(x1)) -> a(t(x1)) o(m(a(x1))) -> t(e(n(x1))) s(a(x1)) -> l(a(t(o(m(a(t(e(x1)))))))) String Reversal Processor: e(t(x1)) -> s(n(x1)) l(a(x1)) -> t(a(x1)) a(m(o(x1))) -> n(e(t(x1))) a(s(x1)) -> e(t(a(m(o(t(a(l(x1)))))))) Bounds Processor: bound: 4 enrichment: match automaton: final states: {9} transitions: n3(97) -> 98* n3(94) -> 95* n3(106) -> 107* e1(34) -> 35* e1(24) -> 25* e3(105) -> 106* t1(17) -> 18* t1(29) -> 30* t1(33) -> 34* t1(23) -> 24* t3(104) -> 105* a1(32) -> 33* a1(16) -> 17* a1(28) -> 29* s3(95) -> 96* s3(98) -> 99* m1(31) -> 32* s4(134) -> 135* o1(30) -> 31* n4(133) -> 134* l1(27) -> 28* l1(73) -> 74* n1(25) -> 26* n1(43) -> 44* n1(13) -> 14* s1(14) -> 15* e2(70) -> 71* e2(88) -> 89* e0(9) -> 9* t2(87) -> 88* t2(69) -> 70* t2(83) -> 84* t0(9) -> 9* a2(82) -> 83* a2(86) -> 87* s0(9) -> 9* m2(85) -> 86* n0(9) -> 9* o2(84) -> 85* l0(9) -> 9* l2(136) -> 137* l2(81) -> 82* l2(108) -> 109* a0(9) -> 9* n2(40) -> 41* n2(49) -> 50* n2(71) -> 72* m0(9) -> 9* s2(50) -> 51* s2(41) -> 42* o0(9) -> 9* 9 -> 27,23,16,13 14 -> 81,73 15 -> 9* 17 -> 43* 18 -> 28,9 23 -> 40* 26 -> 17,9 30 -> 69* 33 -> 49* 35 -> 17,9 42 -> 25* 44 -> 14* 50 -> 108* 51 -> 35,9,23,13,16,27 69 -> 97* 72 -> 33* 74 -> 28* 84 -> 104* 87 -> 94* 89 -> 9,27,16,13,23,40,17 95 -> 136* 96 -> 89* 99 -> 71* 104 -> 133* 107 -> 87* 109 -> 82* 135 -> 106* 137 -> 82* problem: Qed