Problem:
0(1(0(2(x1)))) -> 2(0(3(1(0(x1)))))
0(1(0(2(x1)))) -> 2(0(0(3(1(2(x1))))))
0(1(0(2(x1)))) -> 2(0(3(1(0(4(x1))))))
0(1(0(2(x1)))) -> 2(2(0(3(1(0(x1))))))
0(1(0(2(x1)))) -> 2(3(1(0(0(2(x1))))))
0(1(0(2(x1)))) -> 2(3(1(0(3(0(x1))))))
0(1(0(2(x1)))) -> 4(1(0(3(0(2(x1))))))
0(1(0(2(x1)))) -> 4(1(0(4(0(2(x1))))))
0(1(4(2(x1)))) -> 2(3(1(0(4(x1)))))
0(1(4(2(x1)))) -> 2(4(0(3(1(x1)))))
0(1(4(2(x1)))) -> 3(2(1(0(4(x1)))))
0(1(4(2(x1)))) -> 3(2(1(4(0(x1)))))
0(1(4(2(x1)))) -> 4(0(3(1(2(x1)))))
0(1(4(2(x1)))) -> 4(1(0(3(2(x1)))))
0(1(4(2(x1)))) -> 4(1(0(4(2(x1)))))
0(1(4(2(x1)))) -> 4(1(0(5(2(x1)))))
0(1(4(2(x1)))) -> 2(0(3(1(0(4(x1))))))
0(1(4(2(x1)))) -> 2(0(3(1(4(4(x1))))))
0(1(4(2(x1)))) -> 2(3(1(4(0(4(x1))))))
0(1(4(2(x1)))) -> 2(4(3(0(4(1(x1))))))
0(1(4(2(x1)))) -> 2(4(3(1(0(3(x1))))))
0(1(4(2(x1)))) -> 3(2(1(0(4(1(x1))))))
0(1(4(2(x1)))) -> 3(2(2(1(4(0(x1))))))
0(1(4(2(x1)))) -> 3(2(3(1(0(4(x1))))))
0(1(4(2(x1)))) -> 3(2(3(1(4(0(x1))))))
0(1(4(2(x1)))) -> 4(0(3(1(3(2(x1))))))
0(1(4(2(x1)))) -> 4(0(3(1(4(2(x1))))))
0(1(4(2(x1)))) -> 4(1(0(4(3(2(x1))))))
0(1(4(2(x1)))) -> 4(1(0(4(5(2(x1))))))
0(1(4(2(x1)))) -> 4(1(0(5(3(2(x1))))))
0(1(4(2(x1)))) -> 4(1(1(0(5(2(x1))))))
0(1(4(2(x1)))) -> 4(1(3(0(5(2(x1))))))
0(1(4(2(x1)))) -> 4(3(0(3(1(2(x1))))))
0(1(4(2(x1)))) -> 4(4(0(3(1(2(x1))))))
0(0(1(0(2(x1))))) -> 1(0(0(2(0(4(x1))))))
0(0(1(0(2(x1))))) -> 1(0(4(0(0(2(x1))))))
0(0(1(0(2(x1))))) -> 2(1(0(3(0(0(x1))))))
0(0(1(4(2(x1))))) -> 0(0(3(1(2(4(x1))))))
0(0(1(4(2(x1))))) -> 0(2(3(1(0(4(x1))))))
0(0(1(4(2(x1))))) -> 0(2(4(0(3(1(x1))))))
0(0(1(4(2(x1))))) -> 0(3(1(0(2(4(x1))))))
0(0(1(4(2(x1))))) -> 1(0(3(4(0(2(x1))))))
0(0(1(4(2(x1))))) -> 2(0(0(3(1(4(x1))))))
0(0(1(4(2(x1))))) -> 2(1(0(4(0(0(x1))))))
0(1(2(0(2(x1))))) -> 2(0(1(0(4(2(x1))))))
0(1(2(4(2(x1))))) -> 2(3(1(0(2(4(x1))))))
0(1(2(4(2(x1))))) -> 4(1(0(2(2(4(x1))))))
0(1(3(4(2(x1))))) -> 2(3(1(4(4(0(x1))))))
0(1(3(4(2(x1))))) -> 2(4(3(0(4(1(x1))))))
0(1(3(4(2(x1))))) -> 3(2(1(0(4(0(x1))))))
0(1(3(4(2(x1))))) -> 4(0(3(3(1(2(x1))))))
0(1(3(4(2(x1))))) -> 4(1(4(0(3(2(x1))))))
0(1(4(0(2(x1))))) -> 2(0(3(1(0(4(x1))))))
0(1(5(0(2(x1))))) -> 0(2(3(1(0(5(x1))))))
0(1(5(0(2(x1))))) -> 3(0(5(1(0(2(x1))))))
0(1(5(0(2(x1))))) -> 5(1(3(0(0(2(x1))))))
0(1(5(4(2(x1))))) -> 0(4(4(1(2(5(x1))))))
0(1(5(4(2(x1))))) -> 1(0(4(5(1(2(x1))))))
0(1(5(4(2(x1))))) -> 2(0(4(4(5(1(x1))))))
0(1(5(4(2(x1))))) -> 4(0(2(3(1(5(x1))))))
0(1(5(4(2(x1))))) -> 4(1(0(2(5(2(x1))))))
0(1(5(4(2(x1))))) -> 4(1(0(5(2(5(x1))))))
0(1(5(4(2(x1))))) -> 4(2(1(3(0(5(x1))))))
0(1(5(4(2(x1))))) -> 4(3(1(0(2(5(x1))))))
0(1(5(4(2(x1))))) -> 4(4(0(5(1(2(x1))))))
0(1(5(4(2(x1))))) -> 4(4(2(1(0(5(x1))))))
0(1(5(4(2(x1))))) -> 5(0(4(5(2(1(x1))))))
0(1(5(4(2(x1))))) -> 5(1(2(0(4(3(x1))))))
0(1(5(4(2(x1))))) -> 5(3(1(0(4(2(x1))))))
0(2(1(4(2(x1))))) -> 0(4(4(1(2(2(x1))))))
0(2(1(4(2(x1))))) -> 3(2(2(1(4(0(x1))))))
0(2(1(4(2(x1))))) -> 4(1(0(3(2(2(x1))))))
5(0(1(4(2(x1))))) -> 2(0(4(3(5(1(x1))))))
5(0(1(4(2(x1))))) -> 2(4(0(3(1(5(x1))))))
5(0(1(4(2(x1))))) -> 4(1(0(5(3(2(x1))))))
5(0(1(4(2(x1))))) -> 5(2(1(1(0(4(x1))))))
5(0(2(0(2(x1))))) -> 5(0(3(0(2(2(x1))))))
5(0(2(0(2(x1))))) -> 5(0(4(0(2(2(x1))))))
5(0(2(4(2(x1))))) -> 5(4(0(3(2(2(x1))))))
5(1(5(0(2(x1))))) -> 5(2(1(4(5(0(x1))))))
5(1(5(4(2(x1))))) -> 5(2(1(0(4(5(x1))))))
5(4(1(4(2(x1))))) -> 3(2(1(4(4(5(x1))))))
5(4(1(4(2(x1))))) -> 4(4(3(5(1(2(x1))))))
5(4(2(0(2(x1))))) -> 3(0(5(2(2(4(x1))))))
5(4(2(0(2(x1))))) -> 4(0(5(3(2(2(x1))))))
5(4(2(0(2(x1))))) -> 5(2(2(2(4(0(x1))))))
5(4(2(0(2(x1))))) -> 5(3(2(2(4(0(x1))))))
5(4(2(0(2(x1))))) -> 5(4(2(2(4(0(x1))))))
5(4(2(4(2(x1))))) -> 0(4(4(5(2(2(x1))))))
5(4(2(4(2(x1))))) -> 5(4(4(3(2(2(x1))))))
5(4(5(4(2(x1))))) -> 4(5(0(4(5(2(x1))))))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {6,5}
transitions:
51(257) -> 258*
51(177) -> 178*
51(279) -> 280*
51(274) -> 275*
51(259) -> 260*
51(249) -> 250*
51(251) -> 252*
51(233) -> 234*
51(113) -> 114*
41(262) -> 263*
41(60) -> 61*
41(25) -> 26*
41(127) -> 128*
41(234) -> 235*
41(27) -> 28*
41(219) -> 220*
41(129) -> 130*
41(276) -> 277*
41(261) -> 262*
41(39) -> 40*
41(19) -> 20*
41(201) -> 202*
41(121) -> 122*
41(111) -> 112*
41(81) -> 82*
41(193) -> 194*
41(275) -> 276*
41(235) -> 236*
41(220) -> 221*
41(215) -> 216*
41(13) -> 14*
41(175) -> 176*
31(167) -> 168*
31(57) -> 58*
31(37) -> 38*
31(209) -> 210*
31(79) -> 80*
31(231) -> 232*
31(191) -> 192*
31(151) -> 152*
31(141) -> 142*
31(131) -> 132*
31(101) -> 102*
31(238) -> 239*
31(16) -> 17*
31(153) -> 154*
31(260) -> 261*
31(185) -> 186*
31(145) -> 146*
21(237) -> 238*
21(217) -> 218*
21(77) -> 78*
21(17) -> 18*
21(199) -> 200*
21(99) -> 100*
21(161) -> 162*
21(91) -> 92*
21(56) -> 57*
21(93) -> 94*
01(80) -> 81*
01(277) -> 278*
01(75) -> 76*
01(207) -> 208*
01(142) -> 143*
01(102) -> 103*
01(67) -> 68*
01(119) -> 120*
01(69) -> 70*
01(59) -> 60*
01(221) -> 222*
01(14) -> 15*
01(38) -> 39*
01(130) -> 131*
11(15) -> 16*
11(47) -> 48*
11(169) -> 170*
11(159) -> 160*
11(49) -> 50*
11(236) -> 237*
11(41) -> 42*
11(36) -> 37*
11(218) -> 219*
11(183) -> 184*
11(143) -> 144*
11(103) -> 104*
11(78) -> 79*
42(314) -> 315*
42(311) -> 312*
42(291) -> 292*
00(2) -> 5*
00(4) -> 5*
00(1) -> 5*
00(3) -> 5*
52(313) -> 314*
52(303) -> 304*
52(310) -> 311*
52(305) -> 306*
52(295) -> 296*
52(290) -> 291*
52(297) -> 298*
10(2) -> 1*
10(4) -> 1*
10(1) -> 1*
10(3) -> 1*
02(312) -> 313*
02(292) -> 293*
20(2) -> 2*
20(4) -> 2*
20(1) -> 2*
20(3) -> 2*
22(309) -> 310*
22(294) -> 295*
22(316) -> 317*
22(325) -> 326*
22(327) -> 328*
30(2) -> 3*
30(4) -> 3*
30(1) -> 3*
30(3) -> 3*
12(293) -> 294*
40(2) -> 4*
40(4) -> 4*
40(1) -> 4*
40(3) -> 4*
50(2) -> 6*
50(4) -> 6*
50(1) -> 6*
50(3) -> 6*
1 -> 251,151,93,69,47,25
2 -> 233,141,77,59,36,13
3 -> 257,153,99,75,49,27
4 -> 249,145,91,67,41,19
14 -> 199,121
15 -> 127*
16 -> 201,56
17 -> 119*
18 -> 70,167,5
20 -> 14*
26 -> 14*
28 -> 14*
37 -> 129*
40 -> 17*
42 -> 37*
48 -> 37*
50 -> 37*
57 -> 161*
58 -> 70,5
61 -> 70,207,15
68 -> 60*
70 -> 60*
76 -> 60*
77 -> 309,290
78 -> 217,113,111,101
79 -> 259*
80 -> 209*
81 -> 191*
82 -> 70,193,5
91 -> 325,303
92 -> 78*
93 -> 327,305
94 -> 78*
99 -> 316,297
100 -> 78*
102 -> 177,175,169
103 -> 215,185
104 -> 183,81
112 -> 102*
114 -> 102*
120 -> 17*
122 -> 15*
128 -> 279,15
131 -> 159*
132 -> 39*
144 -> 131*
146 -> 142*
152 -> 142*
154 -> 142*
160 -> 56*
162 -> 57*
168 -> 70,5
170 -> 79*
176 -> 102*
178 -> 102*
184 -> 81*
186 -> 103*
192 -> 81*
194 -> 5*
200 -> 14*
202 -> 70,60,5
208 -> 15*
210 -> 80*
216 -> 15*
218 -> 274,231
222 -> 60,5
232 -> 14*
239 -> 304,291,250,234,6
250 -> 234*
252 -> 234*
258 -> 234*
263 -> 304,291,250,234,6
278 -> 304,291,178,102,250,169,177,6
280 -> 304,291,178,102,250,169,177,6
296 -> 260*
298 -> 291*
304 -> 291*
306 -> 291*
315 -> 178,102,169,177
317 -> 310*
326 -> 310*
328 -> 310*
problem:
Qed