Tool CaT
stdout:
YES(?,O(n^1))
Problem:
0(1(2(x1))) -> 0(0(2(1(x1))))
0(1(2(x1))) -> 0(2(1(3(x1))))
0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
0(3(1(x1))) -> 0(1(3(4(0(x1)))))
0(3(1(x1))) -> 0(1(3(4(4(x1)))))
0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
0(3(2(x1))) -> 0(2(1(3(x1))))
0(3(2(x1))) -> 0(2(3(4(x1))))
0(3(2(x1))) -> 0(0(2(4(3(x1)))))
0(3(2(x1))) -> 0(2(1(4(3(x1)))))
0(3(2(x1))) -> 0(2(4(3(3(x1)))))
0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
0(4(1(x1))) -> 0(1(4(4(x1))))
0(4(1(x1))) -> 0(2(1(4(x1))))
0(4(2(x1))) -> 0(2(1(4(x1))))
0(4(2(x1))) -> 0(2(3(4(x1))))
0(4(2(x1))) -> 0(2(4(3(x1))))
2(0(1(x1))) -> 5(0(2(1(x1))))
2(3(1(x1))) -> 1(3(5(2(x1))))
2(3(1(x1))) -> 0(2(1(3(5(x1)))))
2(3(1(x1))) -> 1(4(3(5(2(x1)))))
0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(x1))))))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {6,5}
transitions:
51(80) -> 81*
51(167) -> 168*
51(117) -> 118*
51(159) -> 160*
51(171) -> 172*
51(161) -> 162*
51(101) -> 102*
51(153) -> 154*
51(123) -> 124*
51(170) -> 171*
51(150) -> 151*
51(115) -> 116*
21(62) -> 63*
21(169) -> 170*
21(104) -> 105*
21(99) -> 100*
21(79) -> 80*
21(91) -> 92*
21(93) -> 94*
11(50) -> 51*
11(10) -> 11*
11(82) -> 83*
11(77) -> 78*
11(69) -> 70*
11(59) -> 60*
11(71) -> 72*
11(61) -> 62*
11(133) -> 134*
11(103) -> 104*
31(132) -> 133*
31(102) -> 103*
31(49) -> 50*
31(9) -> 10*
31(151) -> 152*
31(141) -> 142*
31(81) -> 82*
31(143) -> 144*
31(135) -> 136*
41(45) -> 46*
41(47) -> 48*
41(37) -> 38*
41(39) -> 40*
41(31) -> 32*
41(48) -> 49*
41(8) -> 9*
41(125) -> 126*
01(7) -> 8*
01(29) -> 30*
01(21) -> 22*
01(11) -> 12*
01(23) -> 24*
01(105) -> 106*
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) -> 6*
20(4) -> 6*
20(1) -> 6*
20(3) -> 6*
30(2) -> 2*
30(4) -> 2*
30(1) -> 2*
30(3) -> 2*
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 -> 117,93,39,23
2 -> 101,79,31,7
3 -> 123,99,45,29
4 -> 115,91,37,21
9 -> 59,47
10 -> 167*
12 -> 22,30,8,5
22 -> 8*
24 -> 8*
30 -> 8*
32 -> 150,132,61,8
38 -> 153,135,69,8
40 -> 159,141,71,8
46 -> 161,143,77,8
51 -> 8,5
60 -> 11*
63 -> 11*
70 -> 62*
72 -> 62*
78 -> 62*
82 -> 125*
83 -> 80,6
92 -> 80*
94 -> 80*
100 -> 80*
106 -> 80,6
116 -> 102*
118 -> 102*
124 -> 102*
126 -> 82*
134 -> 169,8
136 -> 133*
142 -> 133*
144 -> 133*
152 -> 8*
154 -> 151*
160 -> 151*
162 -> 151*
168 -> 10*
172 -> 92,80,6
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(1(2(x1))) -> 0(0(2(1(x1))))
, 0(1(2(x1))) -> 0(2(1(3(x1))))
, 0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
, 0(3(1(x1))) -> 0(1(3(4(0(x1)))))
, 0(3(1(x1))) -> 0(1(3(4(4(x1)))))
, 0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
, 0(3(2(x1))) -> 0(2(1(3(x1))))
, 0(3(2(x1))) -> 0(2(3(4(x1))))
, 0(3(2(x1))) -> 0(0(2(4(3(x1)))))
, 0(3(2(x1))) -> 0(2(1(4(3(x1)))))
, 0(3(2(x1))) -> 0(2(4(3(3(x1)))))
, 0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
, 0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
, 0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
, 0(4(1(x1))) -> 0(1(4(4(x1))))
, 0(4(1(x1))) -> 0(2(1(4(x1))))
, 0(4(2(x1))) -> 0(2(1(4(x1))))
, 0(4(2(x1))) -> 0(2(3(4(x1))))
, 0(4(2(x1))) -> 0(2(4(3(x1))))
, 2(0(1(x1))) -> 5(0(2(1(x1))))
, 2(3(1(x1))) -> 1(3(5(2(x1))))
, 2(3(1(x1))) -> 0(2(1(3(5(x1)))))
, 2(3(1(x1))) -> 1(4(3(5(2(x1)))))
, 0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
, 0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
, 0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
, 0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
, 0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
, 0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
, 0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
, 0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
, 0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
, 0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
, 2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
, 2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
, 2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
, 2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
, 0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
, 0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
, 0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
, 0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
, 0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
, 0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
, 0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
, 0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
, 2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
, 2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
, 2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
, 2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(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(1(2(x1))) -> 0(0(2(1(x1))))
, 0(1(2(x1))) -> 0(2(1(3(x1))))
, 0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
, 0(3(1(x1))) -> 0(1(3(4(0(x1)))))
, 0(3(1(x1))) -> 0(1(3(4(4(x1)))))
, 0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
, 0(3(2(x1))) -> 0(2(1(3(x1))))
, 0(3(2(x1))) -> 0(2(3(4(x1))))
, 0(3(2(x1))) -> 0(0(2(4(3(x1)))))
, 0(3(2(x1))) -> 0(2(1(4(3(x1)))))
, 0(3(2(x1))) -> 0(2(4(3(3(x1)))))
, 0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
, 0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
, 0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
, 0(4(1(x1))) -> 0(1(4(4(x1))))
, 0(4(1(x1))) -> 0(2(1(4(x1))))
, 0(4(2(x1))) -> 0(2(1(4(x1))))
, 0(4(2(x1))) -> 0(2(3(4(x1))))
, 0(4(2(x1))) -> 0(2(4(3(x1))))
, 2(0(1(x1))) -> 5(0(2(1(x1))))
, 2(3(1(x1))) -> 1(3(5(2(x1))))
, 2(3(1(x1))) -> 0(2(1(3(5(x1)))))
, 2(3(1(x1))) -> 1(4(3(5(2(x1)))))
, 0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
, 0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
, 0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
, 0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
, 0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
, 0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
, 0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
, 0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
, 0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
, 0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
, 2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
, 2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
, 2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
, 2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
, 0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
, 0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
, 0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
, 0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
, 0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
, 0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
, 0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
, 0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
, 2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
, 2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
, 2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
, 2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(x1))))))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 0_0(2) -> 1
, 0_1(2) -> 6
, 0_1(3) -> 1
, 0_1(3) -> 6
, 0_1(3) -> 11
, 0_2(20) -> 19
, 1_0(2) -> 2
, 1_1(4) -> 3
, 1_1(5) -> 3
, 1_1(6) -> 10
, 1_1(7) -> 1
, 1_1(7) -> 6
, 1_1(7) -> 11
, 1_2(4) -> 21
, 1_2(5) -> 21
, 2_0(2) -> 1
, 2_1(2) -> 11
, 2_1(10) -> 3
, 2_1(11) -> 18
, 2_2(21) -> 20
, 3_0(2) -> 2
, 3_1(5) -> 4
, 3_1(6) -> 7
, 3_1(8) -> 7
, 3_1(12) -> 6
, 4_0(2) -> 2
, 4_1(2) -> 6
, 4_1(5) -> 9
, 4_1(6) -> 5
, 4_1(7) -> 7
, 4_1(9) -> 8
, 5_0(2) -> 2
, 5_1(2) -> 12
, 5_1(4) -> 4
, 5_1(6) -> 12
, 5_1(11) -> 8
, 5_1(17) -> 1
, 5_1(17) -> 11
, 5_1(18) -> 17
, 5_2(19) -> 18}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(1(2(x1))) -> 0(0(2(1(x1))))
, 0(1(2(x1))) -> 0(2(1(3(x1))))
, 0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
, 0(3(1(x1))) -> 0(1(3(4(0(x1)))))
, 0(3(1(x1))) -> 0(1(3(4(4(x1)))))
, 0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
, 0(3(2(x1))) -> 0(2(1(3(x1))))
, 0(3(2(x1))) -> 0(2(3(4(x1))))
, 0(3(2(x1))) -> 0(0(2(4(3(x1)))))
, 0(3(2(x1))) -> 0(2(1(4(3(x1)))))
, 0(3(2(x1))) -> 0(2(4(3(3(x1)))))
, 0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
, 0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
, 0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
, 0(4(1(x1))) -> 0(1(4(4(x1))))
, 0(4(1(x1))) -> 0(2(1(4(x1))))
, 0(4(2(x1))) -> 0(2(1(4(x1))))
, 0(4(2(x1))) -> 0(2(3(4(x1))))
, 0(4(2(x1))) -> 0(2(4(3(x1))))
, 2(0(1(x1))) -> 5(0(2(1(x1))))
, 2(3(1(x1))) -> 1(3(5(2(x1))))
, 2(3(1(x1))) -> 0(2(1(3(5(x1)))))
, 2(3(1(x1))) -> 1(4(3(5(2(x1)))))
, 0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
, 0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
, 0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
, 0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
, 0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
, 0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
, 0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
, 0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
, 0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
, 0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
, 2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
, 2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
, 2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
, 2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
, 0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
, 0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
, 0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
, 0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
, 0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
, 0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
, 0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
, 0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
, 2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
, 2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
, 2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
, 2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(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(1(2(x1))) -> 0(0(2(1(x1))))
, 0(1(2(x1))) -> 0(2(1(3(x1))))
, 0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
, 0(3(1(x1))) -> 0(1(3(4(0(x1)))))
, 0(3(1(x1))) -> 0(1(3(4(4(x1)))))
, 0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
, 0(3(2(x1))) -> 0(2(1(3(x1))))
, 0(3(2(x1))) -> 0(2(3(4(x1))))
, 0(3(2(x1))) -> 0(0(2(4(3(x1)))))
, 0(3(2(x1))) -> 0(2(1(4(3(x1)))))
, 0(3(2(x1))) -> 0(2(4(3(3(x1)))))
, 0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
, 0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
, 0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
, 0(4(1(x1))) -> 0(1(4(4(x1))))
, 0(4(1(x1))) -> 0(2(1(4(x1))))
, 0(4(2(x1))) -> 0(2(1(4(x1))))
, 0(4(2(x1))) -> 0(2(3(4(x1))))
, 0(4(2(x1))) -> 0(2(4(3(x1))))
, 2(0(1(x1))) -> 5(0(2(1(x1))))
, 2(3(1(x1))) -> 1(3(5(2(x1))))
, 2(3(1(x1))) -> 0(2(1(3(5(x1)))))
, 2(3(1(x1))) -> 1(4(3(5(2(x1)))))
, 0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
, 0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
, 0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
, 0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
, 0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
, 0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
, 0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
, 0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
, 0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
, 0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
, 2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
, 2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
, 2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
, 2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
, 0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
, 0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
, 0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
, 0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
, 0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
, 0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
, 0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
, 0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
, 2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
, 2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
, 2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
, 2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(x1))))))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 0_0(2) -> 1
, 0_1(2) -> 6
, 0_1(3) -> 1
, 0_1(3) -> 6
, 0_1(3) -> 11
, 0_2(20) -> 19
, 1_0(2) -> 2
, 1_1(4) -> 3
, 1_1(5) -> 3
, 1_1(6) -> 10
, 1_1(7) -> 1
, 1_1(7) -> 6
, 1_1(7) -> 11
, 1_2(4) -> 21
, 1_2(5) -> 21
, 2_0(2) -> 1
, 2_1(2) -> 11
, 2_1(10) -> 3
, 2_1(11) -> 18
, 2_2(21) -> 20
, 3_0(2) -> 2
, 3_1(5) -> 4
, 3_1(6) -> 7
, 3_1(8) -> 7
, 3_1(12) -> 6
, 4_0(2) -> 2
, 4_1(2) -> 6
, 4_1(5) -> 9
, 4_1(6) -> 5
, 4_1(7) -> 7
, 4_1(9) -> 8
, 5_0(2) -> 2
, 5_1(2) -> 12
, 5_1(4) -> 4
, 5_1(6) -> 12
, 5_1(11) -> 8
, 5_1(17) -> 1
, 5_1(17) -> 11
, 5_1(18) -> 17
, 5_2(19) -> 18}