'Weak Dependency Graph [60.0]'
------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, b(x1) -> d(a(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c(x1) -> x1
, b(x1) -> c(d(x1))}
Details:
We have computed the following set of weak (innermost) dependency pairs:
{ a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b^#(x1) -> c_1(a^#(x1))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, c^#(x1) -> c_3()
, b^#(x1) -> c_4(c^#(d(x1)))}
The usable rules are:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, b(x1) -> d(a(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c(x1) -> x1
, b(x1) -> c(d(x1))}
The estimated dependency graph contains the following edges:
{a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
==> {b^#(x1) -> c_4(c^#(d(x1)))}
{a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
==> {b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))}
{a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
==> {b^#(x1) -> c_1(a^#(x1))}
{b^#(x1) -> c_1(a^#(x1))}
==> {a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
{b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))}
==> {a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
{b^#(x1) -> c_4(c^#(d(x1)))}
==> {c^#(x1) -> c_3()}
We consider the following path(s):
1) { a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))
, b^#(x1) -> c_4(c^#(d(x1)))}
The usable rules for this path are the following:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, b(x1) -> d(a(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c(x1) -> x1
, b(x1) -> c(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:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, b(x1) -> d(a(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c(x1) -> x1
, b(x1) -> c(d(x1))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))
, b^#(x1) -> c_4(c^#(d(x1)))}
Details:
We apply the weight gap principle, strictly orienting the rules
{b(a(c(d(x1)))) -> a(a(a(x1)))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b(a(c(d(x1)))) -> a(a(a(x1)))}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
a^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [1]
b^#(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [0]
c^#(x1) = [1] x1 + [0]
c_3() = [0]
c_4(x1) = [1] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
and weakly orienting the rules
{b(a(c(d(x1)))) -> a(a(a(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
a^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [7]
c^#(x1) = [1] x1 + [0]
c_3() = [0]
c_4(x1) = [1] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))}
and weakly orienting the rules
{ a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b(a(c(d(x1)))) -> a(a(a(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
a^#(x1) = [1] x1 + [0]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [1]
c_2(x1) = [1] x1 + [0]
c^#(x1) = [1] x1 + [0]
c_3() = [0]
c_4(x1) = [1] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{b^#(x1) -> c_4(c^#(d(x1)))}
and weakly orienting the rules
{ b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b(a(c(d(x1)))) -> a(a(a(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b^#(x1) -> c_4(c^#(d(x1)))}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
a^#(x1) = [1] x1 + [8]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [8]
c_1(x1) = [1] x1 + [1]
c_2(x1) = [1] x1 + [1]
c^#(x1) = [1] x1 + [3]
c_3() = [0]
c_4(x1) = [1] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{ a(a(c(x1))) -> b(c(b(a(x1))))
, c(x1) -> x1}
and weakly orienting the rules
{ b^#(x1) -> c_4(c^#(d(x1)))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b(a(c(d(x1)))) -> a(a(a(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, c(x1) -> x1}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [1]
c(x1) = [1] x1 + [1]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [3]
a^#(x1) = [1] x1 + [6]
c_0(x1) = [1] x1 + [1]
b^#(x1) = [1] x1 + [3]
c_1(x1) = [1] x1 + [1]
c_2(x1) = [1] x1 + [0]
c^#(x1) = [1] x1 + [0]
c_3() = [0]
c_4(x1) = [1] 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:
{ b(x1) -> d(a(x1))
, b(x1) -> c(d(x1))
, b^#(x1) -> c_1(a^#(x1))}
Weak Rules:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, c(x1) -> x1
, b^#(x1) -> c_4(c^#(d(x1)))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b(a(c(d(x1)))) -> a(a(a(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:
{ b(x1) -> d(a(x1))
, b(x1) -> c(d(x1))
, b^#(x1) -> c_1(a^#(x1))}
Weak Rules:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, c(x1) -> x1
, b^#(x1) -> c_4(c^#(d(x1)))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b(a(c(d(x1)))) -> a(a(a(x1)))}
Details:
The problem is Match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ d_0(4) -> 4
, d_1(4) -> 13
, a^#_0(4) -> 5
, a^#_1(4) -> 11
, b^#_0(4) -> 7
, c_1_1(11) -> 7
, c^#_0(4) -> 10
, c^#_1(13) -> 12
, c_4_0(10) -> 7
, c_4_1(12) -> 7}
2) { a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))}
The usable rules for this path are the following:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, b(x1) -> d(a(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c(x1) -> x1
, b(x1) -> c(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:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, b(x1) -> d(a(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c(x1) -> x1
, b(x1) -> c(d(x1))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))}
Details:
We apply the weight gap principle, strictly orienting the rules
{b(a(c(d(x1)))) -> a(a(a(x1)))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b(a(c(d(x1)))) -> a(a(a(x1)))}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
a^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [1]
b^#(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_3() = [0]
c_4(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
and weakly orienting the rules
{b(a(c(d(x1)))) -> a(a(a(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
a^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_3() = [0]
c_4(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))}
and weakly orienting the rules
{ a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b(a(c(d(x1)))) -> a(a(a(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
a^#(x1) = [1] x1 + [0]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [1]
c_2(x1) = [1] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_3() = [0]
c_4(x1) = [0] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{ a(a(c(x1))) -> b(c(b(a(x1))))
, c(x1) -> x1}
and weakly orienting the rules
{ b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b(a(c(d(x1)))) -> a(a(a(x1)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, c(x1) -> x1}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [4]
c(x1) = [1] x1 + [5]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [11]
a^#(x1) = [1] x1 + [7]
c_0(x1) = [1] x1 + [0]
b^#(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [1]
c^#(x1) = [0] x1 + [0]
c_3() = [0]
c_4(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:
{ b(x1) -> d(a(x1))
, b(x1) -> c(d(x1))
, b^#(x1) -> c_1(a^#(x1))}
Weak Rules:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, c(x1) -> x1
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b(a(c(d(x1)))) -> a(a(a(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:
{ b(x1) -> d(a(x1))
, b(x1) -> c(d(x1))
, b^#(x1) -> c_1(a^#(x1))}
Weak Rules:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, c(x1) -> x1
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b(a(c(d(x1)))) -> a(a(a(x1)))}
Details:
The problem is Match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ d_0(4) -> 4
, a^#_0(4) -> 5
, a^#_1(4) -> 8
, b^#_0(4) -> 7
, c_1_1(8) -> 7}
3) { a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))
, b^#(x1) -> c_4(c^#(d(x1)))
, c^#(x1) -> c_3()}
The usable rules for this path are the following:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, b(x1) -> d(a(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c(x1) -> x1
, b(x1) -> c(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:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, b(x1) -> d(a(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c(x1) -> x1
, b(x1) -> c(d(x1))
, b^#(x1) -> c_4(c^#(d(x1)))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))
, c^#(x1) -> c_3()}
Details:
We apply the weight gap principle, strictly orienting the rules
{ b(a(c(d(x1)))) -> a(a(a(x1)))
, c^#(x1) -> c_3()}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ b(a(c(d(x1)))) -> a(a(a(x1)))
, c^#(x1) -> c_3()}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
a^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [1]
b^#(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [3]
c_2(x1) = [1] x1 + [0]
c^#(x1) = [1] x1 + [7]
c_3() = [0]
c_4(x1) = [1] x1 + [1]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{ b^#(x1) -> c_4(c^#(d(x1)))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))}
and weakly orienting the rules
{ b(a(c(d(x1)))) -> a(a(a(x1)))
, c^#(x1) -> c_3()}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ b^#(x1) -> c_4(c^#(d(x1)))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
a^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [2]
b^#(x1) = [1] x1 + [8]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [0]
c^#(x1) = [1] x1 + [0]
c_3() = [0]
c_4(x1) = [1] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{ b(x1) -> d(a(x1))
, b(x1) -> c(d(x1))}
and weakly orienting the rules
{ b^#(x1) -> c_4(c^#(d(x1)))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c^#(x1) -> c_3()}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ b(x1) -> d(a(x1))
, b(x1) -> c(d(x1))}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
b(x1) = [1] x1 + [8]
d(x1) = [1] x1 + [0]
a^#(x1) = [1] x1 + [0]
c_0(x1) = [1] x1 + [5]
b^#(x1) = [1] x1 + [0]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [0]
c^#(x1) = [1] x1 + [0]
c_3() = [0]
c_4(x1) = [1] x1 + [0]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{c(x1) -> x1}
and weakly orienting the rules
{ b(x1) -> d(a(x1))
, b(x1) -> c(d(x1))
, b^#(x1) -> c_4(c^#(d(x1)))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c^#(x1) -> c_3()}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{c(x1) -> x1}
Details:
Interpretation Functions:
a(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [8]
b(x1) = [1] x1 + [10]
d(x1) = [1] x1 + [0]
a^#(x1) = [1] x1 + [0]
c_0(x1) = [1] x1 + [1]
b^#(x1) = [1] x1 + [6]
c_1(x1) = [1] x1 + [0]
c_2(x1) = [1] x1 + [0]
c^#(x1) = [1] x1 + [4]
c_3() = [0]
c_4(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:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
Weak Rules:
{ c(x1) -> x1
, b(x1) -> d(a(x1))
, b(x1) -> c(d(x1))
, b^#(x1) -> c_4(c^#(d(x1)))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c^#(x1) -> c_3()}
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:
{ a(a(c(x1))) -> b(c(b(a(x1))))
, a^#(a(c(x1))) -> c_0(b^#(c(b(a(x1)))))}
Weak Rules:
{ c(x1) -> x1
, b(x1) -> d(a(x1))
, b(x1) -> c(d(x1))
, b^#(x1) -> c_4(c^#(d(x1)))
, b^#(a(c(d(x1)))) -> c_2(a^#(a(a(x1))))
, b^#(x1) -> c_1(a^#(x1))
, b(a(c(d(x1)))) -> a(a(a(x1)))
, c^#(x1) -> c_3()}
Details:
The problem is Match-bounded by 0.
The enriched problem is compatible with the following automaton:
{ d_0(4) -> 4
, a^#_0(4) -> 5
, b^#_0(4) -> 7
, c_1_0(5) -> 7
, c^#_0(4) -> 10
, c_3_0() -> 10
, c_4_0(10) -> 7}