Tool CaT
stdout:
YES(?,O(n^1))
Problem:
f(g(x),s(0()),y) -> f(g(s(0())),y,g(x))
g(s(x)) -> s(g(x))
g(0()) -> 0()
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {4,3}
transitions:
01() -> 5,4
s1(5) -> 5,4
g1(2) -> 5*
g1(1) -> 5*
f0(1,1,1) -> 3*
f0(2,2,1) -> 3*
f0(1,1,2) -> 3*
f0(2,2,2) -> 3*
f0(1,2,1) -> 3*
f0(2,1,1) -> 3*
f0(1,2,2) -> 3*
f0(2,1,2) -> 3*
g0(2) -> 4*
g0(1) -> 4*
s0(2) -> 1*
s0(1) -> 1*
00() -> 2*
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:
{ f(g(x), s(0()), y) -> f(g(s(0())), y, g(x))
, g(s(x)) -> s(g(x))
, g(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:
{ f(g(x), s(0()), y) -> f(g(s(0())), y, g(x))
, g(s(x)) -> s(g(x))
, g(0()) -> 0()}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2, 2, 2) -> 1
, g_0(2) -> 1
, g_1(2) -> 3
, s_0(2) -> 2
, s_1(3) -> 1
, s_1(3) -> 3
, 0_0() -> 2
, 0_1() -> 1
, 0_1() -> 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:
{ f(g(x), s(0()), y) -> f(g(s(0())), y, g(x))
, g(s(x)) -> s(g(x))
, g(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:
{ f(g(x), s(0()), y) -> f(g(s(0())), y, g(x))
, g(s(x)) -> s(g(x))
, g(0()) -> 0()}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2, 2, 2) -> 1
, g_0(2) -> 1
, g_1(2) -> 3
, s_0(2) -> 2
, s_1(3) -> 1
, s_1(3) -> 3
, 0_0() -> 2
, 0_1() -> 1
, 0_1() -> 3}