Tool CaT
stdout:
YES(?,O(n^1))
Problem:
0(1(2(3(4(5(1(x1))))))) -> 1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))
0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))))))))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {6}
transitions:
11(45) -> 46*
11(40) -> 41*
11(37) -> 38*
11(39) -> 40*
11(31) -> 32*
21(30) -> 31*
21(44) -> 45*
21(36) -> 37*
31(35) -> 36*
31(29) -> 30*
31(43) -> 44*
41(42) -> 43*
41(34) -> 35*
41(28) -> 29*
51(55) -> 56*
51(47) -> 48*
51(27) -> 28*
51(61) -> 62*
51(41) -> 42*
51(63) -> 64*
51(53) -> 54*
51(33) -> 34*
01(32) -> 33*
01(38) -> 39*
12(85) -> 86*
12(80) -> 81*
12(77) -> 78*
12(79) -> 80*
12(71) -> 72*
00(5) -> 6*
00(2) -> 6*
00(4) -> 6*
00(1) -> 6*
00(3) -> 6*
22(70) -> 71*
22(84) -> 85*
22(76) -> 77*
10(5) -> 1*
10(2) -> 1*
10(4) -> 1*
10(1) -> 1*
10(3) -> 1*
32(75) -> 76*
32(69) -> 70*
32(83) -> 84*
20(5) -> 2*
20(2) -> 2*
20(4) -> 2*
20(1) -> 2*
20(3) -> 2*
42(82) -> 83*
42(74) -> 75*
42(68) -> 69*
30(5) -> 3*
30(2) -> 3*
30(4) -> 3*
30(1) -> 3*
30(3) -> 3*
52(67) -> 68*
52(109) -> 110*
52(111) -> 112*
52(81) -> 82*
52(73) -> 74*
40(5) -> 4*
40(2) -> 4*
40(4) -> 4*
40(1) -> 4*
40(3) -> 4*
02(72) -> 73*
02(78) -> 79*
50(5) -> 5*
50(2) -> 5*
50(4) -> 5*
50(1) -> 5*
50(3) -> 5*
1 -> 55*
2 -> 47*
3 -> 61*
4 -> 53*
5 -> 27*
39 -> 63*
45 -> 67*
46 -> 33,6
48 -> 28*
54 -> 28*
56 -> 28*
62 -> 28*
64 -> 34*
79 -> 109*
85 -> 111*
86 -> 39*
110 -> 74*
112 -> 68*
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(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(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(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(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(10) -> 9
, 0_1(16) -> 15
, 0_2(28) -> 27
, 0_2(34) -> 33
, 1_0(2) -> 2
, 1_1(3) -> 1
, 1_1(3) -> 15
, 1_1(8) -> 7
, 1_1(9) -> 8
, 1_1(11) -> 10
, 1_1(17) -> 16
, 1_2(21) -> 9
, 1_2(26) -> 25
, 1_2(27) -> 26
, 1_2(29) -> 28
, 1_2(35) -> 34
, 2_0(2) -> 2
, 2_1(4) -> 3
, 2_1(12) -> 11
, 2_1(18) -> 17
, 2_2(22) -> 21
, 2_2(30) -> 29
, 2_2(36) -> 35
, 3_0(2) -> 2
, 3_1(5) -> 4
, 3_1(13) -> 12
, 3_1(19) -> 18
, 3_2(23) -> 22
, 3_2(31) -> 30
, 3_2(37) -> 36
, 4_0(2) -> 2
, 4_1(6) -> 5
, 4_1(14) -> 13
, 4_1(20) -> 19
, 4_2(24) -> 23
, 4_2(32) -> 31
, 4_2(38) -> 37
, 5_0(2) -> 2
, 5_1(2) -> 20
, 5_1(7) -> 6
, 5_1(9) -> 14
, 5_1(15) -> 14
, 5_2(3) -> 38
, 5_2(21) -> 32
, 5_2(25) -> 24
, 5_2(27) -> 32
, 5_2(33) -> 32}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(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(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(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(x1)))))))))))))))))))
, 0(1(2(3(4(5(1(x1))))))) ->
1(2(3(4(5(1(1(0(1(2(3(4(5(0(1(2(3(4(5(0(1(2(3(4(5(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(10) -> 9
, 0_1(16) -> 15
, 0_2(28) -> 27
, 0_2(34) -> 33
, 1_0(2) -> 2
, 1_1(3) -> 1
, 1_1(3) -> 15
, 1_1(8) -> 7
, 1_1(9) -> 8
, 1_1(11) -> 10
, 1_1(17) -> 16
, 1_2(21) -> 9
, 1_2(26) -> 25
, 1_2(27) -> 26
, 1_2(29) -> 28
, 1_2(35) -> 34
, 2_0(2) -> 2
, 2_1(4) -> 3
, 2_1(12) -> 11
, 2_1(18) -> 17
, 2_2(22) -> 21
, 2_2(30) -> 29
, 2_2(36) -> 35
, 3_0(2) -> 2
, 3_1(5) -> 4
, 3_1(13) -> 12
, 3_1(19) -> 18
, 3_2(23) -> 22
, 3_2(31) -> 30
, 3_2(37) -> 36
, 4_0(2) -> 2
, 4_1(6) -> 5
, 4_1(14) -> 13
, 4_1(20) -> 19
, 4_2(24) -> 23
, 4_2(32) -> 31
, 4_2(38) -> 37
, 5_0(2) -> 2
, 5_1(2) -> 20
, 5_1(7) -> 6
, 5_1(9) -> 14
, 5_1(15) -> 14
, 5_2(3) -> 38
, 5_2(21) -> 32
, 5_2(25) -> 24
, 5_2(27) -> 32
, 5_2(33) -> 32}