'Weak Dependency Graph [60.0]'
------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))}
Details:
We have computed the following set of weak (innermost) dependency pairs:
{ max^#(L(x)) -> c_0()
, max^#(N(L(0()), L(y))) -> c_1()
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
The usable rules are:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))}
The estimated dependency graph contains the following edges:
{max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))}
==> {max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))}
{max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))}
==> {max^#(N(L(0()), L(y))) -> c_1()}
{max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
==> {max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))}
{max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
==> {max^#(N(L(0()), L(y))) -> c_1()}
We consider the following path(s):
1) { max^#(N(L(x), N(y, z))) ->
c_3(max^#(N(L(x), L(max(N(y, z))))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))
, max^#(N(L(0()), L(y))) -> c_1()}
The usable rules for this path are the following:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))}
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:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))
, max^#(N(L(0()), L(y))) -> c_1()}
Details:
We apply the weight gap principle, strictly orienting the rules
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max^#(N(L(0()), L(y))) -> c_1()}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max^#(N(L(0()), L(y))) -> c_1()}
Details:
Interpretation Functions:
max(x1) = [1] x1 + [1]
L(x1) = [1] x1 + [0]
N(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
max^#(x1) = [1] x1 + [1]
c_0() = [0]
c_1() = [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
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))}
and weakly orienting the rules
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max^#(N(L(0()), L(y))) -> c_1()}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))}
Details:
Interpretation Functions:
max(x1) = [1] x1 + [6]
L(x1) = [1] x1 + [2]
N(x1, x2) = [1] x1 + [1] x2 + [12]
0() = [11]
s(x1) = [1] x1 + [1]
max^#(x1) = [1] x1 + [3]
c_0() = [0]
c_1() = [0]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [1] x1 + [9]
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:
{ max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
Weak Rules:
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))
, max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max^#(N(L(0()), L(y))) -> c_1()}
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:
{ max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
Weak Rules:
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))
, max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max^#(N(L(0()), L(y))) -> c_1()}
Details:
The problem is Match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ max_1(4) -> 7
, max_1(8) -> 7
, max_1(10) -> 9
, max_1(12) -> 9
, L_0(2) -> 2
, L_0(2) -> 7
, L_0(2) -> 9
, L_1(2) -> 5
, L_1(7) -> 6
, L_1(9) -> 13
, N_0(2, 2) -> 2
, N_0(2, 2) -> 7
, N_0(2, 2) -> 9
, N_1(2, 2) -> 8
, N_1(5, 5) -> 10
, N_1(5, 6) -> 4
, N_1(5, 13) -> 12
, 0_0() -> 2
, 0_0() -> 7
, 0_0() -> 9
, s_0(2) -> 2
, s_0(2) -> 7
, s_0(2) -> 9
, s_1(9) -> 7
, s_1(9) -> 9
, max^#_0(2) -> 1
, max^#_1(4) -> 3
, max^#_1(10) -> 11
, max^#_1(12) -> 11
, c_1_0() -> 1
, c_1_1() -> 3
, c_1_1() -> 11
, c_2_0(1) -> 1
, c_2_1(11) -> 3
, c_2_1(11) -> 11
, c_3_1(3) -> 1}
2) { max^#(N(L(x), N(y, z))) ->
c_3(max^#(N(L(x), L(max(N(y, z))))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))}
The usable rules for this path are the following:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))}
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:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))}
Details:
We apply the weight gap principle, strictly orienting the rules
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y}
Details:
Interpretation Functions:
max(x1) = [1] x1 + [1]
L(x1) = [1] x1 + [0]
N(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
max^#(x1) = [1] x1 + [1]
c_0() = [0]
c_1() = [0]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [1] x1 + [3]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))}
and weakly orienting the rules
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))}
Details:
Interpretation Functions:
max(x1) = [1] x1 + [0]
L(x1) = [1] x1 + [0]
N(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [1]
s(x1) = [1] x1 + [2]
max^#(x1) = [1] x1 + [12]
c_0() = [0]
c_1() = [0]
c_2(x1) = [1] x1 + [0]
c_3(x1) = [1] x1 + [11]
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:
{ max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
Weak Rules:
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))
, max(L(x)) -> x
, max(N(L(0()), L(y))) -> y}
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:
{ max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
Weak Rules:
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max^#(N(L(s(x)), L(s(y)))) -> c_2(max^#(N(L(x), L(y))))
, max(L(x)) -> x
, max(N(L(0()), L(y))) -> y}
Details:
The problem is Match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ max_1(4) -> 7
, max_1(8) -> 7
, max_1(10) -> 9
, max_1(12) -> 9
, L_0(2) -> 2
, L_0(2) -> 7
, L_0(2) -> 9
, L_1(2) -> 5
, L_1(7) -> 6
, L_1(9) -> 13
, N_0(2, 2) -> 2
, N_0(2, 2) -> 7
, N_0(2, 2) -> 9
, N_1(2, 2) -> 8
, N_1(5, 5) -> 10
, N_1(5, 6) -> 4
, N_1(5, 13) -> 12
, 0_0() -> 2
, 0_0() -> 7
, 0_0() -> 9
, s_0(2) -> 2
, s_0(2) -> 7
, s_0(2) -> 9
, s_1(9) -> 7
, s_1(9) -> 9
, max^#_0(2) -> 1
, max^#_1(4) -> 3
, max^#_1(10) -> 11
, max^#_1(12) -> 11
, c_2_0(1) -> 1
, c_2_1(11) -> 3
, c_2_1(11) -> 11
, c_3_1(3) -> 1}
3) { max^#(N(L(x), N(y, z))) ->
c_3(max^#(N(L(x), L(max(N(y, z))))))
, max^#(N(L(0()), L(y))) -> c_1()}
The usable rules for this path are the following:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))}
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:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))
, max^#(N(L(0()), L(y))) -> c_1()}
Details:
We apply the weight gap principle, strictly orienting the rules
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max^#(N(L(0()), L(y))) -> c_1()}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max^#(N(L(0()), L(y))) -> c_1()}
Details:
Interpretation Functions:
max(x1) = [1] x1 + [1]
L(x1) = [1] x1 + [0]
N(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
max^#(x1) = [1] x1 + [1]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] x1 + [0]
c_3(x1) = [1] x1 + [1]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))}
and weakly orienting the rules
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max^#(N(L(0()), L(y))) -> c_1()}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))}
Details:
Interpretation Functions:
max(x1) = [1] x1 + [1]
L(x1) = [1] x1 + [0]
N(x1, x2) = [1] x1 + [1] x2 + [1]
0() = [1]
s(x1) = [1] x1 + [3]
max^#(x1) = [1] x1 + [2]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] x1 + [0]
c_3(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:
{ max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
Weak Rules:
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max^#(N(L(0()), L(y))) -> c_1()}
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:
{ max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
Weak Rules:
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max^#(N(L(0()), L(y))) -> c_1()}
Details:
The problem is Match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ max_1(4) -> 7
, max_1(8) -> 7
, max_1(10) -> 9
, L_0(2) -> 2
, L_0(2) -> 7
, L_0(2) -> 9
, L_1(2) -> 5
, L_1(7) -> 6
, L_1(9) -> 5
, N_0(2, 2) -> 2
, N_0(2, 2) -> 7
, N_0(2, 2) -> 9
, N_1(2, 2) -> 8
, N_1(5, 5) -> 10
, N_1(5, 6) -> 4
, 0_0() -> 2
, 0_0() -> 7
, 0_0() -> 9
, s_0(2) -> 2
, s_0(2) -> 7
, s_0(2) -> 9
, s_1(9) -> 7
, s_1(9) -> 9
, max^#_0(2) -> 1
, max^#_1(4) -> 3
, c_1_0() -> 1
, c_1_1() -> 3
, c_3_1(3) -> 1}
4) {max^#(N(L(x), N(y, z))) ->
c_3(max^#(N(L(x), L(max(N(y, z))))))}
The usable rules for this path are the following:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))}
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:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y
, max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
Details:
We apply the weight gap principle, strictly orienting the rules
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y}
Details:
Interpretation Functions:
max(x1) = [1] x1 + [1]
L(x1) = [1] x1 + [0]
N(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [0]
s(x1) = [1] x1 + [0]
max^#(x1) = [1] x1 + [1]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] x1 + [0]
c_3(x1) = [1] x1 + [1]
Finally we apply the subprocessor
We apply the weight gap principle, strictly orienting the rules
{max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))}
and weakly orienting the rules
{ max(L(x)) -> x
, max(N(L(0()), L(y))) -> y}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))}
Details:
Interpretation Functions:
max(x1) = [1] x1 + [0]
L(x1) = [1] x1 + [0]
N(x1, x2) = [1] x1 + [1] x2 + [0]
0() = [11]
s(x1) = [1] x1 + [6]
max^#(x1) = [1] x1 + [0]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] x1 + [0]
c_3(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:
{ max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
Weak Rules:
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(L(x)) -> x
, max(N(L(0()), L(y))) -> y}
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:
{ max(N(L(x), N(y, z))) -> max(N(L(x), L(max(N(y, z)))))
, max^#(N(L(x), N(y, z))) -> c_3(max^#(N(L(x), L(max(N(y, z))))))}
Weak Rules:
{ max(N(L(s(x)), L(s(y)))) -> s(max(N(L(x), L(y))))
, max(L(x)) -> x
, max(N(L(0()), L(y))) -> y}
Details:
The problem is Match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ max_1(4) -> 7
, max_1(8) -> 7
, max_1(10) -> 9
, L_0(2) -> 2
, L_0(2) -> 7
, L_0(2) -> 9
, L_1(2) -> 5
, L_1(7) -> 6
, L_1(9) -> 5
, N_0(2, 2) -> 2
, N_0(2, 2) -> 7
, N_0(2, 2) -> 9
, N_1(2, 2) -> 8
, N_1(5, 5) -> 10
, N_1(5, 6) -> 4
, 0_0() -> 2
, 0_0() -> 7
, 0_0() -> 9
, s_0(2) -> 2
, s_0(2) -> 7
, s_0(2) -> 9
, s_1(9) -> 7
, s_1(9) -> 9
, max^#_0(2) -> 1
, max^#_1(4) -> 3
, c_3_1(3) -> 1}
5) {max^#(L(x)) -> c_0()}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
max(x1) = [0] x1 + [0]
L(x1) = [0] x1 + [0]
N(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
max^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1() = [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: {max^#(L(x)) -> c_0()}
Weak Rules: {}
Details:
We apply the weight gap principle, strictly orienting the rules
{max^#(L(x)) -> c_0()}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{max^#(L(x)) -> c_0()}
Details:
Interpretation Functions:
max(x1) = [0] x1 + [0]
L(x1) = [1] x1 + [0]
N(x1, x2) = [0] x1 + [0] x2 + [0]
0() = [0]
s(x1) = [0] x1 + [0]
max^#(x1) = [1] x1 + [1]
c_0() = [0]
c_1() = [0]
c_2(x1) = [0] 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: {max^#(L(x)) -> c_0()}
Details:
The given problem does not contain any strict rules