21.95/5.94 YES 21.95/5.95 21.95/5.95 Problem: 21.95/5.95 strict: 21.95/5.95 o(l(x1)) -> r(x1) 21.95/5.95 n(l(o(x1))) -> r(o(x1)) 21.95/5.95 L(l(o(x1))) -> L(r(o(x1))) 21.95/5.95 r(o(x1)) -> l(x1) 21.95/5.95 o(r(n(x1))) -> o(l(x1)) 21.95/5.95 o(r(R(x1))) -> o(l(R(x1))) 21.95/5.95 weak: 21.95/5.95 L(x1) -> L(n(x1)) 21.95/5.95 R(x1) -> n(R(x1)) 21.95/5.95 21.95/5.95 Proof: 21.95/5.95 String Reversal Processor: 21.95/5.95 strict: 21.95/5.95 l(o(x1)) -> r(x1) 21.95/5.95 o(l(n(x1))) -> o(r(x1)) 21.95/5.95 o(l(L(x1))) -> o(r(L(x1))) 21.95/5.95 o(r(x1)) -> l(x1) 21.95/5.95 n(r(o(x1))) -> l(o(x1)) 21.95/5.95 R(r(o(x1))) -> R(l(o(x1))) 21.95/5.95 weak: 21.95/5.95 L(x1) -> n(L(x1)) 21.95/5.95 R(x1) -> R(n(x1)) 21.95/5.95 Arctic Interpretation Processor: 21.95/5.95 dimension: 1 21.95/5.95 interpretation: 21.95/5.95 [R](x0) = x0, 21.95/5.95 21.95/5.95 [L](x0) = x0, 21.95/5.95 21.95/5.95 [n](x0) = x0, 21.95/5.95 21.95/5.95 [r](x0) = x0, 21.95/5.95 21.95/5.95 [o](x0) = 1x0, 21.95/5.95 21.95/5.95 [l](x0) = x0 21.95/5.95 orientation: 21.95/5.95 l(o(x1)) = 1x1 >= x1 = r(x1) 21.95/5.95 21.95/5.95 o(l(n(x1))) = 1x1 >= 1x1 = o(r(x1)) 21.95/5.95 21.95/5.95 o(l(L(x1))) = 1x1 >= 1x1 = o(r(L(x1))) 21.95/5.95 21.95/5.95 o(r(x1)) = 1x1 >= x1 = l(x1) 21.95/5.95 21.95/5.95 n(r(o(x1))) = 1x1 >= 1x1 = l(o(x1)) 21.95/5.95 21.95/5.95 R(r(o(x1))) = 1x1 >= 1x1 = R(l(o(x1))) 21.95/5.95 21.95/5.95 L(x1) = x1 >= x1 = n(L(x1)) 21.95/5.95 21.95/5.95 R(x1) = x1 >= x1 = R(n(x1)) 21.95/5.95 problem: 21.95/5.97 strict: 21.95/5.97 o(l(n(x1))) -> o(r(x1)) 21.95/5.97 o(l(L(x1))) -> o(r(L(x1))) 21.95/5.97 n(r(o(x1))) -> l(o(x1)) 21.95/5.97 R(r(o(x1))) -> R(l(o(x1))) 21.95/5.97 weak: 21.95/5.97 L(x1) -> n(L(x1)) 21.95/5.97 R(x1) -> R(n(x1)) 21.95/5.97 String Reversal Processor: 21.95/5.97 strict: 21.95/5.97 n(l(o(x1))) -> r(o(x1)) 21.95/5.97 L(l(o(x1))) -> L(r(o(x1))) 21.95/5.97 o(r(n(x1))) -> o(l(x1)) 21.95/5.97 o(r(R(x1))) -> o(l(R(x1))) 21.95/5.97 weak: 21.95/5.97 L(x1) -> L(n(x1)) 21.95/5.97 R(x1) -> n(R(x1)) 21.95/5.97 Bounds Processor: 21.95/5.97 bound: 1 21.95/5.97 enrichment: match-rt 21.95/5.97 automaton: 21.95/5.97 final states: {7} 21.95/5.97 transitions: 21.95/5.97 r1(40) -> 41* 21.95/5.97 o1(26) -> 27* 21.95/5.97 o1(125) -> 126* 21.95/5.97 L1(62) -> 63* 21.95/5.97 l1(25) -> 26* 21.95/5.97 l1(102) -> 103* 21.95/5.97 R1(93) -> 94* 21.95/5.97 n1(72) -> 73* 21.95/5.97 n1(94) -> 95* 21.95/5.97 n1(150) -> 151* 21.95/5.97 n0(7) -> 7* 21.95/5.97 l0(7) -> 7* 21.95/5.97 o0(7) -> 7* 21.95/5.97 r0(7) -> 7* 21.95/5.97 L0(7) -> 7* 21.95/5.97 R0(7) -> 7* 21.95/5.97 7 -> 125,93,72,25 21.95/5.97 27 -> 126,40,7 21.95/5.97 41 -> 73,62,7 21.95/5.97 62 -> 150* 21.95/5.97 63 -> 7* 21.95/5.97 73 -> 62* 21.95/5.97 94 -> 102* 21.95/5.97 95 -> 94,7 21.95/5.97 103 -> 26* 21.95/5.97 126 -> 40* 21.95/5.97 151 -> 62* 21.95/5.97 problem: 21.95/5.97 strict: 21.95/5.97 n(l(o(x1))) -> r(o(x1)) 21.95/5.97 L(l(o(x1))) -> L(r(o(x1))) 21.95/5.97 o(r(R(x1))) -> o(l(R(x1))) 21.95/5.97 weak: 21.95/5.97 L(x1) -> L(n(x1)) 21.95/5.97 R(x1) -> n(R(x1)) 21.95/5.97 String Reversal Processor: 21.95/5.97 strict: 21.95/5.97 o(l(n(x1))) -> o(r(x1)) 21.95/5.97 o(l(L(x1))) -> o(r(L(x1))) 21.95/5.97 R(r(o(x1))) -> R(l(o(x1))) 21.95/5.97 weak: 21.95/5.97 L(x1) -> n(L(x1)) 21.95/5.97 R(x1) -> R(n(x1)) 21.95/5.97 Bounds Processor: 21.95/5.97 bound: 1 21.95/5.97 enrichment: match-rt 21.95/5.97 automaton: 21.95/5.97 final states: {7} 21.95/5.97 transitions: 21.95/5.97 r1(11) -> 12* 21.95/5.97 r1(63) -> 64* 21.95/5.97 o1(12) -> 13* 21.95/5.97 L1(46) -> 47* 21.95/5.97 l1(39) -> 40* 21.95/5.97 R1(40) -> 41* 21.95/5.97 n1(92) -> 93* 21.95/5.97 n1(47) -> 48* 21.95/5.97 n1(69) -> 70* 21.95/5.97 n0(7) -> 7* 21.95/5.97 l0(7) -> 7* 21.95/5.97 o0(7) -> 7* 21.95/5.97 r0(7) -> 7* 21.95/5.97 L0(7) -> 7* 21.95/5.97 R0(7) -> 7* 21.95/5.97 7 -> 69,46,11 21.95/5.97 13 -> 39,7 21.95/5.97 40 -> 92* 21.95/5.97 41 -> 7* 21.95/5.97 47 -> 63* 21.95/5.97 48 -> 47,7 21.95/5.97 64 -> 12* 21.95/5.97 70 -> 40* 21.95/5.97 93 -> 40* 21.95/5.97 problem: 21.95/5.97 strict: 21.95/5.97 o(l(L(x1))) -> o(r(L(x1))) 21.95/5.97 R(r(o(x1))) -> R(l(o(x1))) 21.95/5.97 weak: 21.95/5.97 L(x1) -> n(L(x1)) 21.95/5.97 R(x1) -> R(n(x1)) 21.95/5.97 Bounds Processor: 21.95/5.97 bound: 1 21.95/5.97 enrichment: match-rt 21.95/5.97 automaton: 21.95/5.97 final states: {7} 21.95/5.97 transitions: 21.95/5.97 r1(25) -> 26* 21.95/5.97 o1(20) -> 21* 21.95/5.97 L1(24) -> 25* 21.95/5.97 l1(21) -> 22* 21.95/5.97 R1(22) -> 23* 21.95/5.97 n1(40) -> 41* 21.95/5.97 n1(42) -> 43* 21.95/5.97 n1(54) -> 55* 21.95/5.97 n0(7) -> 7* 21.95/5.97 l0(7) -> 7* 21.95/5.97 o0(7) -> 7* 21.95/5.97 r0(7) -> 7* 21.95/5.97 L0(7) -> 7* 21.95/5.97 R0(7) -> 7* 21.95/5.97 7 -> 42,24,20 21.95/5.97 22 -> 54* 21.95/5.97 23 -> 7* 21.95/5.97 25 -> 40* 21.95/5.97 26 -> 20* 21.95/5.97 41 -> 25,7 21.95/5.97 43 -> 22* 21.95/5.97 55 -> 22* 21.95/5.97 problem: 21.95/5.97 strict: 21.95/5.97 o(l(L(x1))) -> o(r(L(x1))) 21.95/5.97 weak: 21.95/5.97 L(x1) -> n(L(x1)) 21.95/5.97 R(x1) -> R(n(x1)) 21.95/5.97 String Reversal Processor: 21.95/5.97 strict: 21.95/5.97 L(l(o(x1))) -> L(r(o(x1))) 21.95/5.97 weak: 21.95/5.97 L(x1) -> L(n(x1)) 21.95/5.97 R(x1) -> n(R(x1)) 21.95/5.97 Arctic Interpretation Processor: 21.95/5.97 dimension: 1 21.95/5.97 interpretation: 21.95/5.97 [R](x0) = x0, 21.95/5.97 21.95/5.97 [L](x0) = x0, 21.95/5.97 21.95/5.97 [n](x0) = x0, 21.95/5.97 21.95/5.97 [r](x0) = x0, 21.95/5.97 21.95/5.97 [o](x0) = x0, 21.95/5.97 21.95/5.97 [l](x0) = 6x0 21.95/5.97 orientation: 21.95/5.97 L(l(o(x1))) = 6x1 >= x1 = L(r(o(x1))) 21.95/5.97 21.95/5.97 L(x1) = x1 >= x1 = L(n(x1)) 21.95/5.97 21.95/5.97 R(x1) = x1 >= x1 = n(R(x1)) 21.95/5.97 problem: 21.95/5.97 strict: 21.95/5.97 21.95/5.97 weak: 21.95/5.97 L(x1) -> L(n(x1)) 21.95/5.97 R(x1) -> n(R(x1)) 21.95/5.97 Qed 21.95/5.97 EOF