32.75/8.76 YES 32.92/8.77 32.92/8.77 Problem: 32.92/8.77 tower(0(x1)) -> s(0(p(s(p(s(x1)))))) 32.92/8.77 tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) 32.92/8.77 twoto(0(x1)) -> s(0(x1)) 32.92/8.77 twoto(s(x1)) -> 32.92/8.77 p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) 32.92/8.77 twice(0(x1)) -> 0(x1) 32.92/8.77 twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) 32.92/8.77 p(p(s(x1))) -> p(x1) 32.92/8.77 p(s(x1)) -> x1 32.92/8.77 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) 32.92/8.77 32.92/8.77 Proof: 32.92/8.77 String Reversal Processor: 32.92/8.77 0(tower(x1)) -> s(p(s(p(0(s(x1)))))) 32.92/8.77 s(tower(x1)) -> s(p(s(p(tower(s(p(s(p(twoto(s(p(s(p(x1)))))))))))))) 32.92/8.77 0(twoto(x1)) -> 0(s(x1)) 32.92/8.77 s(twoto(x1)) -> 32.92/8.77 s(p(s(p(twoto(s(s(s(p(p(p(s(p(s(p(twice(s(p(s(s(p(s(s(p(s(s(p(p(p(s(p(p(x1)))))))))))))))))))))))))))))))) 32.92/8.77 0(twice(x1)) -> 0(x1) 32.92/8.77 s(twice(x1)) -> s(s(s(p(p(p(twice(s(s(s(s(s(p(p(p(x1))))))))))))))) 32.92/8.77 s(p(p(x1))) -> p(x1) 32.92/8.77 s(p(x1)) -> x1 32.92/8.77 0(p(x1)) -> s(s(s(s(s(s(s(s(0(x1))))))))) 32.92/8.77 Matrix Interpretation Processor: dim=1 32.92/8.77 32.92/8.77 interpretation: 32.92/8.77 [twice](x0) = x0, 32.92/8.77 32.92/8.77 [twoto](x0) = x0, 32.92/8.78 32.92/8.78 [p](x0) = x0, 32.92/8.78 32.92/8.78 [s](x0) = x0, 32.92/8.78 32.92/8.78 [tower](x0) = 2x0 + 2, 32.92/8.78 32.92/8.78 [0](x0) = 8x0 + 4 32.92/8.78 orientation: 32.92/8.78 0(tower(x1)) = 16x1 + 20 >= 8x1 + 4 = s(p(s(p(0(s(x1)))))) 32.92/8.78 32.92/8.78 s(tower(x1)) = 2x1 + 2 >= 2x1 + 2 = s(p(s(p(tower(s(p(s(p(twoto(s(p(s(p(x1)))))))))))))) 32.92/8.78 32.92/8.78 0(twoto(x1)) = 8x1 + 4 >= 8x1 + 4 = 0(s(x1)) 32.92/8.78 32.92/8.78 s(twoto(x1)) = x1 >= x1 = s(p(s(p(twoto(s(s(s(p(p(p(s(p(s(p(twice(s(p(s(s(p(s(s(p(s(s(p(p(p(s(p(p(x1)))))))))))))))))))))))))))))))) 32.92/8.78 32.92/8.78 0(twice(x1)) = 8x1 + 4 >= 8x1 + 4 = 0(x1) 32.92/8.78 32.92/8.78 s(twice(x1)) = x1 >= x1 = s(s(s(p(p(p(twice(s(s(s(s(s(p(p(p(x1))))))))))))))) 32.92/8.78 32.92/8.78 s(p(p(x1))) = x1 >= x1 = p(x1) 32.92/8.78 32.92/8.78 s(p(x1)) = x1 >= x1 = x1 32.92/8.78 32.92/8.78 0(p(x1)) = 8x1 + 4 >= 8x1 + 4 = s(s(s(s(s(s(s(s(0(x1))))))))) 32.92/8.78 problem: 32.92/8.78 s(tower(x1)) -> s(p(s(p(tower(s(p(s(p(twoto(s(p(s(p(x1)))))))))))))) 32.92/8.78 0(twoto(x1)) -> 0(s(x1)) 32.92/8.78 s(twoto(x1)) -> 32.92/8.78 s(p(s(p(twoto(s(s(s(p(p(p(s(p(s(p(twice(s(p(s(s(p(s(s(p(s(s(p(p(p(s(p(p(x1)))))))))))))))))))))))))))))))) 32.92/8.78 0(twice(x1)) -> 0(x1) 32.92/8.78 s(twice(x1)) -> s(s(s(p(p(p(twice(s(s(s(s(s(p(p(p(x1))))))))))))))) 32.92/8.78 s(p(p(x1))) -> p(x1) 32.92/8.78 s(p(x1)) -> x1 32.92/8.78 0(p(x1)) -> s(s(s(s(s(s(s(s(0(x1))))))))) 32.92/8.78 Matrix Interpretation Processor: dim=2 32.92/8.78 32.92/8.78 interpretation: 32.92/8.78 32.92/8.78 [twice](x0) = x0, 32.92/8.78 32.92/8.78 [0] 32.92/8.78 [twoto](x0) = x0 + [2], 32.92/8.78 32.92/8.78 32.92/8.78 [p](x0) = x0, 32.92/8.78 32.92/8.78 32.92/8.78 [s](x0) = x0, 32.92/8.78 32.92/8.78 [1 0] 32.92/8.78 [tower](x0) = [0 0]x0, 32.92/8.78 32.92/8.78 [2 1] [0] 32.92/8.78 [0](x0) = [0 1]x0 + [3] 32.92/8.78 orientation: 32.92/8.78 [1 0] [1 0] 32.92/8.78 s(tower(x1)) = [0 0]x1 >= [0 0]x1 = s(p(s(p(tower(s(p(s(p(twoto(s(p(s(p(x1)))))))))))))) 32.92/8.78 32.92/8.78 [2 1] [2] [2 1] [0] 32.92/8.78 0(twoto(x1)) = [0 1]x1 + [5] >= [0 1]x1 + [3] = 0(s(x1)) 32.92/8.78 32.92/8.78 [0] [0] 32.92/8.78 s(twoto(x1)) = x1 + [2] >= x1 + [2] = s(p(s(p(twoto(s(s(s(p(p(p(s(p(s(p(twice(s(p(s(s(p(s(s(p(s(s(p(p(p(s(p(p(x1)))))))))))))))))))))))))))))))) 32.92/8.78 32.92/8.78 [2 1] [0] [2 1] [0] 32.92/8.78 0(twice(x1)) = [0 1]x1 + [3] >= [0 1]x1 + [3] = 0(x1) 32.92/8.78 32.92/8.78 32.92/8.78 s(twice(x1)) = x1 >= x1 = s(s(s(p(p(p(twice(s(s(s(s(s(p(p(p(x1))))))))))))))) 32.92/8.78 32.92/8.78 32.92/8.78 s(p(p(x1))) = x1 >= x1 = p(x1) 32.92/8.78 32.92/8.78 32.92/8.78 s(p(x1)) = x1 >= x1 = x1 32.92/8.78 32.92/8.78 [2 1] [0] [2 1] [0] 32.92/8.78 0(p(x1)) = [0 1]x1 + [3] >= [0 1]x1 + [3] = s(s(s(s(s(s(s(s(0(x1))))))))) 32.92/8.78 problem: 32.92/8.78 s(tower(x1)) -> s(p(s(p(tower(s(p(s(p(twoto(s(p(s(p(x1)))))))))))))) 32.92/8.78 s(twoto(x1)) -> 32.92/8.78 s(p(s(p(twoto(s(s(s(p(p(p(s(p(s(p(twice(s(p(s(s(p(s(s(p(s(s(p(p(p(s(p(p(x1)))))))))))))))))))))))))))))))) 32.92/8.78 0(twice(x1)) -> 0(x1) 32.92/8.78 s(twice(x1)) -> s(s(s(p(p(p(twice(s(s(s(s(s(p(p(p(x1))))))))))))))) 32.92/8.78 s(p(p(x1))) -> p(x1) 32.92/8.78 s(p(x1)) -> x1 32.92/8.78 0(p(x1)) -> s(s(s(s(s(s(s(s(0(x1))))))))) 32.92/8.78 String Reversal Processor: 32.92/8.78 tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1)))))))))))))) 32.92/8.78 twoto(s(x1)) -> 32.92/8.78 p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1)))))))))))))))))))))))))))))))) 32.92/8.78 twice(0(x1)) -> 0(x1) 32.92/8.78 twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1))))))))))))))) 32.92/8.78 p(p(s(x1))) -> p(x1) 32.92/8.78 p(s(x1)) -> x1 32.92/8.78 p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1))))))))) 32.92/8.78 Bounds Processor: 32.92/8.78 bound: 1 32.92/8.78 enrichment: match 32.92/8.78 automaton: 32.92/8.78 final states: {60,2,59,45,44,16,1} 32.92/8.78 transitions: 32.92/8.78 p1(80) -> 81* 32.92/8.78 p1(82) -> 83* 32.92/8.78 p1(72) -> 73* 32.92/8.78 p1(104) -> 105* 32.92/8.78 p1(74) -> 75* 32.92/8.78 p1(96) -> 97* 32.92/8.78 p1(66) -> 67* 32.92/8.78 p1(98) -> 99* 32.92/8.78 p1(88) -> 89* 32.92/8.78 p1(90) -> 91* 32.92/8.78 f60() -> 2* 32.92/8.78 p0(40) -> 41* 32.92/8.78 p0(35) -> 36* 32.92/8.78 p0(20) -> 21* 32.92/8.78 p0(15) -> 1* 32.92/8.78 p0(10) -> 11* 32.92/8.78 p0(5) -> 6* 32.92/8.78 p0(57) -> 58* 32.92/8.78 p0(47) -> 48* 32.92/8.78 p0(42) -> 43* 32.92/8.78 p0(32) -> 33* 32.92/8.78 p0(22) -> 23* 32.92/8.78 p0(2) -> 59* 32.92/8.78 p0(49) -> 50* 32.92/8.78 p0(39) -> 40* 32.92/8.78 p0(29) -> 30* 32.92/8.78 p0(24) -> 25* 32.92/8.78 p0(56) -> 57* 32.92/8.78 p0(26) -> 27* 32.92/8.78 p0(21) -> 22* 32.92/8.78 p0(58) -> 45* 32.92/8.78 p0(48) -> 49* 32.92/8.78 p0(43) -> 16* 32.92/8.78 p0(38) -> 39* 32.92/8.78 p0(13) -> 14* 32.92/8.78 p0(8) -> 9* 32.92/8.78 p0(3) -> 4* 32.92/8.78 s0(55) -> 56* 32.92/8.78 s0(30) -> 31* 32.92/8.78 s0(25) -> 26* 32.92/8.78 s0(62) -> 63* 32.92/8.78 s0(52) -> 53* 32.92/8.78 s0(47) -> 61* 32.92/8.78 s0(37) -> 38* 32.92/8.78 s0(17) -> 18* 32.92/8.78 s0(12) -> 13* 32.92/8.78 s0(7) -> 8* 32.92/8.78 s0(2) -> 3* 32.92/8.78 s0(64) -> 65* 32.92/8.78 s0(54) -> 55* 32.92/8.78 s0(34) -> 35* 32.92/8.78 s0(19) -> 20* 32.92/8.78 s0(14) -> 15* 32.92/8.78 s0(9) -> 10* 32.92/8.78 s0(4) -> 5* 32.92/8.78 s0(61) -> 62* 32.92/8.78 s0(51) -> 52* 32.92/8.78 s0(46) -> 47* 32.92/8.78 s0(41) -> 42* 32.92/8.78 s0(36) -> 37* 32.92/8.78 s0(31) -> 32* 32.92/8.78 s0(63) -> 64* 32.92/8.78 s0(53) -> 54* 32.92/8.78 s0(33) -> 34* 32.92/8.78 s0(28) -> 29* 32.92/8.78 s0(23) -> 24* 32.92/8.78 s0(18) -> 19* 32.92/8.78 s0(3) -> 46* 32.92/8.78 twoto0(11) -> 12* 32.92/8.78 twoto0(6) -> 17* 32.92/8.78 tower0(6) -> 7* 32.92/8.78 twice0(50) -> 51* 32.92/8.78 twice0(27) -> 28* 32.92/8.78 00(65) -> 60* 32.92/8.78 00(2) -> 44* 32.92/8.78 1 -> 7,9,11 32.92/8.78 2 -> 59,99,50,4 32.92/8.78 3 -> 73,49,98 32.92/8.78 4 -> 6* 32.92/8.78 7 -> 9* 32.92/8.78 9 -> 11* 32.92/8.78 12 -> 14* 32.92/8.78 14 -> 1* 32.92/8.78 16 -> 17,91,27 32.92/8.78 17 -> 91,23 32.92/8.78 18 -> 81,22,90 32.92/8.78 19 -> 21,80 32.92/8.78 23 -> 25* 32.92/8.78 25 -> 27* 32.92/8.78 28 -> 30* 32.92/8.78 30 -> 105* 32.92/8.78 31 -> 33* 32.92/8.78 33 -> 89,104 32.92/8.78 34 -> 36* 32.92/8.78 36 -> 67,88 32.92/8.78 37 -> 39,66 32.92/8.78 41 -> 43,74 32.92/8.78 44 -> 51* 32.92/8.78 45 -> 51* 32.92/8.78 46 -> 48,72 32.92/8.78 53 -> 97* 32.92/8.78 54 -> 83,96 32.92/8.78 55 -> 57,82 32.92/8.78 60 -> 59* 32.92/8.78 67 -> 40* 32.92/8.78 73 -> 49* 32.92/8.78 75 -> 16* 32.92/8.78 81 -> 22* 32.92/8.78 83 -> 58* 32.92/8.78 89 -> 41,74,43 32.92/8.78 91 -> 23* 32.92/8.78 97 -> 45* 32.92/8.78 99 -> 50* 32.92/8.78 105 -> 75,16 32.92/8.78 problem: 32.92/8.78 32.92/8.78 Qed 32.92/8.78 EOF