Tool CaT
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
stdout:
YES(?,O(n^1))
Problem:
f(f(x)) -> f(c(f(x)))
f(f(x)) -> f(d(f(x)))
g(c(x)) -> x
g(d(x)) -> x
g(c(h(0()))) -> g(d(1()))
g(c(1())) -> g(d(h(0())))
g(h(x)) -> g(x)
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {7,6}
transitions:
g1(32) -> 33*
g1(34) -> 35*
g1(24) -> 25*
g1(9) -> 10*
g1(26) -> 27*
g1(18) -> 19*
d1(8) -> 9*
h1(16) -> 17*
01() -> 16*
11() -> 8*
f0(5) -> 6*
f0(2) -> 6*
f0(4) -> 6*
f0(1) -> 6*
f0(3) -> 6*
c0(5) -> 1*
c0(2) -> 1*
c0(4) -> 1*
c0(1) -> 1*
c0(3) -> 1*
d0(5) -> 2*
d0(2) -> 2*
d0(4) -> 2*
d0(1) -> 2*
d0(3) -> 2*
g0(5) -> 7*
g0(2) -> 7*
g0(4) -> 7*
g0(1) -> 7*
g0(3) -> 7*
h0(5) -> 3*
h0(2) -> 3*
h0(4) -> 3*
h0(1) -> 3*
h0(3) -> 3*
00() -> 4*
10() -> 5*
1 -> 25,33,32,7
2 -> 25,33,24,7
3 -> 25,33,34,7
4 -> 25,33,26,7
5 -> 25,33,18,7
8 -> 10*
10 -> 33,7
17 -> 8*
19 -> 35,7
25 -> 35,7
27 -> 35,7
33 -> 35,7
35 -> 7*
problem:
QedTool IRC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
stdout:
YES(?,O(n^1))
Tool IRC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
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(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
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(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, c_0(2) -> 1
, c_0(2) -> 2
, d_0(2) -> 1
, d_0(2) -> 2
, d_1(4) -> 3
, g_0(2) -> 1
, g_1(2) -> 1
, g_1(3) -> 1
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(5) -> 1
, h_1(5) -> 4
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 5
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 1_1() -> 4}Tool RC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
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(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
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(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, c_0(2) -> 1
, c_0(2) -> 2
, d_0(2) -> 1
, d_0(2) -> 2
, d_1(4) -> 3
, g_0(2) -> 1
, g_1(2) -> 1
, g_1(3) -> 1
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(5) -> 1
, h_1(5) -> 4
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 5
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 1_1() -> 4}Tool pair1rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, c_0(2) -> 1
, c_0(2) -> 2
, d_0(2) -> 1
, d_0(2) -> 2
, d_1(4) -> 3
, g_0(2) -> 1
, g_1(2) -> 1
, g_1(3) -> 1
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(5) -> 1
, h_1(5) -> 4
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 5
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 1_1() -> 4}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, c_0(2) -> 1
, c_0(2) -> 2
, d_0(2) -> 1
, d_0(2) -> 2
, d_1(4) -> 3
, g_0(2) -> 1
, g_1(2) -> 1
, g_1(3) -> 1
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(5) -> 1
, h_1(5) -> 4
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 5
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 1_1() -> 4}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
The input problem contains no overlaps that give rise to inapplicable rules.
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, c_0(2) -> 1
, c_0(2) -> 2
, d_0(2) -> 1
, d_0(2) -> 2
, d_1(4) -> 3
, g_0(2) -> 1
, g_1(2) -> 1
, g_1(3) -> 1
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(5) -> 1
, h_1(5) -> 4
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 5
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 1_1() -> 4}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, c_0(2) -> 1
, c_0(2) -> 2
, d_0(2) -> 1
, d_0(2) -> 2
, d_1(4) -> 3
, g_0(2) -> 1
, g_1(2) -> 1
, g_1(3) -> 1
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(5) -> 1
, h_1(5) -> 4
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 5
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 1_1() -> 4}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match' (timeout of 100.0 seconds)' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, c_0(2) -> 1
, c_0(2) -> 2
, d_0(2) -> 1
, d_0(2) -> 2
, d_1(4) -> 3
, g_0(2) -> 1
, g_1(2) -> 1
, g_1(3) -> 1
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(5) -> 1
, h_1(5) -> 4
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 5
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 1_1() -> 4}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 7.868099e-2ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | AG01 3.51 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
The input problem contains no overlaps that give rise to inapplicable rules.
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ f(f(x)) -> f(c(f(x)))
, f(f(x)) -> f(d(f(x)))
, g(c(x)) -> x
, g(d(x)) -> x
, g(c(h(0()))) -> g(d(1()))
, g(c(1())) -> g(d(h(0())))
, g(h(x)) -> g(x)}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ f_0(2) -> 1
, c_0(2) -> 1
, c_0(2) -> 2
, d_0(2) -> 1
, d_0(2) -> 2
, d_1(4) -> 3
, g_0(2) -> 1
, g_1(2) -> 1
, g_1(3) -> 1
, h_0(2) -> 1
, h_0(2) -> 2
, h_1(5) -> 1
, h_1(5) -> 4
, 0_0() -> 1
, 0_0() -> 2
, 0_1() -> 5
, 1_0() -> 1
, 1_0() -> 2
, 1_1() -> 1
, 1_1() -> 4}
Hurray, we answered YES(?,O(n^1))