Tool CaT
stdout:
YES(?,O(n^1))
Problem:
c(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(x1))))))))))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {3}
transitions:
a1(22) -> 23*
a1(24) -> 25*
a1(19) -> 20*
a1(21) -> 22*
a1(16) -> 17*
b1(15) -> 16*
b1(26) -> 27*
b1(23) -> 24*
b1(18) -> 19*
c1(20) -> 21*
c1(17) -> 18*
a2(37) -> 38*
a2(39) -> 40*
a2(34) -> 35*
a2(36) -> 37*
a2(31) -> 32*
c0(2) -> 3*
c0(1) -> 3*
b2(30) -> 31*
b2(38) -> 39*
b2(33) -> 34*
a0(2) -> 1*
a0(1) -> 1*
c2(35) -> 36*
c2(32) -> 33*
b0(2) -> 2*
b0(1) -> 2*
1 -> 26*
2 -> 15*
24 -> 30*
25 -> 18,3
27 -> 16*
40 -> 21*
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(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(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(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(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(7) -> 6
, c_1(10) -> 9
, c_2(16) -> 15
, c_2(19) -> 18
, a_0(2) -> 2
, a_1(3) -> 1
, a_1(3) -> 9
, a_1(5) -> 4
, a_1(6) -> 5
, a_1(8) -> 7
, a_1(11) -> 10
, a_2(12) -> 6
, a_2(14) -> 13
, a_2(15) -> 14
, a_2(17) -> 16
, a_2(20) -> 19
, b_0(2) -> 2
, b_1(2) -> 11
, b_1(4) -> 3
, b_1(9) -> 8
, b_2(3) -> 20
, b_2(13) -> 12
, b_2(18) -> 17}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(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(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(a(b(a(x1)))) -> a(b(a(a(c(a(b(c(a(b(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(7) -> 6
, c_1(10) -> 9
, c_2(16) -> 15
, c_2(19) -> 18
, a_0(2) -> 2
, a_1(3) -> 1
, a_1(3) -> 9
, a_1(5) -> 4
, a_1(6) -> 5
, a_1(8) -> 7
, a_1(11) -> 10
, a_2(12) -> 6
, a_2(14) -> 13
, a_2(15) -> 14
, a_2(17) -> 16
, a_2(20) -> 19
, b_0(2) -> 2
, b_1(2) -> 11
, b_1(4) -> 3
, b_1(9) -> 8
, b_2(3) -> 20
, b_2(13) -> 12
, b_2(18) -> 17}