Tool CaT
stdout:
YES(?,O(n^1))
Problem:
0(0(1(x1))) -> 0(0(2(1(2(x1)))))
0(0(1(x1))) -> 0(0(3(1(4(x1)))))
0(1(0(x1))) -> 0(0(1(2(4(x1)))))
0(1(0(x1))) -> 2(1(2(0(0(x1)))))
0(1(0(x1))) -> 0(0(1(2(2(4(x1))))))
0(1(0(x1))) -> 0(0(2(4(1(4(x1))))))
0(4(0(x1))) -> 3(4(3(2(0(0(x1))))))
0(0(1(0(x1)))) -> 0(0(0(1(4(x1)))))
0(0(4(1(x1)))) -> 0(0(2(1(4(x1)))))
0(0(4(1(x1)))) -> 0(0(2(1(4(3(x1))))))
0(1(0(4(x1)))) -> 0(0(3(4(1(2(x1))))))
0(1(3(0(x1)))) -> 0(0(3(1(4(x1)))))
0(1(3(0(x1)))) -> 0(3(0(1(2(x1)))))
0(1(3(0(x1)))) -> 0(0(1(3(2(5(x1))))))
0(1(4(0(x1)))) -> 0(2(0(3(1(4(x1))))))
0(1(5(1(x1)))) -> 2(1(1(4(5(0(x1))))))
0(1(5(4(x1)))) -> 1(2(4(2(5(0(x1))))))
0(1(5(4(x1)))) -> 4(1(0(3(2(5(x1))))))
0(1(5(4(x1)))) -> 5(0(2(4(1(4(x1))))))
0(3(0(1(x1)))) -> 0(0(3(1(2(2(x1))))))
0(3(1(0(x1)))) -> 0(0(3(1(4(x1)))))
0(4(0(1(x1)))) -> 0(0(2(1(4(x1)))))
0(4(5(1(x1)))) -> 1(2(4(2(5(0(x1))))))
0(4(5(1(x1)))) -> 3(1(4(5(0(2(x1))))))
0(4(5(1(x1)))) -> 3(2(5(1(4(0(x1))))))
0(4(5(1(x1)))) -> 5(3(0(5(1(4(x1))))))
0(4(5(1(x1)))) -> 5(5(0(5(1(4(x1))))))
0(4(5(4(x1)))) -> 5(2(4(4(0(4(x1))))))
0(5(1(0(x1)))) -> 0(0(5(1(2(x1)))))
3(5(0(1(x1)))) -> 3(0(2(1(2(5(x1))))))
3(5(1(0(x1)))) -> 0(5(1(3(2(x1)))))
3(5(1(0(x1)))) -> 2(1(2(0(5(3(x1))))))
3(5(1(0(x1)))) -> 3(1(2(2(0(5(x1))))))
3(5(1(0(x1)))) -> 5(1(3(2(0(2(x1))))))
0(1(3(3(0(x1))))) -> 3(3(2(0(0(1(x1))))))
0(1(3(5(1(x1))))) -> 1(1(3(4(5(0(x1))))))
0(1(3(5(1(x1))))) -> 1(1(5(0(3(3(x1))))))
0(1(5(2(0(x1))))) -> 5(0(3(1(0(2(x1))))))
0(1(5(4(1(x1))))) -> 5(3(4(1(0(1(x1))))))
0(1(5(4(4(x1))))) -> 4(5(2(1(4(0(x1))))))
0(1(5(4(4(x1))))) -> 5(0(4(3(4(1(x1))))))
0(3(1(0(4(x1))))) -> 0(0(3(1(2(4(x1))))))
0(4(3(3(0(x1))))) -> 0(2(3(4(0(3(x1))))))
0(4(5(2(0(x1))))) -> 0(2(2(5(0(4(x1))))))
0(5(1(5(1(x1))))) -> 5(5(3(0(1(1(x1))))))
3(0(1(5(4(x1))))) -> 0(5(3(4(1(2(x1))))))
3(5(0(1(0(x1))))) -> 5(1(2(0(0(3(x1))))))
3(5(4(0(0(x1))))) -> 5(0(3(0(4(4(x1))))))
3(5(5(0(1(x1))))) -> 5(5(0(3(1(2(x1))))))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {6,5}
transitions:
51(15) -> 16*
51(97) -> 98*
51(67) -> 68*
51(139) -> 140*
51(74) -> 75*
51(59) -> 60*
51(176) -> 177*
51(61) -> 62*
51(123) -> 124*
51(43) -> 44*
51(135) -> 136*
31(45) -> 46*
31(137) -> 138*
31(191) -> 192*
31(186) -> 187*
31(100) -> 101*
01(27) -> 28*
01(154) -> 155*
01(29) -> 30*
01(14) -> 15*
01(136) -> 137*
01(96) -> 97*
01(46) -> 47*
01(21) -> 22*
01(148) -> 149*
01(73) -> 74*
01(190) -> 191*
11(70) -> 71*
11(167) -> 168*
11(122) -> 123*
11(47) -> 48*
11(17) -> 18*
11(189) -> 190*
11(99) -> 100*
11(41) -> 42*
11(173) -> 174*
11(153) -> 154*
11(18) -> 19*
11(165) -> 166*
11(155) -> 156*
41(85) -> 86*
41(187) -> 188*
41(87) -> 88*
41(149) -> 150*
41(69) -> 70*
41(39) -> 40*
41(156) -> 157*
41(121) -> 122*
41(71) -> 72*
41(16) -> 17*
41(98) -> 99*
41(93) -> 94*
41(48) -> 49*
41(185) -> 186*
41(150) -> 151*
21(40) -> 41*
21(72) -> 73*
21(124) -> 125*
21(119) -> 120*
21(44) -> 45*
21(19) -> 20*
21(151) -> 152*
21(111) -> 112*
21(113) -> 114*
21(38) -> 39*
21(175) -> 176*
21(95) -> 96*
00(2) -> 5*
00(4) -> 5*
00(1) -> 5*
00(3) -> 5*
10(2) -> 1*
10(4) -> 1*
10(1) -> 1*
10(3) -> 1*
20(2) -> 2*
20(4) -> 2*
20(1) -> 2*
20(3) -> 2*
30(2) -> 6*
30(4) -> 6*
30(1) -> 6*
30(3) -> 6*
40(2) -> 3*
40(4) -> 3*
40(1) -> 3*
40(3) -> 3*
50(2) -> 4*
50(4) -> 4*
50(1) -> 4*
50(3) -> 4*
1 -> 167,113,87,61,27
2 -> 153,95,69,43,14
3 -> 173,119,93,67,29
4 -> 165,111,85,59,21
15 -> 121*
16 -> 38*
20 -> 28,15,155,121,5
22 -> 15*
28 -> 15*
30 -> 15*
42 -> 30,149,28,155,121,5
49 -> 28,155,121,5
60 -> 44*
62 -> 44*
68 -> 44*
70 -> 148*
71 -> 135*
75 -> 22,30,149,28,155,121,5
86 -> 70*
88 -> 70*
94 -> 70*
101 -> 30,15,149,121,5
112 -> 96*
114 -> 96*
120 -> 96*
123 -> 175*
125 -> 100*
137 -> 139*
138 -> 74*
140 -> 74*
152 -> 74*
154 -> 189,185
157 -> 137*
166 -> 154*
168 -> 154*
174 -> 154*
177 -> 48*
188 -> 73*
192 -> 139*
problem:
QedTool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(0(1(x1))) -> 0(0(2(1(2(x1)))))
, 0(0(1(x1))) -> 0(0(3(1(4(x1)))))
, 0(1(0(x1))) -> 0(0(1(2(4(x1)))))
, 0(1(0(x1))) -> 2(1(2(0(0(x1)))))
, 0(1(0(x1))) -> 0(0(1(2(2(4(x1))))))
, 0(1(0(x1))) -> 0(0(2(4(1(4(x1))))))
, 0(4(0(x1))) -> 3(4(3(2(0(0(x1))))))
, 0(0(1(0(x1)))) -> 0(0(0(1(4(x1)))))
, 0(0(4(1(x1)))) -> 0(0(2(1(4(x1)))))
, 0(0(4(1(x1)))) -> 0(0(2(1(4(3(x1))))))
, 0(1(0(4(x1)))) -> 0(0(3(4(1(2(x1))))))
, 0(1(3(0(x1)))) -> 0(0(3(1(4(x1)))))
, 0(1(3(0(x1)))) -> 0(3(0(1(2(x1)))))
, 0(1(3(0(x1)))) -> 0(0(1(3(2(5(x1))))))
, 0(1(4(0(x1)))) -> 0(2(0(3(1(4(x1))))))
, 0(1(5(1(x1)))) -> 2(1(1(4(5(0(x1))))))
, 0(1(5(4(x1)))) -> 1(2(4(2(5(0(x1))))))
, 0(1(5(4(x1)))) -> 4(1(0(3(2(5(x1))))))
, 0(1(5(4(x1)))) -> 5(0(2(4(1(4(x1))))))
, 0(3(0(1(x1)))) -> 0(0(3(1(2(2(x1))))))
, 0(3(1(0(x1)))) -> 0(0(3(1(4(x1)))))
, 0(4(0(1(x1)))) -> 0(0(2(1(4(x1)))))
, 0(4(5(1(x1)))) -> 1(2(4(2(5(0(x1))))))
, 0(4(5(1(x1)))) -> 3(1(4(5(0(2(x1))))))
, 0(4(5(1(x1)))) -> 3(2(5(1(4(0(x1))))))
, 0(4(5(1(x1)))) -> 5(3(0(5(1(4(x1))))))
, 0(4(5(1(x1)))) -> 5(5(0(5(1(4(x1))))))
, 0(4(5(4(x1)))) -> 5(2(4(4(0(4(x1))))))
, 0(5(1(0(x1)))) -> 0(0(5(1(2(x1)))))
, 3(5(0(1(x1)))) -> 3(0(2(1(2(5(x1))))))
, 3(5(1(0(x1)))) -> 0(5(1(3(2(x1)))))
, 3(5(1(0(x1)))) -> 2(1(2(0(5(3(x1))))))
, 3(5(1(0(x1)))) -> 3(1(2(2(0(5(x1))))))
, 3(5(1(0(x1)))) -> 5(1(3(2(0(2(x1))))))
, 0(1(3(3(0(x1))))) -> 3(3(2(0(0(1(x1))))))
, 0(1(3(5(1(x1))))) -> 1(1(3(4(5(0(x1))))))
, 0(1(3(5(1(x1))))) -> 1(1(5(0(3(3(x1))))))
, 0(1(5(2(0(x1))))) -> 5(0(3(1(0(2(x1))))))
, 0(1(5(4(1(x1))))) -> 5(3(4(1(0(1(x1))))))
, 0(1(5(4(4(x1))))) -> 4(5(2(1(4(0(x1))))))
, 0(1(5(4(4(x1))))) -> 5(0(4(3(4(1(x1))))))
, 0(3(1(0(4(x1))))) -> 0(0(3(1(2(4(x1))))))
, 0(4(3(3(0(x1))))) -> 0(2(3(4(0(3(x1))))))
, 0(4(5(2(0(x1))))) -> 0(2(2(5(0(4(x1))))))
, 0(5(1(5(1(x1))))) -> 5(5(3(0(1(1(x1))))))
, 3(0(1(5(4(x1))))) -> 0(5(3(4(1(2(x1))))))
, 3(5(0(1(0(x1))))) -> 5(1(2(0(0(3(x1))))))
, 3(5(4(0(0(x1))))) -> 5(0(3(0(4(4(x1))))))
, 3(5(5(0(1(x1))))) -> 5(5(0(3(1(2(x1))))))}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ 0(0(1(x1))) -> 0(0(2(1(2(x1)))))
, 0(0(1(x1))) -> 0(0(3(1(4(x1)))))
, 0(1(0(x1))) -> 0(0(1(2(4(x1)))))
, 0(1(0(x1))) -> 2(1(2(0(0(x1)))))
, 0(1(0(x1))) -> 0(0(1(2(2(4(x1))))))
, 0(1(0(x1))) -> 0(0(2(4(1(4(x1))))))
, 0(4(0(x1))) -> 3(4(3(2(0(0(x1))))))
, 0(0(1(0(x1)))) -> 0(0(0(1(4(x1)))))
, 0(0(4(1(x1)))) -> 0(0(2(1(4(x1)))))
, 0(0(4(1(x1)))) -> 0(0(2(1(4(3(x1))))))
, 0(1(0(4(x1)))) -> 0(0(3(4(1(2(x1))))))
, 0(1(3(0(x1)))) -> 0(0(3(1(4(x1)))))
, 0(1(3(0(x1)))) -> 0(3(0(1(2(x1)))))
, 0(1(3(0(x1)))) -> 0(0(1(3(2(5(x1))))))
, 0(1(4(0(x1)))) -> 0(2(0(3(1(4(x1))))))
, 0(1(5(1(x1)))) -> 2(1(1(4(5(0(x1))))))
, 0(1(5(4(x1)))) -> 1(2(4(2(5(0(x1))))))
, 0(1(5(4(x1)))) -> 4(1(0(3(2(5(x1))))))
, 0(1(5(4(x1)))) -> 5(0(2(4(1(4(x1))))))
, 0(3(0(1(x1)))) -> 0(0(3(1(2(2(x1))))))
, 0(3(1(0(x1)))) -> 0(0(3(1(4(x1)))))
, 0(4(0(1(x1)))) -> 0(0(2(1(4(x1)))))
, 0(4(5(1(x1)))) -> 1(2(4(2(5(0(x1))))))
, 0(4(5(1(x1)))) -> 3(1(4(5(0(2(x1))))))
, 0(4(5(1(x1)))) -> 3(2(5(1(4(0(x1))))))
, 0(4(5(1(x1)))) -> 5(3(0(5(1(4(x1))))))
, 0(4(5(1(x1)))) -> 5(5(0(5(1(4(x1))))))
, 0(4(5(4(x1)))) -> 5(2(4(4(0(4(x1))))))
, 0(5(1(0(x1)))) -> 0(0(5(1(2(x1)))))
, 3(5(0(1(x1)))) -> 3(0(2(1(2(5(x1))))))
, 3(5(1(0(x1)))) -> 0(5(1(3(2(x1)))))
, 3(5(1(0(x1)))) -> 2(1(2(0(5(3(x1))))))
, 3(5(1(0(x1)))) -> 3(1(2(2(0(5(x1))))))
, 3(5(1(0(x1)))) -> 5(1(3(2(0(2(x1))))))
, 0(1(3(3(0(x1))))) -> 3(3(2(0(0(1(x1))))))
, 0(1(3(5(1(x1))))) -> 1(1(3(4(5(0(x1))))))
, 0(1(3(5(1(x1))))) -> 1(1(5(0(3(3(x1))))))
, 0(1(5(2(0(x1))))) -> 5(0(3(1(0(2(x1))))))
, 0(1(5(4(1(x1))))) -> 5(3(4(1(0(1(x1))))))
, 0(1(5(4(4(x1))))) -> 4(5(2(1(4(0(x1))))))
, 0(1(5(4(4(x1))))) -> 5(0(4(3(4(1(x1))))))
, 0(3(1(0(4(x1))))) -> 0(0(3(1(2(4(x1))))))
, 0(4(3(3(0(x1))))) -> 0(2(3(4(0(3(x1))))))
, 0(4(5(2(0(x1))))) -> 0(2(2(5(0(4(x1))))))
, 0(5(1(5(1(x1))))) -> 5(5(3(0(1(1(x1))))))
, 3(0(1(5(4(x1))))) -> 0(5(3(4(1(2(x1))))))
, 3(5(0(1(0(x1))))) -> 5(1(2(0(0(3(x1))))))
, 3(5(4(0(0(x1))))) -> 5(0(3(0(4(4(x1))))))
, 3(5(5(0(1(x1))))) -> 5(5(0(3(1(2(x1))))))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ 0_0(2) -> 1
, 0_1(2) -> 7
, 0_1(13) -> 12
, 0_1(17) -> 16
, 0_1(20) -> 33
, 0_1(25) -> 24
, 0_1(30) -> 29
, 0_1(36) -> 35
, 0_1(41) -> 40
, 1_0(2) -> 2
, 1_1(2) -> 36
, 1_1(4) -> 3
, 1_1(5) -> 4
, 1_1(8) -> 1
, 1_1(8) -> 7
, 1_1(8) -> 33
, 1_1(8) -> 35
, 1_1(12) -> 11
, 1_1(20) -> 19
, 1_1(22) -> 21
, 1_1(28) -> 27
, 1_1(35) -> 34
, 1_1(36) -> 41
, 2_0(2) -> 2
, 2_1(2) -> 25
, 2_1(3) -> 1
, 2_1(3) -> 7
, 2_1(3) -> 35
, 2_1(6) -> 10
, 2_1(9) -> 8
, 2_1(15) -> 14
, 2_1(18) -> 17
, 2_1(26) -> 21
, 2_1(27) -> 37
, 2_1(31) -> 16
, 3_0(2) -> 1
, 3_1(14) -> 13
, 3_1(21) -> 1
, 3_1(21) -> 7
, 3_1(21) -> 33
, 3_1(29) -> 16
, 3_1(39) -> 38
, 3_1(40) -> 29
, 4_0(2) -> 2
, 4_1(2) -> 20
, 4_1(6) -> 5
, 4_1(7) -> 28
, 4_1(10) -> 9
, 4_1(11) -> 1
, 4_1(11) -> 7
, 4_1(11) -> 35
, 4_1(19) -> 18
, 4_1(23) -> 22
, 4_1(32) -> 31
, 4_1(33) -> 32
, 4_1(34) -> 29
, 4_1(36) -> 39
, 4_1(38) -> 17
, 5_0(2) -> 2
, 5_1(2) -> 15
, 5_1(7) -> 6
, 5_1(16) -> 1
, 5_1(16) -> 7
, 5_1(16) -> 33
, 5_1(16) -> 35
, 5_1(19) -> 30
, 5_1(24) -> 23
, 5_1(27) -> 26
, 5_1(29) -> 16
, 5_1(37) -> 11}Tool RC1
stdout:
MAYBE
Tool RC2
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ 0(0(1(x1))) -> 0(0(2(1(2(x1)))))
, 0(0(1(x1))) -> 0(0(3(1(4(x1)))))
, 0(1(0(x1))) -> 0(0(1(2(4(x1)))))
, 0(1(0(x1))) -> 2(1(2(0(0(x1)))))
, 0(1(0(x1))) -> 0(0(1(2(2(4(x1))))))
, 0(1(0(x1))) -> 0(0(2(4(1(4(x1))))))
, 0(4(0(x1))) -> 3(4(3(2(0(0(x1))))))
, 0(0(1(0(x1)))) -> 0(0(0(1(4(x1)))))
, 0(0(4(1(x1)))) -> 0(0(2(1(4(x1)))))
, 0(0(4(1(x1)))) -> 0(0(2(1(4(3(x1))))))
, 0(1(0(4(x1)))) -> 0(0(3(4(1(2(x1))))))
, 0(1(3(0(x1)))) -> 0(0(3(1(4(x1)))))
, 0(1(3(0(x1)))) -> 0(3(0(1(2(x1)))))
, 0(1(3(0(x1)))) -> 0(0(1(3(2(5(x1))))))
, 0(1(4(0(x1)))) -> 0(2(0(3(1(4(x1))))))
, 0(1(5(1(x1)))) -> 2(1(1(4(5(0(x1))))))
, 0(1(5(4(x1)))) -> 1(2(4(2(5(0(x1))))))
, 0(1(5(4(x1)))) -> 4(1(0(3(2(5(x1))))))
, 0(1(5(4(x1)))) -> 5(0(2(4(1(4(x1))))))
, 0(3(0(1(x1)))) -> 0(0(3(1(2(2(x1))))))
, 0(3(1(0(x1)))) -> 0(0(3(1(4(x1)))))
, 0(4(0(1(x1)))) -> 0(0(2(1(4(x1)))))
, 0(4(5(1(x1)))) -> 1(2(4(2(5(0(x1))))))
, 0(4(5(1(x1)))) -> 3(1(4(5(0(2(x1))))))
, 0(4(5(1(x1)))) -> 3(2(5(1(4(0(x1))))))
, 0(4(5(1(x1)))) -> 5(3(0(5(1(4(x1))))))
, 0(4(5(1(x1)))) -> 5(5(0(5(1(4(x1))))))
, 0(4(5(4(x1)))) -> 5(2(4(4(0(4(x1))))))
, 0(5(1(0(x1)))) -> 0(0(5(1(2(x1)))))
, 3(5(0(1(x1)))) -> 3(0(2(1(2(5(x1))))))
, 3(5(1(0(x1)))) -> 0(5(1(3(2(x1)))))
, 3(5(1(0(x1)))) -> 2(1(2(0(5(3(x1))))))
, 3(5(1(0(x1)))) -> 3(1(2(2(0(5(x1))))))
, 3(5(1(0(x1)))) -> 5(1(3(2(0(2(x1))))))
, 0(1(3(3(0(x1))))) -> 3(3(2(0(0(1(x1))))))
, 0(1(3(5(1(x1))))) -> 1(1(3(4(5(0(x1))))))
, 0(1(3(5(1(x1))))) -> 1(1(5(0(3(3(x1))))))
, 0(1(5(2(0(x1))))) -> 5(0(3(1(0(2(x1))))))
, 0(1(5(4(1(x1))))) -> 5(3(4(1(0(1(x1))))))
, 0(1(5(4(4(x1))))) -> 4(5(2(1(4(0(x1))))))
, 0(1(5(4(4(x1))))) -> 5(0(4(3(4(1(x1))))))
, 0(3(1(0(4(x1))))) -> 0(0(3(1(2(4(x1))))))
, 0(4(3(3(0(x1))))) -> 0(2(3(4(0(3(x1))))))
, 0(4(5(2(0(x1))))) -> 0(2(2(5(0(4(x1))))))
, 0(5(1(5(1(x1))))) -> 5(5(3(0(1(1(x1))))))
, 3(0(1(5(4(x1))))) -> 0(5(3(4(1(2(x1))))))
, 3(5(0(1(0(x1))))) -> 5(1(2(0(0(3(x1))))))
, 3(5(4(0(0(x1))))) -> 5(0(3(0(4(4(x1))))))
, 3(5(5(0(1(x1))))) -> 5(5(0(3(1(2(x1))))))}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ 0(0(1(x1))) -> 0(0(2(1(2(x1)))))
, 0(0(1(x1))) -> 0(0(3(1(4(x1)))))
, 0(1(0(x1))) -> 0(0(1(2(4(x1)))))
, 0(1(0(x1))) -> 2(1(2(0(0(x1)))))
, 0(1(0(x1))) -> 0(0(1(2(2(4(x1))))))
, 0(1(0(x1))) -> 0(0(2(4(1(4(x1))))))
, 0(4(0(x1))) -> 3(4(3(2(0(0(x1))))))
, 0(0(1(0(x1)))) -> 0(0(0(1(4(x1)))))
, 0(0(4(1(x1)))) -> 0(0(2(1(4(x1)))))
, 0(0(4(1(x1)))) -> 0(0(2(1(4(3(x1))))))
, 0(1(0(4(x1)))) -> 0(0(3(4(1(2(x1))))))
, 0(1(3(0(x1)))) -> 0(0(3(1(4(x1)))))
, 0(1(3(0(x1)))) -> 0(3(0(1(2(x1)))))
, 0(1(3(0(x1)))) -> 0(0(1(3(2(5(x1))))))
, 0(1(4(0(x1)))) -> 0(2(0(3(1(4(x1))))))
, 0(1(5(1(x1)))) -> 2(1(1(4(5(0(x1))))))
, 0(1(5(4(x1)))) -> 1(2(4(2(5(0(x1))))))
, 0(1(5(4(x1)))) -> 4(1(0(3(2(5(x1))))))
, 0(1(5(4(x1)))) -> 5(0(2(4(1(4(x1))))))
, 0(3(0(1(x1)))) -> 0(0(3(1(2(2(x1))))))
, 0(3(1(0(x1)))) -> 0(0(3(1(4(x1)))))
, 0(4(0(1(x1)))) -> 0(0(2(1(4(x1)))))
, 0(4(5(1(x1)))) -> 1(2(4(2(5(0(x1))))))
, 0(4(5(1(x1)))) -> 3(1(4(5(0(2(x1))))))
, 0(4(5(1(x1)))) -> 3(2(5(1(4(0(x1))))))
, 0(4(5(1(x1)))) -> 5(3(0(5(1(4(x1))))))
, 0(4(5(1(x1)))) -> 5(5(0(5(1(4(x1))))))
, 0(4(5(4(x1)))) -> 5(2(4(4(0(4(x1))))))
, 0(5(1(0(x1)))) -> 0(0(5(1(2(x1)))))
, 3(5(0(1(x1)))) -> 3(0(2(1(2(5(x1))))))
, 3(5(1(0(x1)))) -> 0(5(1(3(2(x1)))))
, 3(5(1(0(x1)))) -> 2(1(2(0(5(3(x1))))))
, 3(5(1(0(x1)))) -> 3(1(2(2(0(5(x1))))))
, 3(5(1(0(x1)))) -> 5(1(3(2(0(2(x1))))))
, 0(1(3(3(0(x1))))) -> 3(3(2(0(0(1(x1))))))
, 0(1(3(5(1(x1))))) -> 1(1(3(4(5(0(x1))))))
, 0(1(3(5(1(x1))))) -> 1(1(5(0(3(3(x1))))))
, 0(1(5(2(0(x1))))) -> 5(0(3(1(0(2(x1))))))
, 0(1(5(4(1(x1))))) -> 5(3(4(1(0(1(x1))))))
, 0(1(5(4(4(x1))))) -> 4(5(2(1(4(0(x1))))))
, 0(1(5(4(4(x1))))) -> 5(0(4(3(4(1(x1))))))
, 0(3(1(0(4(x1))))) -> 0(0(3(1(2(4(x1))))))
, 0(4(3(3(0(x1))))) -> 0(2(3(4(0(3(x1))))))
, 0(4(5(2(0(x1))))) -> 0(2(2(5(0(4(x1))))))
, 0(5(1(5(1(x1))))) -> 5(5(3(0(1(1(x1))))))
, 3(0(1(5(4(x1))))) -> 0(5(3(4(1(2(x1))))))
, 3(5(0(1(0(x1))))) -> 5(1(2(0(0(3(x1))))))
, 3(5(4(0(0(x1))))) -> 5(0(3(0(4(4(x1))))))
, 3(5(5(0(1(x1))))) -> 5(5(0(3(1(2(x1))))))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ 0_0(2) -> 1
, 0_1(2) -> 7
, 0_1(13) -> 12
, 0_1(17) -> 16
, 0_1(20) -> 33
, 0_1(25) -> 24
, 0_1(30) -> 29
, 0_1(36) -> 35
, 0_1(41) -> 40
, 1_0(2) -> 2
, 1_1(2) -> 36
, 1_1(4) -> 3
, 1_1(5) -> 4
, 1_1(8) -> 1
, 1_1(8) -> 7
, 1_1(8) -> 33
, 1_1(8) -> 35
, 1_1(12) -> 11
, 1_1(20) -> 19
, 1_1(22) -> 21
, 1_1(28) -> 27
, 1_1(35) -> 34
, 1_1(36) -> 41
, 2_0(2) -> 2
, 2_1(2) -> 25
, 2_1(3) -> 1
, 2_1(3) -> 7
, 2_1(3) -> 35
, 2_1(6) -> 10
, 2_1(9) -> 8
, 2_1(15) -> 14
, 2_1(18) -> 17
, 2_1(26) -> 21
, 2_1(27) -> 37
, 2_1(31) -> 16
, 3_0(2) -> 1
, 3_1(14) -> 13
, 3_1(21) -> 1
, 3_1(21) -> 7
, 3_1(21) -> 33
, 3_1(29) -> 16
, 3_1(39) -> 38
, 3_1(40) -> 29
, 4_0(2) -> 2
, 4_1(2) -> 20
, 4_1(6) -> 5
, 4_1(7) -> 28
, 4_1(10) -> 9
, 4_1(11) -> 1
, 4_1(11) -> 7
, 4_1(11) -> 35
, 4_1(19) -> 18
, 4_1(23) -> 22
, 4_1(32) -> 31
, 4_1(33) -> 32
, 4_1(34) -> 29
, 4_1(36) -> 39
, 4_1(38) -> 17
, 5_0(2) -> 2
, 5_1(2) -> 15
, 5_1(7) -> 6
, 5_1(16) -> 1
, 5_1(16) -> 7
, 5_1(16) -> 33
, 5_1(16) -> 35
, 5_1(19) -> 30
, 5_1(24) -> 23
, 5_1(27) -> 26
, 5_1(29) -> 16
, 5_1(37) -> 11}