Tool CaT
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
stdout:
YES(?,O(n^1))
Problem:
a(c(d(x))) -> c(x)
u(b(d(d(x)))) -> b(x)
v(a(a(x))) -> u(v(x))
v(a(c(x))) -> u(b(d(x)))
v(c(x)) -> b(x)
w(a(a(x))) -> u(w(x))
w(a(c(x))) -> u(b(d(x)))
w(c(x)) -> b(x)
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {7,6,5,4}
transitions:
b1(20) -> 21*
b1(26) -> 27*
b1(28) -> 29*
c1(10) -> 11*
c1(12) -> 13*
c1(18) -> 19*
a0(2) -> 4*
a0(1) -> 4*
a0(3) -> 4*
c0(2) -> 1*
c0(1) -> 1*
c0(3) -> 1*
d0(2) -> 2*
d0(1) -> 2*
d0(3) -> 2*
u0(2) -> 5*
u0(1) -> 5*
u0(3) -> 5*
b0(2) -> 3*
b0(1) -> 3*
b0(3) -> 3*
v0(2) -> 6*
v0(1) -> 6*
v0(3) -> 6*
w0(2) -> 7*
w0(1) -> 7*
w0(3) -> 7*
1 -> 26,12
2 -> 20,10
3 -> 28,18
11 -> 4*
13 -> 4*
19 -> 4*
21 -> 7,6,5
27 -> 7,6,5
29 -> 7,6,5
problem:
QedTool IRC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
stdout:
YES(?,O(n^1))
Tool IRC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
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:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(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:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(x)}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, c_0(2) -> 2
, c_1(2) -> 1
, d_0(2) -> 2
, u_0(2) -> 1
, b_0(2) -> 2
, b_1(2) -> 1
, v_0(2) -> 1
, w_0(2) -> 1}Tool RC1
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(x)}
Proof Output:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with perSymbol-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with perSymbol-enrichment and initial automaton 'match''
----------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(x)}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ a_0(2) -> 1
, a_0(3) -> 1
, a_0(5) -> 1
, c_0(2) -> 2
, c_0(3) -> 2
, c_0(5) -> 2
, c_1(2) -> 1
, c_1(3) -> 1
, c_1(5) -> 1
, d_0(2) -> 3
, d_0(3) -> 3
, d_0(5) -> 3
, u_0(2) -> 4
, u_0(3) -> 4
, u_0(5) -> 4
, b_0(2) -> 5
, b_0(3) -> 5
, b_0(5) -> 5
, b_1(2) -> 4
, b_1(2) -> 6
, b_1(2) -> 7
, b_1(3) -> 4
, b_1(3) -> 6
, b_1(3) -> 7
, b_1(5) -> 4
, b_1(5) -> 6
, b_1(5) -> 7
, v_0(2) -> 6
, v_0(3) -> 6
, v_0(5) -> 6
, w_0(2) -> 7
, w_0(3) -> 7
, w_0(5) -> 7}Tool pair1rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(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:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(x)}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with perSymbol-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:
{ a_0(2) -> 1
, a_0(3) -> 1
, a_0(5) -> 1
, c_0(2) -> 2
, c_0(3) -> 2
, c_0(5) -> 2
, c_1(2) -> 1
, c_1(3) -> 1
, c_1(5) -> 1
, d_0(2) -> 3
, d_0(3) -> 3
, d_0(5) -> 3
, u_0(2) -> 4
, u_0(3) -> 4
, u_0(5) -> 4
, b_0(2) -> 5
, b_0(3) -> 5
, b_0(5) -> 5
, b_1(2) -> 4
, b_1(2) -> 6
, b_1(2) -> 7
, b_1(3) -> 4
, b_1(3) -> 6
, b_1(3) -> 7
, b_1(5) -> 4
, b_1(5) -> 6
, b_1(5) -> 7
, v_0(2) -> 6
, v_0(3) -> 6
, v_0(5) -> 6
, w_0(2) -> 7
, w_0(3) -> 7
, w_0(5) -> 7}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(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:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(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:
{ a_0(2) -> 1
, c_0(2) -> 2
, c_1(2) -> 1
, d_0(2) -> 2
, u_0(2) -> 1
, b_0(2) -> 2
, b_1(2) -> 1
, v_0(2) -> 1
, w_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(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:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(x)}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with perSymbol-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:
{ a_0(2) -> 1
, a_0(3) -> 1
, a_0(5) -> 1
, c_0(2) -> 2
, c_0(3) -> 2
, c_0(5) -> 2
, c_1(2) -> 1
, c_1(3) -> 1
, c_1(5) -> 1
, d_0(2) -> 3
, d_0(3) -> 3
, d_0(5) -> 3
, u_0(2) -> 4
, u_0(3) -> 4
, u_0(5) -> 4
, b_0(2) -> 5
, b_0(3) -> 5
, b_0(5) -> 5
, b_1(2) -> 4
, b_1(2) -> 6
, b_1(2) -> 7
, b_1(3) -> 4
, b_1(3) -> 6
, b_1(3) -> 7
, b_1(5) -> 4
, b_1(5) -> 6
, b_1(5) -> 7
, v_0(2) -> 6
, v_0(3) -> 6
, v_0(5) -> 6
, w_0(2) -> 7
, w_0(3) -> 7
, w_0(5) -> 7}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(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:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(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:
{ a_0(2) -> 1
, c_0(2) -> 2
, c_1(2) -> 1
, d_0(2) -> 2
, u_0(2) -> 1
, b_0(2) -> 2
, b_1(2) -> 1
, v_0(2) -> 1
, w_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(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:
{ a_0(2) -> 1
, c_0(2) -> 2
, c_1(2) -> 1
, d_0(2) -> 2
, u_0(2) -> 1
, b_0(2) -> 2
, b_1(2) -> 1
, v_0(2) -> 1
, w_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 7.242489e-2ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | SK90 2.49 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(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:
{ a(c(d(x))) -> c(x)
, u(b(d(d(x)))) -> b(x)
, v(a(a(x))) -> u(v(x))
, v(a(c(x))) -> u(b(d(x)))
, v(c(x)) -> b(x)
, w(a(a(x))) -> u(w(x))
, w(a(c(x))) -> u(b(d(x)))
, w(c(x)) -> b(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:
{ a_0(2) -> 1
, c_0(2) -> 2
, c_1(2) -> 1
, d_0(2) -> 2
, u_0(2) -> 1
, b_0(2) -> 2
, b_1(2) -> 1
, v_0(2) -> 1
, w_0(2) -> 1}
Hurray, we answered YES(?,O(n^1))