Tool CaT
stdout:
YES(?,O(n^1))
Problem:
g(0()) -> 0()
g(s(x)) -> f(g(x))
f(0()) -> 0()
Proof:
Bounds Processor:
bound: 2
enrichment: match
automaton:
final states: {4,3}
transitions:
01() -> 6*
f1(8) -> 9*
g1(15) -> 16*
g1(7) -> 8*
02() -> 17*
g0(2) -> 3*
g0(1) -> 3*
00() -> 1*
s0(2) -> 2*
s0(1) -> 2*
f0(2) -> 4*
f0(1) -> 4*
1 -> 15*
2 -> 7*
6 -> 16,8,4,3
9 -> 8,3
16 -> 8*
17 -> 9,3,8
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:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0()}
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:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0()}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ g_0(2) -> 1
, g_1(2) -> 3
, 0_0() -> 2
, 0_1() -> 1
, 0_1() -> 3
, 0_2() -> 1
, 0_2() -> 3
, s_0(2) -> 2
, f_0(2) -> 1
, f_1(3) -> 1
, f_1(3) -> 3}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:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0()}
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:
{ g(0()) -> 0()
, g(s(x)) -> f(g(x))
, f(0()) -> 0()}
Proof Output:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ g_0(2) -> 1
, g_1(2) -> 3
, 0_0() -> 2
, 0_1() -> 1
, 0_1() -> 3
, 0_2() -> 1
, 0_2() -> 3
, s_0(2) -> 2
, f_0(2) -> 1
, f_1(3) -> 1
, f_1(3) -> 3}