Tool CaT
stdout:
YES(?,O(n^1))
Problem:
c(a(b(a(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(x1)))))))))))))
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {3}
transitions:
a1(30) -> 31*
a1(25) -> 26*
a1(32) -> 33*
a1(21) -> 22*
a1(28) -> 29*
a1(18) -> 19*
b1(20) -> 21*
b1(27) -> 28*
b1(29) -> 30*
b1(24) -> 25*
b1(26) -> 27*
b1(23) -> 24*
c1(22) -> 23*
c1(19) -> 20*
a2(39) -> 40*
a2(46) -> 47*
a2(36) -> 37*
a2(48) -> 49*
a2(43) -> 44*
c0(2) -> 3*
c0(1) -> 3*
b2(45) -> 46*
b2(47) -> 48*
b2(42) -> 43*
b2(44) -> 45*
b2(41) -> 42*
b2(38) -> 39*
a0(2) -> 1*
a0(1) -> 1*
c2(40) -> 41*
c2(37) -> 38*
b0(2) -> 2*
b0(1) -> 2*
1 -> 32*
2 -> 18*
29 -> 36*
31 -> 20,3
33 -> 19*
49 -> 23*
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(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(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(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(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(11) -> 10
, c_1(14) -> 13
, c_2(23) -> 22
, c_2(26) -> 25
, a_0(2) -> 2
, a_1(2) -> 14
, a_1(3) -> 1
, a_1(3) -> 13
, a_1(5) -> 4
, a_1(8) -> 7
, a_1(12) -> 11
, a_2(4) -> 26
, a_2(15) -> 10
, a_2(17) -> 16
, a_2(20) -> 19
, a_2(24) -> 23
, b_0(2) -> 2
, b_1(4) -> 3
, b_1(6) -> 5
, b_1(7) -> 6
, b_1(9) -> 8
, b_1(10) -> 9
, b_1(13) -> 12
, b_2(16) -> 15
, b_2(18) -> 17
, b_2(19) -> 18
, b_2(21) -> 20
, b_2(22) -> 21
, b_2(25) -> 24}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(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(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(b(x1))))) -> a(b(a(b(b(a(b(b(c(a(b(c(a(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(11) -> 10
, c_1(14) -> 13
, c_2(23) -> 22
, c_2(26) -> 25
, a_0(2) -> 2
, a_1(2) -> 14
, a_1(3) -> 1
, a_1(3) -> 13
, a_1(5) -> 4
, a_1(8) -> 7
, a_1(12) -> 11
, a_2(4) -> 26
, a_2(15) -> 10
, a_2(17) -> 16
, a_2(20) -> 19
, a_2(24) -> 23
, b_0(2) -> 2
, b_1(4) -> 3
, b_1(6) -> 5
, b_1(7) -> 6
, b_1(9) -> 8
, b_1(10) -> 9
, b_1(13) -> 12
, b_2(16) -> 15
, b_2(18) -> 17
, b_2(19) -> 18
, b_2(21) -> 20
, b_2(22) -> 21
, b_2(25) -> 24}