Tool CaT
stdout:
YES(?,O(n^1))
Problem:
a(a(x1)) -> b(b(x1))
c(c(b(x1))) -> d(c(a(x1)))
a(x1) -> d(c(c(x1)))
c(d(x1)) -> b(c(x1))
Proof:
Bounds Processor:
bound: 3
enrichment: match
automaton:
final states: {4,3}
transitions:
d3(70) -> 71*
b1(17) -> 18*
b1(23) -> 24*
c3(85) -> 86*
c3(77) -> 78*
c3(69) -> 70*
c3(91) -> 92*
c3(68) -> 69*
c1(15) -> 16*
c1(5) -> 6*
c1(26) -> 27*
c1(6) -> 7*
b3(92) -> 93*
b3(86) -> 87*
d1(27) -> 28*
d1(7) -> 8*
a1(35) -> 36*
a1(25) -> 26*
d2(57) -> 58*
d2(39) -> 40*
a0(2) -> 3*
a0(1) -> 3*
c2(65) -> 66*
c2(47) -> 48*
c2(37) -> 38*
c2(49) -> 50*
c2(56) -> 57*
c2(38) -> 39*
b0(2) -> 1*
b0(1) -> 1*
b2(50) -> 51*
b2(66) -> 67*
c0(2) -> 4*
c0(1) -> 4*
a2(55) -> 56*
a2(59) -> 60*
d0(2) -> 2*
d0(1) -> 2*
1 -> 35,5
2 -> 25,15
6 -> 23*
8 -> 3*
16 -> 17,6
17 -> 55*
18 -> 38,16,17,6,23,4
23 -> 59*
24 -> 38,16,17,6,23,4
25 -> 37*
27 -> 65*
28 -> 69,39,7
35 -> 47*
36 -> 26*
39 -> 49*
40 -> 36,26
48 -> 38*
51 -> 27*
55 -> 77*
57 -> 91*
58 -> 70,50
59 -> 68*
60 -> 56*
67 -> 70,50
70 -> 85*
71 -> 60,56
78 -> 69*
87 -> 57*
93 -> 86*
problem:
QedTool IRC1
stdout:
YES(?,O(n^1))
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:
{ a(a(x1)) -> b(b(x1))
, c(c(b(x1))) -> d(c(a(x1)))
, a(x1) -> d(c(c(x1)))
, c(d(x1)) -> b(c(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:
{ a(a(x1)) -> b(b(x1))
, c(c(b(x1))) -> d(c(a(x1)))
, a(x1) -> d(c(c(x1)))
, c(d(x1)) -> b(c(x1))}
Proof Output:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, a_1(2) -> 6
, a_2(4) -> 11
, b_0(2) -> 2
, b_1(4) -> 1
, b_1(4) -> 4
, b_1(4) -> 8
, b_2(9) -> 5
, b_2(14) -> 9
, b_2(14) -> 12
, b_3(15) -> 10
, b_3(16) -> 15
, c_0(2) -> 1
, c_1(2) -> 4
, c_1(4) -> 3
, c_1(6) -> 5
, c_2(2) -> 8
, c_2(5) -> 14
, c_2(7) -> 9
, c_2(8) -> 7
, c_2(11) -> 10
, c_3(4) -> 13
, c_3(10) -> 16
, c_3(12) -> 15
, c_3(13) -> 12
, d_0(2) -> 2
, d_1(3) -> 1
, d_1(5) -> 3
, d_1(5) -> 7
, d_1(5) -> 13
, d_2(7) -> 6
, d_2(10) -> 9
, d_2(10) -> 12
, d_3(12) -> 11}Tool RC1
stdout:
YES(?,O(n^1))
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:
{ a(a(x1)) -> b(b(x1))
, c(c(b(x1))) -> d(c(a(x1)))
, a(x1) -> d(c(c(x1)))
, c(d(x1)) -> b(c(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:
{ a(a(x1)) -> b(b(x1))
, c(c(b(x1))) -> d(c(a(x1)))
, a(x1) -> d(c(c(x1)))
, c(d(x1)) -> b(c(x1))}
Proof Output:
The problem is match-bounded by 3.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, a_1(2) -> 6
, a_2(4) -> 11
, b_0(2) -> 2
, b_1(4) -> 1
, b_1(4) -> 4
, b_1(4) -> 8
, b_2(9) -> 5
, b_2(14) -> 9
, b_2(14) -> 12
, b_3(15) -> 10
, b_3(16) -> 15
, c_0(2) -> 1
, c_1(2) -> 4
, c_1(4) -> 3
, c_1(6) -> 5
, c_2(2) -> 8
, c_2(5) -> 14
, c_2(7) -> 9
, c_2(8) -> 7
, c_2(11) -> 10
, c_3(4) -> 13
, c_3(10) -> 16
, c_3(12) -> 15
, c_3(13) -> 12
, d_0(2) -> 2
, d_1(3) -> 1
, d_1(5) -> 3
, d_1(5) -> 7
, d_1(5) -> 13
, d_2(7) -> 6
, d_2(10) -> 9
, d_2(10) -> 12
, d_3(12) -> 11}