'Weak Dependency Graph [60.0]'
------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ d(a(x1)) -> b(d(x1))
, b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))}
Details:
We have computed the following set of weak (innermost) dependency pairs:
{ d^#(a(x1)) -> c_0(b^#(d(x1)))
, b^#(x1) -> c_1()
, c^#(d(c(x1))) -> c_2(d^#(x1))
, b^#(d(d(x1))) -> c_3(c^#(c(d(d(c(x1))))))}
The usable rules are:
{ d(a(x1)) -> b(d(x1))
, c(d(c(x1))) -> a(d(x1))
, b(x1) -> a(a(a(x1)))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))}
The estimated dependency graph contains the following edges:
{d^#(a(x1)) -> c_0(b^#(d(x1)))}
==> {b^#(d(d(x1))) -> c_3(c^#(c(d(d(c(x1))))))}
{d^#(a(x1)) -> c_0(b^#(d(x1)))}
==> {b^#(x1) -> c_1()}
{c^#(d(c(x1))) -> c_2(d^#(x1))}
==> {d^#(a(x1)) -> c_0(b^#(d(x1)))}
We consider the following path(s):
1) { c^#(d(c(x1))) -> c_2(d^#(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))
, b^#(x1) -> c_1()}
The usable rules for this path are the following:
{ d(a(x1)) -> b(d(x1))
, b(x1) -> a(a(a(x1)))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))
, c(d(c(x1))) -> a(d(x1))}
We have applied the subprocessor on the union of usable rules and weak (innermost) dependency pairs.
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ d(a(x1)) -> b(d(x1))
, b(x1) -> a(a(a(x1)))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))
, c(d(c(x1))) -> a(d(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))
, c^#(d(c(x1))) -> c_2(d^#(x1))
, b^#(x1) -> c_1()}
Details:
We apply the weight gap principle, strictly orienting the rules
{c^#(d(c(x1))) -> c_2(d^#(x1))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{c^#(d(c(x1))) -> c_2(d^#(x1))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1() = [0]
c^#(x1) = [1] x1 + [8]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{b^#(x1) -> c_1()}
and weakly orienting the rules
{c^#(d(c(x1))) -> c_2(d^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b^#(x1) -> c_1()}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [8]
c_1() = [0]
c^#(x1) = [1] x1 + [15]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{d^#(a(x1)) -> c_0(b^#(d(x1)))}
and weakly orienting the rules
{ b^#(x1) -> c_1()
, c^#(d(c(x1))) -> c_2(d^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{d^#(a(x1)) -> c_0(b^#(d(x1)))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [5]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1() = [0]
c^#(x1) = [1] x1 + [8]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{c(d(c(x1))) -> a(d(x1))}
and weakly orienting the rules
{ d^#(a(x1)) -> c_0(b^#(d(x1)))
, b^#(x1) -> c_1()
, c^#(d(c(x1))) -> c_2(d^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{c(d(c(x1))) -> a(d(x1))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [8]
d^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1() = [0]
c^#(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{b(x1) -> a(a(a(x1)))}
and weakly orienting the rules
{ c(d(c(x1))) -> a(d(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))
, b^#(x1) -> c_1()
, c^#(d(c(x1))) -> c_2(d^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b(x1) -> a(a(a(x1)))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [8]
c(x1) = [1] x1 + [5]
d^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1() = [0]
c^#(x1) = [1] x1 + [5]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{b(d(d(x1))) -> c(c(d(d(c(x1)))))}
and weakly orienting the rules
{ b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))
, b^#(x1) -> c_1()
, c^#(d(c(x1))) -> c_2(d^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b(d(d(x1))) -> c(c(d(d(c(x1)))))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [8]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1() = [0]
c^#(x1) = [1] x1 + [1]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
'fastest of 'combine', 'Bounds with default enrichment', 'Bounds with default enrichment''
------------------------------------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost relative runtime-complexity with respect to
Strict Rules: {d(a(x1)) -> b(d(x1))}
Weak Rules:
{ b(d(d(x1))) -> c(c(d(d(c(x1)))))
, b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))
, b^#(x1) -> c_1()
, c^#(d(c(x1))) -> c_2(d^#(x1))}
Details:
The problem was solved by processor 'Bounds with default enrichment':
'Bounds with default enrichment'
--------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost relative runtime-complexity with respect to
Strict Rules: {d(a(x1)) -> b(d(x1))}
Weak Rules:
{ b(d(d(x1))) -> c(c(d(d(c(x1)))))
, b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))
, b^#(x1) -> c_1()
, c^#(d(c(x1))) -> c_2(d^#(x1))}
Details:
The problem is Match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ d_0(2) -> 4
, d_1(2) -> 5
, a_0(2) -> 2
, a_1(5) -> 7
, a_1(6) -> 4
, a_1(6) -> 5
, a_1(7) -> 6
, b_1(5) -> 4
, b_1(5) -> 5
, d^#_0(2) -> 1
, c_0_0(3) -> 1
, c_0_1(8) -> 1
, b^#_0(2) -> 1
, b^#_0(4) -> 3
, b^#_1(5) -> 8
, c_1_0() -> 1
, c_1_0() -> 3
, c_1_1() -> 8
, c^#_0(2) -> 1}
2) { c^#(d(c(x1))) -> c_2(d^#(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))}
The usable rules for this path are the following:
{ d(a(x1)) -> b(d(x1))
, b(x1) -> a(a(a(x1)))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))
, c(d(c(x1))) -> a(d(x1))}
We have applied the subprocessor on the union of usable rules and weak (innermost) dependency pairs.
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ d(a(x1)) -> b(d(x1))
, b(x1) -> a(a(a(x1)))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))
, c(d(c(x1))) -> a(d(x1))
, c^#(d(c(x1))) -> c_2(d^#(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))}
Details:
We apply the weight gap principle, strictly orienting the rules
{d^#(a(x1)) -> c_0(b^#(d(x1)))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{d^#(a(x1)) -> c_0(b^#(d(x1)))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [8]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1() = [0]
c^#(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [1]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{c^#(d(c(x1))) -> c_2(d^#(x1))}
and weakly orienting the rules
{d^#(a(x1)) -> c_0(b^#(d(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{c^#(d(c(x1))) -> c_2(d^#(x1))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [2]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [1]
c_1() = [0]
c^#(x1) = [1] x1 + [8]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{c(d(c(x1))) -> a(d(x1))}
and weakly orienting the rules
{ c^#(d(c(x1))) -> c_2(d^#(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{c(d(c(x1))) -> a(d(x1))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [8]
d^#(x1) = [1] x1 + [8]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1() = [0]
c^#(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [1]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{b(x1) -> a(a(a(x1)))}
and weakly orienting the rules
{ c(d(c(x1))) -> a(d(x1))
, c^#(d(c(x1))) -> c_2(d^#(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b(x1) -> a(a(a(x1)))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [8]
c(x1) = [1] x1 + [10]
d^#(x1) = [1] x1 + [8]
c_0(x1) = [1] x1 + [1]
b^#(x1) = [1] x1 + [1]
c_1() = [0]
c^#(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [1]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{b(d(d(x1))) -> c(c(d(d(c(x1)))))}
and weakly orienting the rules
{ b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, c^#(d(c(x1))) -> c_2(d^#(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b(d(d(x1))) -> c(c(d(d(c(x1)))))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [8]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1() = [0]
c^#(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
'fastest of 'combine', 'Bounds with default enrichment', 'Bounds with default enrichment''
------------------------------------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost relative runtime-complexity with respect to
Strict Rules: {d(a(x1)) -> b(d(x1))}
Weak Rules:
{ b(d(d(x1))) -> c(c(d(d(c(x1)))))
, b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, c^#(d(c(x1))) -> c_2(d^#(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))}
Details:
The problem was solved by processor 'Bounds with default enrichment':
'Bounds with default enrichment'
--------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost relative runtime-complexity with respect to
Strict Rules: {d(a(x1)) -> b(d(x1))}
Weak Rules:
{ b(d(d(x1))) -> c(c(d(d(c(x1)))))
, b(x1) -> a(a(a(x1)))
, c(d(c(x1))) -> a(d(x1))
, c^#(d(c(x1))) -> c_2(d^#(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))}
Details:
The problem is Match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ d_0(2) -> 11
, d_1(2) -> 12
, a_0(2) -> 2
, a_1(12) -> 14
, a_1(13) -> 11
, a_1(13) -> 12
, a_1(14) -> 13
, b_1(12) -> 11
, b_1(12) -> 12
, d^#_0(2) -> 5
, c_0_0(10) -> 5
, c_0_1(15) -> 5
, b^#_0(2) -> 7
, b^#_0(11) -> 10
, b^#_1(12) -> 15
, c^#_0(2) -> 9}
3) { c^#(d(c(x1))) -> c_2(d^#(x1))
, d^#(a(x1)) -> c_0(b^#(d(x1)))
, b^#(d(d(x1))) -> c_3(c^#(c(d(d(c(x1))))))}
The usable rules for this path are the following:
{ d(a(x1)) -> b(d(x1))
, c(d(c(x1))) -> a(d(x1))
, b(x1) -> a(a(a(x1)))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))}
We have applied the subprocessor on the union of usable rules and weak (innermost) dependency pairs.
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ d(a(x1)) -> b(d(x1))
, c(d(c(x1))) -> a(d(x1))
, b(x1) -> a(a(a(x1)))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))
, d^#(a(x1)) -> c_0(b^#(d(x1)))
, c^#(d(c(x1))) -> c_2(d^#(x1))
, b^#(d(d(x1))) -> c_3(c^#(c(d(d(c(x1))))))}
Details:
We apply the weight gap principle, strictly orienting the rules
{c^#(d(c(x1))) -> c_2(d^#(x1))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{c^#(d(c(x1))) -> c_2(d^#(x1))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [8]
b^#(x1) = [1] x1 + [0]
c_1() = [0]
c^#(x1) = [1] x1 + [4]
c_2(x1) = [1] x1 + [3]
c_3(x1) = [1] x1 + [11]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{b^#(d(d(x1))) -> c_3(c^#(c(d(d(c(x1))))))}
and weakly orienting the rules
{c^#(d(c(x1))) -> c_2(d^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b^#(d(d(x1))) -> c_3(c^#(c(d(d(c(x1))))))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [1]
a(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [8]
c_1() = [0]
c^#(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [1] x1 + [1]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{ d(a(x1)) -> b(d(x1))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))
, d^#(a(x1)) -> c_0(b^#(d(x1)))}
and weakly orienting the rules
{ b^#(d(d(x1))) -> c_3(c^#(c(d(d(c(x1))))))
, c^#(d(c(x1))) -> c_2(d^#(x1))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ d(a(x1)) -> b(d(x1))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))
, d^#(a(x1)) -> c_0(b^#(d(x1)))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [0]
a(x1) = [1] x1 + [14]
b(x1) = [1] x1 + [1]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [0]
c_0(x1) = [1] x1 + [1]
b^#(x1) = [1] x1 + [8]
c_1() = [0]
c^#(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [1] x1 + [1]
Finally we apply the subprocessor
'fastest of 'combine', 'Bounds with default enrichment', 'Bounds with default enrichment''
------------------------------------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost relative runtime-complexity with respect to
Strict Rules:
{ c(d(c(x1))) -> a(d(x1))
, b(x1) -> a(a(a(x1)))}
Weak Rules:
{ d(a(x1)) -> b(d(x1))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))
, d^#(a(x1)) -> c_0(b^#(d(x1)))
, b^#(d(d(x1))) -> c_3(c^#(c(d(d(c(x1))))))
, c^#(d(c(x1))) -> c_2(d^#(x1))}
Details:
The problem was solved by processor 'Bounds with default enrichment':
'Bounds with default enrichment'
--------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost relative runtime-complexity with respect to
Strict Rules:
{ c(d(c(x1))) -> a(d(x1))
, b(x1) -> a(a(a(x1)))}
Weak Rules:
{ d(a(x1)) -> b(d(x1))
, b(d(d(x1))) -> c(c(d(d(c(x1)))))
, d^#(a(x1)) -> c_0(b^#(d(x1)))
, b^#(d(d(x1))) -> c_3(c^#(c(d(d(c(x1))))))
, c^#(d(c(x1))) -> c_2(d^#(x1))}
Details:
The problem is Match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ d_0(2) -> 11
, d_1(2) -> 15
, a_0(2) -> 2
, a_1(11) -> 13
, a_1(12) -> 11
, a_1(13) -> 12
, a_2(15) -> 17
, a_2(16) -> 15
, a_2(17) -> 16
, b_0(11) -> 11
, b_1(15) -> 15
, d^#_0(2) -> 5
, c_0_0(10) -> 5
, c_0_1(14) -> 5
, b^#_0(2) -> 7
, b^#_0(11) -> 10
, b^#_1(15) -> 14
, c^#_0(2) -> 9}
4) {c^#(d(c(x1))) -> c_2(d^#(x1))}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
d(x1) = [0] x1 + [0]
a(x1) = [0] x1 + [0]
b(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
b^#(x1) = [0] x1 + [0]
c_1() = [0]
c^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3(x1) = [0] x1 + [0]
We have applied the subprocessor on the resulting DP-problem:
'Weight Gap Principle'
----------------------
Answer: YES(?,O(n^1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {c^#(d(c(x1))) -> c_2(d^#(x1))}
Weak Rules: {}
Details:
We apply the weight gap principle, strictly orienting the rules
{c^#(d(c(x1))) -> c_2(d^#(x1))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{c^#(d(c(x1))) -> c_2(d^#(x1))}
Details:
Interpretation Functions:
d(x1) = [1] x1 + [0]
a(x1) = [0] x1 + [0]
b(x1) = [0] x1 + [0]
c(x1) = [1] x1 + [0]
d^#(x1) = [1] x1 + [0]
c_0(x1) = [0] x1 + [0]
b^#(x1) = [0] x1 + [0]
c_1() = [0]
c^#(x1) = [1] x1 + [1]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [0] x1 + [0]
Finally we apply the subprocessor
'Empty TRS'
-----------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {}
Weak Rules: {c^#(d(c(x1))) -> c_2(d^#(x1))}
Details:
The given problem does not contain any strict rules