Tool CaT
stdout:
YES(?,O(n^1))
Problem:
c(b(a(a(x1)))) -> a(a(b(a(a(b(c(b(a(c(x1))))))))))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {3}
transitions:
a1(10) -> 11*
a1(5) -> 6*
a1(12) -> 13*
a1(9) -> 10*
a1(13) -> 14*
b1(11) -> 12*
b1(6) -> 7*
b1(8) -> 9*
c1(7) -> 8*
c1(4) -> 5*
c1(28) -> 29*
a2(35) -> 36*
a2(39) -> 40*
a2(36) -> 37*
a2(31) -> 32*
a2(38) -> 39*
c0(2) -> 3*
c0(1) -> 3*
b2(37) -> 38*
b2(32) -> 33*
b2(34) -> 35*
b0(2) -> 1*
b0(1) -> 1*
c2(30) -> 31*
c2(33) -> 34*
a0(2) -> 2*
a0(1) -> 2*
1 -> 28*
2 -> 4*
13 -> 30*
14 -> 29,5,3
29 -> 5*
40 -> 8*
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: {c(b(a(a(x1)))) -> a(a(b(a(a(b(c(b(a(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: {c(b(a(a(x1)))) -> a(a(b(a(a(b(c(b(a(c(x1))))))))))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ c_0(2) -> 1
, c_1(2) -> 11
, c_1(9) -> 8
, c_2(3) -> 20
, c_2(18) -> 17
, b_0(2) -> 2
, b_1(5) -> 4
, b_1(8) -> 7
, b_1(10) -> 9
, b_2(14) -> 13
, b_2(17) -> 16
, b_2(19) -> 18
, a_0(2) -> 2
, a_1(3) -> 1
, a_1(3) -> 11
, a_1(4) -> 3
, a_1(6) -> 5
, a_1(7) -> 6
, a_1(11) -> 10
, a_2(12) -> 8
, a_2(13) -> 12
, a_2(15) -> 14
, a_2(16) -> 15
, a_2(20) -> 19}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: {c(b(a(a(x1)))) -> a(a(b(a(a(b(c(b(a(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: {c(b(a(a(x1)))) -> a(a(b(a(a(b(c(b(a(c(x1))))))))))}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ c_0(2) -> 1
, c_1(2) -> 11
, c_1(9) -> 8
, c_2(3) -> 20
, c_2(18) -> 17
, b_0(2) -> 2
, b_1(5) -> 4
, b_1(8) -> 7
, b_1(10) -> 9
, b_2(14) -> 13
, b_2(17) -> 16
, b_2(19) -> 18
, a_0(2) -> 2
, a_1(3) -> 1
, a_1(3) -> 11
, a_1(4) -> 3
, a_1(6) -> 5
, a_1(7) -> 6
, a_1(11) -> 10
, a_2(12) -> 8
, a_2(13) -> 12
, a_2(15) -> 14
, a_2(16) -> 15
, a_2(20) -> 19}