Tool CaT
stdout:
YES(?,O(n^1))
Problem:
0(1(2(x1))) -> 0(2(1(0(x1))))
0(1(2(x1))) -> 1(0(2(3(x1))))
0(1(2(x1))) -> 0(2(4(1(5(x1)))))
0(1(2(x1))) -> 0(3(2(1(0(x1)))))
0(1(2(x1))) -> 1(0(3(2(3(x1)))))
0(1(2(x1))) -> 0(1(3(4(2(3(x1))))))
0(5(2(x1))) -> 0(2(4(5(3(x1)))))
0(5(2(x1))) -> 5(4(2(3(0(4(x1))))))
2(0(1(x1))) -> 3(0(2(1(x1))))
2(0(1(x1))) -> 0(2(1(1(4(x1)))))
2(0(1(x1))) -> 0(3(2(4(1(x1)))))
2(0(1(x1))) -> 3(0(2(1(4(x1)))))
2(0(1(x1))) -> 0(2(2(3(4(1(x1))))))
2(0(1(x1))) -> 0(3(2(3(1(1(x1))))))
2(0(1(x1))) -> 4(0(4(2(1(4(x1))))))
2(5(1(x1))) -> 0(2(1(5(1(x1)))))
2(5(1(x1))) -> 1(4(5(4(2(x1)))))
2(5(1(x1))) -> 5(0(2(1(4(x1)))))
2(5(1(x1))) -> 5(2(1(4(1(x1)))))
2(5(1(x1))) -> 1(5(0(2(4(1(x1))))))
2(5(1(x1))) -> 5(2(1(1(1(1(x1))))))
0(1(2(1(x1)))) -> 3(1(4(0(2(1(x1))))))
0(1(3(1(x1)))) -> 5(0(3(1(1(x1)))))
0(1(3(1(x1)))) -> 1(0(3(4(2(1(x1))))))
0(1(5(1(x1)))) -> 5(0(3(1(1(x1)))))
0(2(1(2(x1)))) -> 0(2(2(1(5(x1)))))
0(2(5(1(x1)))) -> 1(1(5(0(2(1(x1))))))
0(5(3(1(x1)))) -> 0(1(4(4(3(5(x1))))))
0(5(5(2(x1)))) -> 5(4(2(3(5(0(x1))))))
2(0(1(2(x1)))) -> 0(2(3(2(1(1(x1))))))
2(0(1(2(x1)))) -> 4(0(2(1(1(2(x1))))))
2(0(4(1(x1)))) -> 3(0(2(4(1(x1)))))
2(0(5(1(x1)))) -> 5(4(2(1(0(x1)))))
2(2(5(1(x1)))) -> 3(2(2(4(5(1(x1))))))
2(4(0(1(x1)))) -> 1(0(2(4(4(x1)))))
2(4(0(1(x1)))) -> 3(0(0(2(4(1(x1))))))
2(4(0(1(x1)))) -> 5(4(0(2(1(1(x1))))))
2(5(2(1(x1)))) -> 1(5(2(2(3(1(x1))))))
2(5(4(1(x1)))) -> 4(5(2(1(4(4(x1))))))
2(5(5(1(x1)))) -> 1(5(4(2(4(5(x1))))))
2(5(5(2(x1)))) -> 5(5(2(3(2(x1)))))
0(1(3(0(1(x1))))) -> 0(3(1(0(1(1(x1))))))
0(2(4(3(1(x1))))) -> 1(3(4(2(3(0(x1))))))
0(2(4(3(1(x1))))) -> 4(0(3(2(1(0(x1))))))
0(2(5(3(1(x1))))) -> 5(0(2(3(5(1(x1))))))
2(0(5(4(1(x1))))) -> 0(4(5(3(2(1(x1))))))
2(2(0(1(2(x1))))) -> 2(4(0(2(2(1(x1))))))
2(4(0(5(1(x1))))) -> 1(4(5(0(4(2(x1))))))
2(4(2(3(1(x1))))) -> 4(2(2(3(3(1(x1))))))
2(5(2(0(1(x1))))) -> 0(2(4(1(5(2(x1))))))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {6,5}
transitions:
11(25) -> 26*
11(15) -> 16*
11(62) -> 63*
11(27) -> 28*
11(119) -> 120*
11(99) -> 100*
11(84) -> 85*
11(19) -> 20*
11(41) -> 42*
11(148) -> 149*
11(98) -> 99*
11(13) -> 14*
11(125) -> 126*
51(65) -> 66*
51(137) -> 138*
51(139) -> 140*
51(89) -> 90*
51(39) -> 40*
51(14) -> 15*
51(121) -> 122*
51(103) -> 104*
51(150) -> 151*
51(145) -> 146*
41(75) -> 76*
41(40) -> 41*
41(147) -> 148*
41(67) -> 68*
41(124) -> 125*
41(151) -> 152*
41(116) -> 117*
41(61) -> 62*
41(163) -> 164*
41(123) -> 124*
41(83) -> 84*
41(73) -> 74*
41(38) -> 39*
41(165) -> 166*
21(87) -> 88*
21(37) -> 38*
21(164) -> 165*
21(149) -> 150*
21(49) -> 50*
21(51) -> 52*
21(16) -> 17*
21(63) -> 64*
21(43) -> 44*
21(115) -> 116*
21(85) -> 86*
01(102) -> 103*
01(17) -> 18*
01(64) -> 65*
01(126) -> 127*
01(118) -> 119*
01(88) -> 89*
31(122) -> 123*
31(117) -> 118*
31(101) -> 102*
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 -> 139,73,49,25
2 -> 121,61,37,13
3 -> 145,75,51,27
4 -> 137,67,43,19
14 -> 115,98,83
18 -> 44,6
20 -> 14*
26 -> 14*
28 -> 14*
42 -> 44,6
44 -> 38*
50 -> 38*
52 -> 38*
62 -> 147*
66 -> 44,6
68 -> 62*
74 -> 62*
76 -> 62*
84 -> 87*
86 -> 65*
90 -> 41*
99 -> 101*
100 -> 84*
104 -> 5*
120 -> 5*
122 -> 163*
127 -> 5*
138 -> 122*
140 -> 122*
146 -> 122*
152 -> 44,38,6
166 -> 89*
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(2(1(0(x1))))
, 0(1(2(x1))) -> 1(0(2(3(x1))))
, 0(1(2(x1))) -> 0(2(4(1(5(x1)))))
, 0(1(2(x1))) -> 0(3(2(1(0(x1)))))
, 0(1(2(x1))) -> 1(0(3(2(3(x1)))))
, 0(1(2(x1))) -> 0(1(3(4(2(3(x1))))))
, 0(5(2(x1))) -> 0(2(4(5(3(x1)))))
, 0(5(2(x1))) -> 5(4(2(3(0(4(x1))))))
, 2(0(1(x1))) -> 3(0(2(1(x1))))
, 2(0(1(x1))) -> 0(2(1(1(4(x1)))))
, 2(0(1(x1))) -> 0(3(2(4(1(x1)))))
, 2(0(1(x1))) -> 3(0(2(1(4(x1)))))
, 2(0(1(x1))) -> 0(2(2(3(4(1(x1))))))
, 2(0(1(x1))) -> 0(3(2(3(1(1(x1))))))
, 2(0(1(x1))) -> 4(0(4(2(1(4(x1))))))
, 2(5(1(x1))) -> 0(2(1(5(1(x1)))))
, 2(5(1(x1))) -> 1(4(5(4(2(x1)))))
, 2(5(1(x1))) -> 5(0(2(1(4(x1)))))
, 2(5(1(x1))) -> 5(2(1(4(1(x1)))))
, 2(5(1(x1))) -> 1(5(0(2(4(1(x1))))))
, 2(5(1(x1))) -> 5(2(1(1(1(1(x1))))))
, 0(1(2(1(x1)))) -> 3(1(4(0(2(1(x1))))))
, 0(1(3(1(x1)))) -> 5(0(3(1(1(x1)))))
, 0(1(3(1(x1)))) -> 1(0(3(4(2(1(x1))))))
, 0(1(5(1(x1)))) -> 5(0(3(1(1(x1)))))
, 0(2(1(2(x1)))) -> 0(2(2(1(5(x1)))))
, 0(2(5(1(x1)))) -> 1(1(5(0(2(1(x1))))))
, 0(5(3(1(x1)))) -> 0(1(4(4(3(5(x1))))))
, 0(5(5(2(x1)))) -> 5(4(2(3(5(0(x1))))))
, 2(0(1(2(x1)))) -> 0(2(3(2(1(1(x1))))))
, 2(0(1(2(x1)))) -> 4(0(2(1(1(2(x1))))))
, 2(0(4(1(x1)))) -> 3(0(2(4(1(x1)))))
, 2(0(5(1(x1)))) -> 5(4(2(1(0(x1)))))
, 2(2(5(1(x1)))) -> 3(2(2(4(5(1(x1))))))
, 2(4(0(1(x1)))) -> 1(0(2(4(4(x1)))))
, 2(4(0(1(x1)))) -> 3(0(0(2(4(1(x1))))))
, 2(4(0(1(x1)))) -> 5(4(0(2(1(1(x1))))))
, 2(5(2(1(x1)))) -> 1(5(2(2(3(1(x1))))))
, 2(5(4(1(x1)))) -> 4(5(2(1(4(4(x1))))))
, 2(5(5(1(x1)))) -> 1(5(4(2(4(5(x1))))))
, 2(5(5(2(x1)))) -> 5(5(2(3(2(x1)))))
, 0(1(3(0(1(x1))))) -> 0(3(1(0(1(1(x1))))))
, 0(2(4(3(1(x1))))) -> 1(3(4(2(3(0(x1))))))
, 0(2(4(3(1(x1))))) -> 4(0(3(2(1(0(x1))))))
, 0(2(5(3(1(x1))))) -> 5(0(2(3(5(1(x1))))))
, 2(0(5(4(1(x1))))) -> 0(4(5(3(2(1(x1))))))
, 2(2(0(1(2(x1))))) -> 2(4(0(2(2(1(x1))))))
, 2(4(0(5(1(x1))))) -> 1(4(5(0(4(2(x1))))))
, 2(4(2(3(1(x1))))) -> 4(2(2(3(3(1(x1))))))
, 2(5(2(0(1(x1))))) -> 0(2(4(1(5(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(1(2(x1))) -> 0(2(1(0(x1))))
, 0(1(2(x1))) -> 1(0(2(3(x1))))
, 0(1(2(x1))) -> 0(2(4(1(5(x1)))))
, 0(1(2(x1))) -> 0(3(2(1(0(x1)))))
, 0(1(2(x1))) -> 1(0(3(2(3(x1)))))
, 0(1(2(x1))) -> 0(1(3(4(2(3(x1))))))
, 0(5(2(x1))) -> 0(2(4(5(3(x1)))))
, 0(5(2(x1))) -> 5(4(2(3(0(4(x1))))))
, 2(0(1(x1))) -> 3(0(2(1(x1))))
, 2(0(1(x1))) -> 0(2(1(1(4(x1)))))
, 2(0(1(x1))) -> 0(3(2(4(1(x1)))))
, 2(0(1(x1))) -> 3(0(2(1(4(x1)))))
, 2(0(1(x1))) -> 0(2(2(3(4(1(x1))))))
, 2(0(1(x1))) -> 0(3(2(3(1(1(x1))))))
, 2(0(1(x1))) -> 4(0(4(2(1(4(x1))))))
, 2(5(1(x1))) -> 0(2(1(5(1(x1)))))
, 2(5(1(x1))) -> 1(4(5(4(2(x1)))))
, 2(5(1(x1))) -> 5(0(2(1(4(x1)))))
, 2(5(1(x1))) -> 5(2(1(4(1(x1)))))
, 2(5(1(x1))) -> 1(5(0(2(4(1(x1))))))
, 2(5(1(x1))) -> 5(2(1(1(1(1(x1))))))
, 0(1(2(1(x1)))) -> 3(1(4(0(2(1(x1))))))
, 0(1(3(1(x1)))) -> 5(0(3(1(1(x1)))))
, 0(1(3(1(x1)))) -> 1(0(3(4(2(1(x1))))))
, 0(1(5(1(x1)))) -> 5(0(3(1(1(x1)))))
, 0(2(1(2(x1)))) -> 0(2(2(1(5(x1)))))
, 0(2(5(1(x1)))) -> 1(1(5(0(2(1(x1))))))
, 0(5(3(1(x1)))) -> 0(1(4(4(3(5(x1))))))
, 0(5(5(2(x1)))) -> 5(4(2(3(5(0(x1))))))
, 2(0(1(2(x1)))) -> 0(2(3(2(1(1(x1))))))
, 2(0(1(2(x1)))) -> 4(0(2(1(1(2(x1))))))
, 2(0(4(1(x1)))) -> 3(0(2(4(1(x1)))))
, 2(0(5(1(x1)))) -> 5(4(2(1(0(x1)))))
, 2(2(5(1(x1)))) -> 3(2(2(4(5(1(x1))))))
, 2(4(0(1(x1)))) -> 1(0(2(4(4(x1)))))
, 2(4(0(1(x1)))) -> 3(0(0(2(4(1(x1))))))
, 2(4(0(1(x1)))) -> 5(4(0(2(1(1(x1))))))
, 2(5(2(1(x1)))) -> 1(5(2(2(3(1(x1))))))
, 2(5(4(1(x1)))) -> 4(5(2(1(4(4(x1))))))
, 2(5(5(1(x1)))) -> 1(5(4(2(4(5(x1))))))
, 2(5(5(2(x1)))) -> 5(5(2(3(2(x1)))))
, 0(1(3(0(1(x1))))) -> 0(3(1(0(1(1(x1))))))
, 0(2(4(3(1(x1))))) -> 1(3(4(2(3(0(x1))))))
, 0(2(4(3(1(x1))))) -> 4(0(3(2(1(0(x1))))))
, 0(2(5(3(1(x1))))) -> 5(0(2(3(5(1(x1))))))
, 2(0(5(4(1(x1))))) -> 0(4(5(3(2(1(x1))))))
, 2(2(0(1(2(x1))))) -> 2(4(0(2(2(1(x1))))))
, 2(4(0(5(1(x1))))) -> 1(4(5(0(4(2(x1))))))
, 2(4(2(3(1(x1))))) -> 4(2(2(3(3(1(x1))))))
, 2(5(2(0(1(x1))))) -> 0(2(4(1(5(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(3) -> 1
, 0_1(3) -> 10
, 0_1(12) -> 11
, 0_1(18) -> 17
, 0_1(20) -> 7
, 1_0(2) -> 2
, 1_1(2) -> 6
, 1_1(5) -> 4
, 1_1(6) -> 19
, 1_1(7) -> 1
, 1_1(7) -> 10
, 1_1(14) -> 13
, 1_1(16) -> 15
, 1_1(19) -> 16
, 1_1(23) -> 3
, 1_1(30) -> 29
, 2_0(2) -> 1
, 2_1(2) -> 10
, 2_1(4) -> 3
, 2_1(6) -> 22
, 2_1(13) -> 12
, 2_1(15) -> 11
, 2_1(16) -> 18
, 2_1(29) -> 28
, 2_1(32) -> 31
, 3_0(2) -> 2
, 3_1(19) -> 12
, 3_1(21) -> 20
, 3_1(26) -> 25
, 4_0(2) -> 2
, 4_1(2) -> 14
, 4_1(6) -> 16
, 4_1(8) -> 7
, 4_1(10) -> 9
, 4_1(14) -> 30
, 4_1(22) -> 21
, 4_1(24) -> 23
, 4_1(25) -> 24
, 4_1(26) -> 32
, 4_1(27) -> 1
, 4_1(27) -> 10
, 4_1(31) -> 17
, 5_0(2) -> 2
, 5_1(2) -> 26
, 5_1(6) -> 5
, 5_1(9) -> 8
, 5_1(11) -> 1
, 5_1(11) -> 10
, 5_1(17) -> 7
, 5_1(28) -> 27}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(2(1(0(x1))))
, 0(1(2(x1))) -> 1(0(2(3(x1))))
, 0(1(2(x1))) -> 0(2(4(1(5(x1)))))
, 0(1(2(x1))) -> 0(3(2(1(0(x1)))))
, 0(1(2(x1))) -> 1(0(3(2(3(x1)))))
, 0(1(2(x1))) -> 0(1(3(4(2(3(x1))))))
, 0(5(2(x1))) -> 0(2(4(5(3(x1)))))
, 0(5(2(x1))) -> 5(4(2(3(0(4(x1))))))
, 2(0(1(x1))) -> 3(0(2(1(x1))))
, 2(0(1(x1))) -> 0(2(1(1(4(x1)))))
, 2(0(1(x1))) -> 0(3(2(4(1(x1)))))
, 2(0(1(x1))) -> 3(0(2(1(4(x1)))))
, 2(0(1(x1))) -> 0(2(2(3(4(1(x1))))))
, 2(0(1(x1))) -> 0(3(2(3(1(1(x1))))))
, 2(0(1(x1))) -> 4(0(4(2(1(4(x1))))))
, 2(5(1(x1))) -> 0(2(1(5(1(x1)))))
, 2(5(1(x1))) -> 1(4(5(4(2(x1)))))
, 2(5(1(x1))) -> 5(0(2(1(4(x1)))))
, 2(5(1(x1))) -> 5(2(1(4(1(x1)))))
, 2(5(1(x1))) -> 1(5(0(2(4(1(x1))))))
, 2(5(1(x1))) -> 5(2(1(1(1(1(x1))))))
, 0(1(2(1(x1)))) -> 3(1(4(0(2(1(x1))))))
, 0(1(3(1(x1)))) -> 5(0(3(1(1(x1)))))
, 0(1(3(1(x1)))) -> 1(0(3(4(2(1(x1))))))
, 0(1(5(1(x1)))) -> 5(0(3(1(1(x1)))))
, 0(2(1(2(x1)))) -> 0(2(2(1(5(x1)))))
, 0(2(5(1(x1)))) -> 1(1(5(0(2(1(x1))))))
, 0(5(3(1(x1)))) -> 0(1(4(4(3(5(x1))))))
, 0(5(5(2(x1)))) -> 5(4(2(3(5(0(x1))))))
, 2(0(1(2(x1)))) -> 0(2(3(2(1(1(x1))))))
, 2(0(1(2(x1)))) -> 4(0(2(1(1(2(x1))))))
, 2(0(4(1(x1)))) -> 3(0(2(4(1(x1)))))
, 2(0(5(1(x1)))) -> 5(4(2(1(0(x1)))))
, 2(2(5(1(x1)))) -> 3(2(2(4(5(1(x1))))))
, 2(4(0(1(x1)))) -> 1(0(2(4(4(x1)))))
, 2(4(0(1(x1)))) -> 3(0(0(2(4(1(x1))))))
, 2(4(0(1(x1)))) -> 5(4(0(2(1(1(x1))))))
, 2(5(2(1(x1)))) -> 1(5(2(2(3(1(x1))))))
, 2(5(4(1(x1)))) -> 4(5(2(1(4(4(x1))))))
, 2(5(5(1(x1)))) -> 1(5(4(2(4(5(x1))))))
, 2(5(5(2(x1)))) -> 5(5(2(3(2(x1)))))
, 0(1(3(0(1(x1))))) -> 0(3(1(0(1(1(x1))))))
, 0(2(4(3(1(x1))))) -> 1(3(4(2(3(0(x1))))))
, 0(2(4(3(1(x1))))) -> 4(0(3(2(1(0(x1))))))
, 0(2(5(3(1(x1))))) -> 5(0(2(3(5(1(x1))))))
, 2(0(5(4(1(x1))))) -> 0(4(5(3(2(1(x1))))))
, 2(2(0(1(2(x1))))) -> 2(4(0(2(2(1(x1))))))
, 2(4(0(5(1(x1))))) -> 1(4(5(0(4(2(x1))))))
, 2(4(2(3(1(x1))))) -> 4(2(2(3(3(1(x1))))))
, 2(5(2(0(1(x1))))) -> 0(2(4(1(5(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(1(2(x1))) -> 0(2(1(0(x1))))
, 0(1(2(x1))) -> 1(0(2(3(x1))))
, 0(1(2(x1))) -> 0(2(4(1(5(x1)))))
, 0(1(2(x1))) -> 0(3(2(1(0(x1)))))
, 0(1(2(x1))) -> 1(0(3(2(3(x1)))))
, 0(1(2(x1))) -> 0(1(3(4(2(3(x1))))))
, 0(5(2(x1))) -> 0(2(4(5(3(x1)))))
, 0(5(2(x1))) -> 5(4(2(3(0(4(x1))))))
, 2(0(1(x1))) -> 3(0(2(1(x1))))
, 2(0(1(x1))) -> 0(2(1(1(4(x1)))))
, 2(0(1(x1))) -> 0(3(2(4(1(x1)))))
, 2(0(1(x1))) -> 3(0(2(1(4(x1)))))
, 2(0(1(x1))) -> 0(2(2(3(4(1(x1))))))
, 2(0(1(x1))) -> 0(3(2(3(1(1(x1))))))
, 2(0(1(x1))) -> 4(0(4(2(1(4(x1))))))
, 2(5(1(x1))) -> 0(2(1(5(1(x1)))))
, 2(5(1(x1))) -> 1(4(5(4(2(x1)))))
, 2(5(1(x1))) -> 5(0(2(1(4(x1)))))
, 2(5(1(x1))) -> 5(2(1(4(1(x1)))))
, 2(5(1(x1))) -> 1(5(0(2(4(1(x1))))))
, 2(5(1(x1))) -> 5(2(1(1(1(1(x1))))))
, 0(1(2(1(x1)))) -> 3(1(4(0(2(1(x1))))))
, 0(1(3(1(x1)))) -> 5(0(3(1(1(x1)))))
, 0(1(3(1(x1)))) -> 1(0(3(4(2(1(x1))))))
, 0(1(5(1(x1)))) -> 5(0(3(1(1(x1)))))
, 0(2(1(2(x1)))) -> 0(2(2(1(5(x1)))))
, 0(2(5(1(x1)))) -> 1(1(5(0(2(1(x1))))))
, 0(5(3(1(x1)))) -> 0(1(4(4(3(5(x1))))))
, 0(5(5(2(x1)))) -> 5(4(2(3(5(0(x1))))))
, 2(0(1(2(x1)))) -> 0(2(3(2(1(1(x1))))))
, 2(0(1(2(x1)))) -> 4(0(2(1(1(2(x1))))))
, 2(0(4(1(x1)))) -> 3(0(2(4(1(x1)))))
, 2(0(5(1(x1)))) -> 5(4(2(1(0(x1)))))
, 2(2(5(1(x1)))) -> 3(2(2(4(5(1(x1))))))
, 2(4(0(1(x1)))) -> 1(0(2(4(4(x1)))))
, 2(4(0(1(x1)))) -> 3(0(0(2(4(1(x1))))))
, 2(4(0(1(x1)))) -> 5(4(0(2(1(1(x1))))))
, 2(5(2(1(x1)))) -> 1(5(2(2(3(1(x1))))))
, 2(5(4(1(x1)))) -> 4(5(2(1(4(4(x1))))))
, 2(5(5(1(x1)))) -> 1(5(4(2(4(5(x1))))))
, 2(5(5(2(x1)))) -> 5(5(2(3(2(x1)))))
, 0(1(3(0(1(x1))))) -> 0(3(1(0(1(1(x1))))))
, 0(2(4(3(1(x1))))) -> 1(3(4(2(3(0(x1))))))
, 0(2(4(3(1(x1))))) -> 4(0(3(2(1(0(x1))))))
, 0(2(5(3(1(x1))))) -> 5(0(2(3(5(1(x1))))))
, 2(0(5(4(1(x1))))) -> 0(4(5(3(2(1(x1))))))
, 2(2(0(1(2(x1))))) -> 2(4(0(2(2(1(x1))))))
, 2(4(0(5(1(x1))))) -> 1(4(5(0(4(2(x1))))))
, 2(4(2(3(1(x1))))) -> 4(2(2(3(3(1(x1))))))
, 2(5(2(0(1(x1))))) -> 0(2(4(1(5(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(3) -> 1
, 0_1(3) -> 10
, 0_1(12) -> 11
, 0_1(18) -> 17
, 0_1(20) -> 7
, 1_0(2) -> 2
, 1_1(2) -> 6
, 1_1(5) -> 4
, 1_1(6) -> 19
, 1_1(7) -> 1
, 1_1(7) -> 10
, 1_1(14) -> 13
, 1_1(16) -> 15
, 1_1(19) -> 16
, 1_1(23) -> 3
, 1_1(30) -> 29
, 2_0(2) -> 1
, 2_1(2) -> 10
, 2_1(4) -> 3
, 2_1(6) -> 22
, 2_1(13) -> 12
, 2_1(15) -> 11
, 2_1(16) -> 18
, 2_1(29) -> 28
, 2_1(32) -> 31
, 3_0(2) -> 2
, 3_1(19) -> 12
, 3_1(21) -> 20
, 3_1(26) -> 25
, 4_0(2) -> 2
, 4_1(2) -> 14
, 4_1(6) -> 16
, 4_1(8) -> 7
, 4_1(10) -> 9
, 4_1(14) -> 30
, 4_1(22) -> 21
, 4_1(24) -> 23
, 4_1(25) -> 24
, 4_1(26) -> 32
, 4_1(27) -> 1
, 4_1(27) -> 10
, 4_1(31) -> 17
, 5_0(2) -> 2
, 5_1(2) -> 26
, 5_1(6) -> 5
, 5_1(9) -> 8
, 5_1(11) -> 1
, 5_1(11) -> 10
, 5_1(17) -> 7
, 5_1(28) -> 27}