YES Problem: 0(0(1(x1))) -> 0(1(2(0(x1)))) 0(0(1(x1))) -> 0(3(1(0(x1)))) 0(0(1(x1))) -> 1(0(4(0(x1)))) 0(0(1(x1))) -> 0(1(3(0(2(x1))))) 0(0(1(x1))) -> 0(1(3(0(4(x1))))) 0(0(1(x1))) -> 0(2(0(1(2(x1))))) 0(0(1(x1))) -> 0(3(0(1(2(x1))))) 0(0(1(x1))) -> 0(3(0(3(1(x1))))) 0(0(1(x1))) -> 0(4(0(4(1(x1))))) 0(0(1(x1))) -> 1(2(0(2(0(x1))))) 0(0(1(x1))) -> 1(2(2(0(0(x1))))) 0(0(1(x1))) -> 0(0(2(2(1(2(x1)))))) 0(0(1(x1))) -> 0(1(2(4(2(0(x1)))))) 0(0(1(x1))) -> 1(2(0(3(0(4(x1)))))) 0(1(1(x1))) -> 0(2(1(1(x1)))) 0(1(1(x1))) -> 0(3(1(1(x1)))) 0(1(1(x1))) -> 1(1(3(0(4(x1))))) 0(1(1(x1))) -> 1(2(0(2(1(x1))))) 0(1(1(x1))) -> 1(0(3(1(2(4(x1)))))) 0(1(1(x1))) -> 1(0(4(2(1(2(x1)))))) 0(1(1(x1))) -> 1(1(2(4(3(0(x1)))))) 0(1(1(x1))) -> 1(2(1(0(4(4(x1)))))) 0(1(1(x1))) -> 1(2(2(1(3(0(x1)))))) 0(5(1(x1))) -> 0(3(1(5(x1)))) 0(5(1(x1))) -> 0(4(5(1(x1)))) 0(5(1(x1))) -> 0(2(3(1(5(x1))))) 0(5(1(x1))) -> 0(3(1(5(2(x1))))) 0(5(1(x1))) -> 0(3(1(2(5(2(x1)))))) 5(0(1(x1))) -> 5(1(2(4(0(x1))))) 5(0(1(x1))) -> 5(0(2(1(2(4(x1)))))) 5(0(1(x1))) -> 5(1(2(3(0(4(x1)))))) 0(0(1(5(x1)))) -> 0(4(1(0(5(x1))))) 0(0(2(1(x1)))) -> 2(0(3(0(2(1(x1)))))) 0(0(2(1(x1)))) -> 2(3(0(2(0(1(x1)))))) 0(1(0(1(x1)))) -> 1(0(2(0(1(x1))))) 0(1(1(1(x1)))) -> 1(1(3(1(0(x1))))) 5(0(1(1(x1)))) -> 1(5(1(2(0(x1))))) 5(3(0(1(x1)))) -> 5(1(2(3(0(x1))))) 5(3(1(5(x1)))) -> 5(3(1(2(5(x1))))) 5(3(2(1(x1)))) -> 1(2(3(5(2(x1))))) 5(4(0(1(x1)))) -> 1(2(5(0(4(x1))))) 0(0(5(1(5(x1))))) -> 1(2(5(5(0(0(x1)))))) 0(5(3(0(1(x1))))) -> 1(0(5(3(0(4(x1)))))) 0(5(3(4(1(x1))))) -> 1(0(3(5(4(5(x1)))))) 0(5(4(0(1(x1))))) -> 0(1(3(0(4(5(x1)))))) 5(4(2(1(1(x1))))) -> 5(4(1(2(1(2(x1)))))) Proof: String Reversal Processor: 1(0(0(x1))) -> 0(2(1(0(x1)))) 1(0(0(x1))) -> 0(1(3(0(x1)))) 1(0(0(x1))) -> 0(4(0(1(x1)))) 1(0(0(x1))) -> 2(0(3(1(0(x1))))) 1(0(0(x1))) -> 4(0(3(1(0(x1))))) 1(0(0(x1))) -> 2(1(0(2(0(x1))))) 1(0(0(x1))) -> 2(1(0(3(0(x1))))) 1(0(0(x1))) -> 1(3(0(3(0(x1))))) 1(0(0(x1))) -> 1(4(0(4(0(x1))))) 1(0(0(x1))) -> 0(2(0(2(1(x1))))) 1(0(0(x1))) -> 0(0(2(2(1(x1))))) 1(0(0(x1))) -> 2(1(2(2(0(0(x1)))))) 1(0(0(x1))) -> 0(2(4(2(1(0(x1)))))) 1(0(0(x1))) -> 4(0(3(0(2(1(x1)))))) 1(1(0(x1))) -> 1(1(2(0(x1)))) 1(1(0(x1))) -> 1(1(3(0(x1)))) 1(1(0(x1))) -> 4(0(3(1(1(x1))))) 1(1(0(x1))) -> 1(2(0(2(1(x1))))) 1(1(0(x1))) -> 4(2(1(3(0(1(x1)))))) 1(1(0(x1))) -> 2(1(2(4(0(1(x1)))))) 1(1(0(x1))) -> 0(3(4(2(1(1(x1)))))) 1(1(0(x1))) -> 4(4(0(1(2(1(x1)))))) 1(1(0(x1))) -> 0(3(1(2(2(1(x1)))))) 1(5(0(x1))) -> 5(1(3(0(x1)))) 1(5(0(x1))) -> 1(5(4(0(x1)))) 1(5(0(x1))) -> 5(1(3(2(0(x1))))) 1(5(0(x1))) -> 2(5(1(3(0(x1))))) 1(5(0(x1))) -> 2(5(2(1(3(0(x1)))))) 1(0(5(x1))) -> 0(4(2(1(5(x1))))) 1(0(5(x1))) -> 4(2(1(2(0(5(x1)))))) 1(0(5(x1))) -> 4(0(3(2(1(5(x1)))))) 5(1(0(0(x1)))) -> 5(0(1(4(0(x1))))) 1(2(0(0(x1)))) -> 1(2(0(3(0(2(x1)))))) 1(2(0(0(x1)))) -> 1(0(2(0(3(2(x1)))))) 1(0(1(0(x1)))) -> 1(0(2(0(1(x1))))) 1(1(1(0(x1)))) -> 0(1(3(1(1(x1))))) 1(1(0(5(x1)))) -> 0(2(1(5(1(x1))))) 1(0(3(5(x1)))) -> 0(3(2(1(5(x1))))) 5(1(3(5(x1)))) -> 5(2(1(3(5(x1))))) 1(2(3(5(x1)))) -> 2(5(3(2(1(x1))))) 1(0(4(5(x1)))) -> 4(0(5(2(1(x1))))) 5(1(5(0(0(x1))))) -> 0(0(5(5(2(1(x1)))))) 1(0(3(5(0(x1))))) -> 4(0(3(5(0(1(x1)))))) 1(4(3(5(0(x1))))) -> 5(4(5(3(0(1(x1)))))) 1(0(4(5(0(x1))))) -> 5(4(0(3(1(0(x1)))))) 1(1(2(4(5(x1))))) -> 2(1(2(1(4(5(x1)))))) Matrix Interpretation Processor: dim=1 interpretation: [4](x0) = x0, [0](x0) = 2x0 + 1, [3](x0) = x0, [5](x0) = x0, [1](x0) = 2x0, [2](x0) = x0 orientation: 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 5 = 0(2(1(0(x1)))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 5 = 0(1(3(0(x1)))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 3 = 0(4(0(1(x1)))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 5 = 2(0(3(1(0(x1))))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 5 = 4(0(3(1(0(x1))))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 6 = 2(1(0(2(0(x1))))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 6 = 2(1(0(3(0(x1))))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 6 = 1(3(0(3(0(x1))))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 6 = 1(4(0(4(0(x1))))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 3 = 0(2(0(2(1(x1))))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 3 = 0(0(2(2(1(x1))))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 6 = 2(1(2(2(0(0(x1)))))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 5 = 0(2(4(2(1(0(x1)))))) 1(0(0(x1))) = 8x1 + 6 >= 8x1 + 3 = 4(0(3(0(2(1(x1)))))) 1(1(0(x1))) = 8x1 + 4 >= 8x1 + 4 = 1(1(2(0(x1)))) 1(1(0(x1))) = 8x1 + 4 >= 8x1 + 4 = 1(1(3(0(x1)))) 1(1(0(x1))) = 8x1 + 4 >= 8x1 + 1 = 4(0(3(1(1(x1))))) 1(1(0(x1))) = 8x1 + 4 >= 8x1 + 2 = 1(2(0(2(1(x1))))) 1(1(0(x1))) = 8x1 + 4 >= 8x1 + 2 = 4(2(1(3(0(1(x1)))))) 1(1(0(x1))) = 8x1 + 4 >= 8x1 + 2 = 2(1(2(4(0(1(x1)))))) 1(1(0(x1))) = 8x1 + 4 >= 8x1 + 1 = 0(3(4(2(1(1(x1)))))) 1(1(0(x1))) = 8x1 + 4 >= 8x1 + 1 = 4(4(0(1(2(1(x1)))))) 1(1(0(x1))) = 8x1 + 4 >= 8x1 + 1 = 0(3(1(2(2(1(x1)))))) 1(5(0(x1))) = 4x1 + 2 >= 4x1 + 2 = 5(1(3(0(x1)))) 1(5(0(x1))) = 4x1 + 2 >= 4x1 + 2 = 1(5(4(0(x1)))) 1(5(0(x1))) = 4x1 + 2 >= 4x1 + 2 = 5(1(3(2(0(x1))))) 1(5(0(x1))) = 4x1 + 2 >= 4x1 + 2 = 2(5(1(3(0(x1))))) 1(5(0(x1))) = 4x1 + 2 >= 4x1 + 2 = 2(5(2(1(3(0(x1)))))) 1(0(5(x1))) = 4x1 + 2 >= 4x1 + 1 = 0(4(2(1(5(x1))))) 1(0(5(x1))) = 4x1 + 2 >= 4x1 + 2 = 4(2(1(2(0(5(x1)))))) 1(0(5(x1))) = 4x1 + 2 >= 4x1 + 1 = 4(0(3(2(1(5(x1)))))) 5(1(0(0(x1)))) = 8x1 + 6 >= 8x1 + 5 = 5(0(1(4(0(x1))))) 1(2(0(0(x1)))) = 8x1 + 6 >= 8x1 + 6 = 1(2(0(3(0(2(x1)))))) 1(2(0(0(x1)))) = 8x1 + 6 >= 8x1 + 6 = 1(0(2(0(3(2(x1)))))) 1(0(1(0(x1)))) = 16x1 + 10 >= 16x1 + 6 = 1(0(2(0(1(x1))))) 1(1(1(0(x1)))) = 16x1 + 8 >= 16x1 + 1 = 0(1(3(1(1(x1))))) 1(1(0(5(x1)))) = 8x1 + 4 >= 8x1 + 1 = 0(2(1(5(1(x1))))) 1(0(3(5(x1)))) = 4x1 + 2 >= 4x1 + 1 = 0(3(2(1(5(x1))))) 5(1(3(5(x1)))) = 2x1 >= 2x1 = 5(2(1(3(5(x1))))) 1(2(3(5(x1)))) = 2x1 >= 2x1 = 2(5(3(2(1(x1))))) 1(0(4(5(x1)))) = 4x1 + 2 >= 4x1 + 1 = 4(0(5(2(1(x1))))) 5(1(5(0(0(x1))))) = 8x1 + 6 >= 8x1 + 3 = 0(0(5(5(2(1(x1)))))) 1(0(3(5(0(x1))))) = 8x1 + 6 >= 8x1 + 3 = 4(0(3(5(0(1(x1)))))) 1(4(3(5(0(x1))))) = 4x1 + 2 >= 4x1 + 1 = 5(4(5(3(0(1(x1)))))) 1(0(4(5(0(x1))))) = 8x1 + 6 >= 8x1 + 5 = 5(4(0(3(1(0(x1)))))) 1(1(2(4(5(x1))))) = 4x1 >= 4x1 = 2(1(2(1(4(5(x1)))))) problem: 1(0(0(x1))) -> 2(1(0(2(0(x1))))) 1(0(0(x1))) -> 2(1(0(3(0(x1))))) 1(0(0(x1))) -> 1(3(0(3(0(x1))))) 1(0(0(x1))) -> 1(4(0(4(0(x1))))) 1(0(0(x1))) -> 2(1(2(2(0(0(x1)))))) 1(1(0(x1))) -> 1(1(2(0(x1)))) 1(1(0(x1))) -> 1(1(3(0(x1)))) 1(5(0(x1))) -> 5(1(3(0(x1)))) 1(5(0(x1))) -> 1(5(4(0(x1)))) 1(5(0(x1))) -> 5(1(3(2(0(x1))))) 1(5(0(x1))) -> 2(5(1(3(0(x1))))) 1(5(0(x1))) -> 2(5(2(1(3(0(x1)))))) 1(0(5(x1))) -> 4(2(1(2(0(5(x1)))))) 1(2(0(0(x1)))) -> 1(2(0(3(0(2(x1)))))) 1(2(0(0(x1)))) -> 1(0(2(0(3(2(x1)))))) 5(1(3(5(x1)))) -> 5(2(1(3(5(x1))))) 1(2(3(5(x1)))) -> 2(5(3(2(1(x1))))) 1(1(2(4(5(x1))))) -> 2(1(2(1(4(5(x1)))))) String Reversal Processor: 0(0(1(x1))) -> 0(2(0(1(2(x1))))) 0(0(1(x1))) -> 0(3(0(1(2(x1))))) 0(0(1(x1))) -> 0(3(0(3(1(x1))))) 0(0(1(x1))) -> 0(4(0(4(1(x1))))) 0(0(1(x1))) -> 0(0(2(2(1(2(x1)))))) 0(1(1(x1))) -> 0(2(1(1(x1)))) 0(1(1(x1))) -> 0(3(1(1(x1)))) 0(5(1(x1))) -> 0(3(1(5(x1)))) 0(5(1(x1))) -> 0(4(5(1(x1)))) 0(5(1(x1))) -> 0(2(3(1(5(x1))))) 0(5(1(x1))) -> 0(3(1(5(2(x1))))) 0(5(1(x1))) -> 0(3(1(2(5(2(x1)))))) 5(0(1(x1))) -> 5(0(2(1(2(4(x1)))))) 0(0(2(1(x1)))) -> 2(0(3(0(2(1(x1)))))) 0(0(2(1(x1)))) -> 2(3(0(2(0(1(x1)))))) 5(3(1(5(x1)))) -> 5(3(1(2(5(x1))))) 5(3(2(1(x1)))) -> 1(2(3(5(2(x1))))) 5(4(2(1(1(x1))))) -> 5(4(1(2(1(2(x1)))))) Bounds Processor: bound: 0 enrichment: match automaton: final states: {67,64,60,55,50,44,40,36,34,31,27,25,22,18,14,9,7,1} transitions: 40(2) -> 45* 40(68) -> 69* 40(32) -> 33* 40(16) -> 17* 40(10) -> 15* 00(13) -> 9* 00(57) -> 58* 00(39) -> 36* 00(20) -> 21* 00(35) -> 34* 00(15) -> 16* 00(33) -> 31* 00(53) -> 54* 00(6) -> 1* 00(11) -> 12* 00(17) -> 14* 00(26) -> 25* 00(21) -> 18* 00(8) -> 7* 00(4) -> 5* 00(43) -> 40* 00(24) -> 22* 00(30) -> 27* 00(48) -> 49* 00(10) -> 56* 00(51) -> 52* 30(5) -> 8* 30(29) -> 30* 30(52) -> 53* 30(10) -> 11* 30(38) -> 39* 30(62) -> 63* 30(23) -> 26* 30(12) -> 13* 30(37) -> 65* 30(42) -> 43* 30(58) -> 59* 10(2) -> 10* 10(28) -> 29* 10(10) -> 23* 10(61) -> 62* 10(66) -> 64* 10(3) -> 4* 10(41) -> 42* 10(37) -> 38* 10(46) -> 47* 10(19) -> 68* 20(4) -> 19* 20(2) -> 3* 20(10) -> 51* 20(5) -> 6* 20(54) -> 50* 20(47) -> 48* 20(28) -> 61* 20(56) -> 57* 20(45) -> 46* 20(19) -> 20* 20(37) -> 41* 20(59) -> 55* 20(30) -> 35* 20(23) -> 24* 20(65) -> 66* 50(10) -> 32* 50(3) -> 37* 50(2) -> 28* 50(49) -> 44* 50(63) -> 60* 50(69) -> 67* f60() -> 2* 64 -> 28* 67 -> 28* 22 -> 56* 44 -> 28* 60 -> 28* 25 -> 56* problem: Qed