YES Problem: 2(7(x1)) -> 1(8(x1)) 2(8(1(x1))) -> 8(x1) 2(8(x1)) -> 4(x1) 5(9(x1)) -> 0(x1) 4(x1) -> 5(2(3(x1))) 5(3(x1)) -> 6(0(x1)) 2(8(x1)) -> 7(x1) 4(7(x1)) -> 1(3(x1)) 5(2(6(x1))) -> 6(2(4(x1))) 9(7(x1)) -> 7(5(x1)) 7(2(x1)) -> 4(x1) 7(0(x1)) -> 9(3(x1)) 6(9(x1)) -> 9(x1) 9(5(9(x1))) -> 5(7(x1)) 4(x1) -> 9(6(6(x1))) 9(x1) -> 6(7(x1)) 6(2(x1)) -> 7(7(x1)) 2(4(x1)) -> 0(7(x1)) 6(6(x1)) -> 3(x1) 0(3(x1)) -> 5(3(x1)) Proof: String Reversal Processor: 7(2(x1)) -> 8(1(x1)) 1(8(2(x1))) -> 8(x1) 8(2(x1)) -> 4(x1) 9(5(x1)) -> 0(x1) 4(x1) -> 3(2(5(x1))) 3(5(x1)) -> 0(6(x1)) 8(2(x1)) -> 7(x1) 7(4(x1)) -> 3(1(x1)) 6(2(5(x1))) -> 4(2(6(x1))) 7(9(x1)) -> 5(7(x1)) 2(7(x1)) -> 4(x1) 0(7(x1)) -> 3(9(x1)) 9(6(x1)) -> 9(x1) 9(5(9(x1))) -> 7(5(x1)) 4(x1) -> 6(6(9(x1))) 9(x1) -> 7(6(x1)) 2(6(x1)) -> 7(7(x1)) 4(2(x1)) -> 7(0(x1)) 6(6(x1)) -> 3(x1) 3(0(x1)) -> 3(5(x1)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [6](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [3](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [5](x0) = [0 0 0]x0 [0 1 0] , [1 1 0] [9](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [4](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [0] [1](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 0] [8](x0) = [0 0 1]x0 [0 0 0] , [1 1 1] [0] [2](x0) = [0 0 1]x0 + [0] [0 0 1] [1], [1 1 0] [7](x0) = [0 0 0]x0 [0 0 0] orientation: [1 1 2] [1 1 0] 7(2(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 8(1(x1)) [0 0 0] [0 0 0] [1 1 2] [1] [1 0 0] 1(8(2(x1))) = [0 0 1]x1 + [2] >= [0 0 1]x1 = 8(x1) [0 0 0] [0] [0 0 0] [1 1 1] [0] [1 1 0] 8(2(x1)) = [0 0 1]x1 + [1] >= [0 0 0]x1 = 4(x1) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] 9(5(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 0(x1) [0 0 0] [0 0 0] [1 1 0] [1 1 0] 4(x1) = [0 0 0]x1 >= [0 0 0]x1 = 3(2(5(x1))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] 3(5(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 0(6(x1)) [0 0 0] [0 0 0] [1 1 1] [0] [1 1 0] 8(2(x1)) = [0 0 1]x1 + [1] >= [0 0 0]x1 = 7(x1) [0 0 0] [0] [0 0 0] [1 1 0] [1 1 0] 7(4(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 3(1(x1)) [0 0 0] [0 0 0] [1 1 0] [1 1 0] 6(2(5(x1))) = [0 1 0]x1 >= [0 0 0]x1 = 4(2(6(x1))) [0 0 0] [0 0 0] [1 1 0] [1 1 0] 7(9(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 5(7(x1)) [0 0 0] [0 0 0] [1 1 0] [0] [1 1 0] 2(7(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = 4(x1) [0 0 0] [1] [0 0 0] [1 1 0] [1 1 0] 0(7(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 3(9(x1)) [0 0 0] [0 0 0] [1 1 0] [1 1 0] 9(6(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 9(x1) [0 0 0] [0 0 0] [1 1 0] [1 0 0] 9(5(9(x1))) = [0 0 0]x1 >= [0 0 0]x1 = 7(5(x1)) [0 0 0] [0 0 0] [1 1 0] [1 1 0] 4(x1) = [0 0 0]x1 >= [0 0 0]x1 = 6(6(9(x1))) [0 0 0] [0 0 0] [1 1 0] [1 1 0] 9(x1) = [0 0 0]x1 >= [0 0 0]x1 = 7(6(x1)) [0 0 0] [0 0 0] [1 1 0] [0] [1 1 0] 2(6(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = 7(7(x1)) [0 0 0] [1] [0 0 0] [1 1 2] [1 0 0] 4(2(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 7(0(x1)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] 6(6(x1)) = [0 1 0]x1 >= [0 0 0]x1 = 3(x1) [0 0 0] [0 0 0] [1 0 0] [1 0 0] 3(0(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 3(5(x1)) [0 0 0] [0 0 0] problem: 7(2(x1)) -> 8(1(x1)) 8(2(x1)) -> 4(x1) 9(5(x1)) -> 0(x1) 4(x1) -> 3(2(5(x1))) 3(5(x1)) -> 0(6(x1)) 8(2(x1)) -> 7(x1) 7(4(x1)) -> 3(1(x1)) 6(2(5(x1))) -> 4(2(6(x1))) 7(9(x1)) -> 5(7(x1)) 2(7(x1)) -> 4(x1) 0(7(x1)) -> 3(9(x1)) 9(6(x1)) -> 9(x1) 9(5(9(x1))) -> 7(5(x1)) 4(x1) -> 6(6(9(x1))) 9(x1) -> 7(6(x1)) 2(6(x1)) -> 7(7(x1)) 4(2(x1)) -> 7(0(x1)) 6(6(x1)) -> 3(x1) 3(0(x1)) -> 3(5(x1)) String Reversal Processor: 2(7(x1)) -> 1(8(x1)) 2(8(x1)) -> 4(x1) 5(9(x1)) -> 0(x1) 4(x1) -> 5(2(3(x1))) 5(3(x1)) -> 6(0(x1)) 2(8(x1)) -> 7(x1) 4(7(x1)) -> 1(3(x1)) 5(2(6(x1))) -> 6(2(4(x1))) 9(7(x1)) -> 7(5(x1)) 7(2(x1)) -> 4(x1) 7(0(x1)) -> 9(3(x1)) 6(9(x1)) -> 9(x1) 9(5(9(x1))) -> 5(7(x1)) 4(x1) -> 9(6(6(x1))) 9(x1) -> 6(7(x1)) 6(2(x1)) -> 7(7(x1)) 2(4(x1)) -> 0(7(x1)) 6(6(x1)) -> 3(x1) 0(3(x1)) -> 5(3(x1)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [6](x0) = [1 0 0]x0 + [1] [1 0 0] [1], [1 0 0] [3](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [0](x0) = [1 0 0]x0 + [1] [1 0 0] [1], [1 0 0] [0] [5](x0) = [1 0 0]x0 + [1] [1 0 0] [1], [1 0 0] [0] [9](x0) = [1 0 0]x0 + [1] [1 0 0] [1], [1 0 0] [0] [4](x0) = [1 0 0]x0 + [1] [1 0 0] [1], [1 0 0] [0] [1](x0) = [0 0 0]x0 + [0] [0 1 0] [1], [1 0 1] [0] [8](x0) = [1 0 0]x0 + [0] [1 1 1] [1], [1 1 1] [0] [2](x0) = [0 0 1]x0 + [0] [1 0 0] [1], [1 0 0] [7](x0) = [0 0 1]x0 [0 0 1] orientation: [1 0 2] [0] [1 0 1] [0] 2(7(x1)) = [0 0 1]x1 + [0] >= [0 0 0]x1 + [0] = 1(8(x1)) [1 0 0] [1] [1 0 0] [1] [3 1 2] [1] [1 0 0] [0] 2(8(x1)) = [1 1 1]x1 + [1] >= [1 0 0]x1 + [1] = 4(x1) [1 0 1] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] 5(9(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 0(x1) [1 0 0] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] 4(x1) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 5(2(3(x1))) [1 0 0] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] 5(3(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 6(0(x1)) [1 0 0] [1] [1 0 0] [1] [3 1 2] [1] [1 0 0] 2(8(x1)) = [1 1 1]x1 + [1] >= [0 0 1]x1 = 7(x1) [1 0 1] [1] [0 0 1] [1 0 0] [0] [1 0 0] [0] 4(7(x1)) = [1 0 0]x1 + [1] >= [0 0 0]x1 + [0] = 1(3(x1)) [1 0 0] [1] [0 0 0] [1] [3 0 0] [2] [3 0 0] [2] 5(2(6(x1))) = [3 0 0]x1 + [3] >= [3 0 0]x1 + [3] = 6(2(4(x1))) [3 0 0] [3] [3 0 0] [3] [1 0 0] [0] [1 0 0] [0] 9(7(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 7(5(x1)) [1 0 0] [1] [1 0 0] [1] [1 1 1] [0] [1 0 0] [0] 7(2(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 4(x1) [1 0 0] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] 7(0(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 9(3(x1)) [1 0 0] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] 6(9(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 9(x1) [1 0 0] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] 9(5(9(x1))) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 5(7(x1)) [1 0 0] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] 4(x1) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 9(6(6(x1))) [1 0 0] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] 9(x1) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 6(7(x1)) [1 0 0] [1] [1 0 0] [1] [1 1 1] [0] [1 0 0] 6(2(x1)) = [1 1 1]x1 + [1] >= [0 0 1]x1 = 7(7(x1)) [1 1 1] [1] [0 0 1] [3 0 0] [2] [1 0 0] [0] 2(4(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 0(7(x1)) [1 0 0] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] 6(6(x1)) = [1 0 0]x1 + [1] >= [0 0 0]x1 = 3(x1) [1 0 0] [1] [0 0 0] [1 0 0] [0] [1 0 0] [0] 0(3(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = 5(3(x1)) [1 0 0] [1] [1 0 0] [1] problem: 2(7(x1)) -> 1(8(x1)) 5(9(x1)) -> 0(x1) 4(x1) -> 5(2(3(x1))) 5(3(x1)) -> 6(0(x1)) 4(7(x1)) -> 1(3(x1)) 5(2(6(x1))) -> 6(2(4(x1))) 9(7(x1)) -> 7(5(x1)) 7(2(x1)) -> 4(x1) 7(0(x1)) -> 9(3(x1)) 6(9(x1)) -> 9(x1) 9(5(9(x1))) -> 5(7(x1)) 4(x1) -> 9(6(6(x1))) 9(x1) -> 6(7(x1)) 6(2(x1)) -> 7(7(x1)) 6(6(x1)) -> 3(x1) 0(3(x1)) -> 5(3(x1)) String Reversal Processor: 7(2(x1)) -> 8(1(x1)) 9(5(x1)) -> 0(x1) 4(x1) -> 3(2(5(x1))) 3(5(x1)) -> 0(6(x1)) 7(4(x1)) -> 3(1(x1)) 6(2(5(x1))) -> 4(2(6(x1))) 7(9(x1)) -> 5(7(x1)) 2(7(x1)) -> 4(x1) 0(7(x1)) -> 3(9(x1)) 9(6(x1)) -> 9(x1) 9(5(9(x1))) -> 7(5(x1)) 4(x1) -> 6(6(9(x1))) 9(x1) -> 7(6(x1)) 2(6(x1)) -> 7(7(x1)) 6(6(x1)) -> 3(x1) 3(0(x1)) -> 3(5(x1)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [6](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [3](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [5](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [0] [9](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1] [4](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [0] [1](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [8](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [0] [2](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [0] [7](x0) = [0 0 0]x0 + [0] [0 0 0] [1] orientation: [1 0 1] [0] [1 0 0] [0] 7(2(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 8(1(x1)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] 9(5(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = 0(x1) [0 0 0] [1] [0 0 0] [1 0 0] [1] [1 0 0] [1] 4(x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 3(2(5(x1))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] 3(5(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 0(6(x1)) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] 7(4(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = 3(1(x1)) [0 0 0] [1] [0 0 0] [1 0 0] [1] [1 0 0] [1] 6(2(5(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 4(2(6(x1))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] 7(9(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 5(7(x1)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] 2(7(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 4(x1) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1 0 0] 0(7(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 3(9(x1)) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] 9(6(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 9(x1) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] 9(5(9(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 7(5(x1)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] 4(x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 = 6(6(9(x1))) [0 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] [0] 9(x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 7(6(x1)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] 2(6(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = 7(7(x1)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] 6(6(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 3(x1) [0 0 0] [0 0 0] [1 0 0] [1 0 0] 3(0(x1)) = [0 0 0]x1 >= [0 0 0]x1 = 3(5(x1)) [0 0 0] [0 0 0] problem: 7(2(x1)) -> 8(1(x1)) 9(5(x1)) -> 0(x1) 4(x1) -> 3(2(5(x1))) 3(5(x1)) -> 0(6(x1)) 6(2(5(x1))) -> 4(2(6(x1))) 7(9(x1)) -> 5(7(x1)) 2(7(x1)) -> 4(x1) 0(7(x1)) -> 3(9(x1)) 9(6(x1)) -> 9(x1) 9(5(9(x1))) -> 7(5(x1)) 9(x1) -> 7(6(x1)) 2(6(x1)) -> 7(7(x1)) 6(6(x1)) -> 3(x1) 3(0(x1)) -> 3(5(x1)) String Reversal Processor: 2(7(x1)) -> 1(8(x1)) 5(9(x1)) -> 0(x1) 4(x1) -> 5(2(3(x1))) 5(3(x1)) -> 6(0(x1)) 5(2(6(x1))) -> 6(2(4(x1))) 9(7(x1)) -> 7(5(x1)) 7(2(x1)) -> 4(x1) 7(0(x1)) -> 9(3(x1)) 6(9(x1)) -> 9(x1) 9(5(9(x1))) -> 5(7(x1)) 9(x1) -> 6(7(x1)) 6(2(x1)) -> 7(7(x1)) 6(6(x1)) -> 3(x1) 0(3(x1)) -> 5(3(x1)) Bounds Processor: bound: 2 enrichment: match automaton: final states: {20,6,19,18,16,15,14,10,12,9,8,5,4,1} transitions: f100() -> 2* 10(3) -> 1* 80(2) -> 3* 00(2) -> 4* 50(17) -> 16* 50(7) -> 5* 50(2) -> 13* 50(6) -> 20* 20(10) -> 11* 20(6) -> 7* 30(2) -> 6* 60(17) -> 18* 60(4) -> 8* 60(11) -> 9* 40(2) -> 10* 70(17) -> 19* 70(2) -> 17* 70(13) -> 12* 90(2) -> 15* 90(6) -> 14* 71(50) -> 51* 71(51) -> 52* 71(41) -> 42* 71(38) -> 39* 61(30) -> 31* 61(42) -> 43* 61(39) -> 40* 01(29) -> 30* 01(63) -> 64* 51(27) -> 28* 51(83) -> 84* 21(26) -> 27* 31(95) -> 96* 31(25) -> 26* 31(71) -> 72* 91(55) -> 56* 91(69) -> 70* 62(89) -> 90* 62(79) -> 80* 62(58) -> 59* 72(57) -> 58* 72(78) -> 79* 02(88) -> 89* 32(99) -> 100* 32(91) -> 92* 2 -> 41,29,25 4 -> 13* 6 -> 69,63,38 8 -> 13* 9 -> 13* 10 -> 42,17,50 12 -> 15* 14 -> 42,17 16 -> 15* 20 -> 89,30,4 25 -> 88* 26 -> 83,55 28 -> 10* 30 -> 99,95 31 -> 20* 39 -> 91,71 40 -> 14* 43 -> 15* 52 -> 9* 55 -> 57* 56 -> 12* 59 -> 56,12 64 -> 16* 69 -> 78* 70 -> 43,15,18 72 -> 18* 80 -> 70,18 84 -> 64,16 90 -> 84,64 92 -> 43,15 96 -> 8* 100 -> 90,84,64,16,31,20,4,95 problem: Qed