'Weak Dependency Graph [60.0]'
------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(f(X)) -> c(n__f(g(n__f(X))))
, c(X) -> d(activate(X))
, h(X) -> c(n__d(X))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X}
Details:
We have computed the following set of weak (innermost) dependency pairs:
{ f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))
, c^#(X) -> c_1(d^#(activate(X)))
, h^#(X) -> c_2(c^#(n__d(X)))
, f^#(X) -> c_3()
, d^#(X) -> c_4()
, activate^#(n__f(X)) -> c_5(f^#(X))
, activate^#(n__d(X)) -> c_6(d^#(X))
, activate^#(X) -> c_7()}
The usable rules are:
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))}
The estimated dependency graph contains the following edges:
{f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))}
==> {c^#(X) -> c_1(d^#(activate(X)))}
{c^#(X) -> c_1(d^#(activate(X)))}
==> {d^#(X) -> c_4()}
{h^#(X) -> c_2(c^#(n__d(X)))}
==> {c^#(X) -> c_1(d^#(activate(X)))}
{activate^#(n__f(X)) -> c_5(f^#(X))}
==> {f^#(X) -> c_3()}
{activate^#(n__f(X)) -> c_5(f^#(X))}
==> {f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))}
{activate^#(n__d(X)) -> c_6(d^#(X))}
==> {d^#(X) -> c_4()}
We consider the following path(s):
1) { activate^#(n__f(X)) -> c_5(f^#(X))
, f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))
, c^#(X) -> c_1(d^#(activate(X)))}
The usable rules for this path are the following:
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))}
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [1] x1 + [8]
c(x1) = [1] x1 + [11]
n__f(x1) = [1] x1 + [0]
g(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
activate(x1) = [1] x1 + [9]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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^#(X) -> c_1(d^#(activate(X)))}
Weak Rules:
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))
, activate^#(n__f(X)) -> c_5(f^#(X))}
Details:
We apply the weight gap principle, strictly orienting the rules
{c^#(X) -> c_1(d^#(activate(X)))}
and weakly orienting the rules
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))
, activate^#(n__f(X)) -> c_5(f^#(X))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{c^#(X) -> c_1(d^#(activate(X)))}
Details:
Interpretation Functions:
f(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
n__f(x1) = [1] x1 + [0]
g(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [0]
activate(x1) = [1] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [1] x1 + [9]
c_0(x1) = [1] x1 + [1]
c^#(x1) = [1] x1 + [2]
c_1(x1) = [1] x1 + [1]
d^#(x1) = [1] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [1] x1 + [12]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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^#(X) -> c_1(d^#(activate(X)))
, activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))
, activate^#(n__f(X)) -> c_5(f^#(X))}
Details:
The given problem does not contain any strict rules
2) { activate^#(n__f(X)) -> c_5(f^#(X))
, f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))
, c^#(X) -> c_1(d^#(activate(X)))
, d^#(X) -> c_4()}
The usable rules for this path are the following:
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))}
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [1] x1 + [8]
c(x1) = [1] x1 + [11]
n__f(x1) = [1] x1 + [0]
g(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
activate(x1) = [1] x1 + [9]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {d^#(X) -> c_4()}
Weak Rules:
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, c^#(X) -> c_1(d^#(activate(X)))
, f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))
, activate^#(n__f(X)) -> c_5(f^#(X))}
Details:
We apply the weight gap principle, strictly orienting the rules
{d^#(X) -> c_4()}
and weakly orienting the rules
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, c^#(X) -> c_1(d^#(activate(X)))
, f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))
, activate^#(n__f(X)) -> c_5(f^#(X))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{d^#(X) -> c_4()}
Details:
Interpretation Functions:
f(x1) = [1] x1 + [1]
c(x1) = [1] x1 + [2]
n__f(x1) = [1] x1 + [0]
g(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [0]
activate(x1) = [1] x1 + [1]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [1] x1 + [2]
c_0(x1) = [1] x1 + [0]
c^#(x1) = [1] x1 + [3]
c_1(x1) = [1] x1 + [1]
d^#(x1) = [1] x1 + [1]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [1] x1 + [13]
c_5(x1) = [1] x1 + [6]
c_6(x1) = [0] x1 + [0]
c_7() = [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:
{ d^#(X) -> c_4()
, activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, c^#(X) -> c_1(d^#(activate(X)))
, f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))
, activate^#(n__f(X)) -> c_5(f^#(X))}
Details:
The given problem does not contain any strict rules
3) { h^#(X) -> c_2(c^#(n__d(X)))
, c^#(X) -> c_1(d^#(activate(X)))}
The usable rules for this path are the following:
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))}
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [1] x1 + [8]
c(x1) = [1] x1 + [11]
n__f(x1) = [1] x1 + [0]
g(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
activate(x1) = [1] x1 + [9]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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^#(X) -> c_1(d^#(activate(X)))}
Weak Rules:
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, h^#(X) -> c_2(c^#(n__d(X)))}
Details:
We apply the weight gap principle, strictly orienting the rules
{c^#(X) -> c_1(d^#(activate(X)))}
and weakly orienting the rules
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, h^#(X) -> c_2(c^#(n__d(X)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{c^#(X) -> c_1(d^#(activate(X)))}
Details:
Interpretation Functions:
f(x1) = [1] x1 + [0]
c(x1) = [1] x1 + [0]
n__f(x1) = [1] x1 + [0]
g(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [0]
activate(x1) = [1] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [1] x1 + [8]
c_1(x1) = [1] x1 + [1]
d^#(x1) = [1] x1 + [0]
h^#(x1) = [1] x1 + [12]
c_2(x1) = [1] x1 + [1]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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^#(X) -> c_1(d^#(activate(X)))
, activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, h^#(X) -> c_2(c^#(n__d(X)))}
Details:
The given problem does not contain any strict rules
4) { h^#(X) -> c_2(c^#(n__d(X)))
, c^#(X) -> c_1(d^#(activate(X)))
, d^#(X) -> c_4()}
The usable rules for this path are the following:
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))}
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [1] x1 + [8]
c(x1) = [1] x1 + [11]
n__f(x1) = [1] x1 + [0]
g(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [1]
activate(x1) = [1] x1 + [9]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {d^#(X) -> c_4()}
Weak Rules:
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, c^#(X) -> c_1(d^#(activate(X)))
, h^#(X) -> c_2(c^#(n__d(X)))}
Details:
We apply the weight gap principle, strictly orienting the rules
{d^#(X) -> c_4()}
and weakly orienting the rules
{ activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, c^#(X) -> c_1(d^#(activate(X)))
, h^#(X) -> c_2(c^#(n__d(X)))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{d^#(X) -> c_4()}
Details:
Interpretation Functions:
f(x1) = [1] x1 + [1]
c(x1) = [1] x1 + [2]
n__f(x1) = [1] x1 + [0]
g(x1) = [1] x1 + [0]
d(x1) = [1] x1 + [0]
activate(x1) = [1] x1 + [1]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [1] x1 + [8]
c_1(x1) = [1] x1 + [2]
d^#(x1) = [1] x1 + [2]
h^#(x1) = [1] x1 + [12]
c_2(x1) = [1] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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:
{ d^#(X) -> c_4()
, activate(n__f(X)) -> f(X)
, activate(n__d(X)) -> d(X)
, activate(X) -> X
, f(f(X)) -> c(n__f(g(n__f(X))))
, f(X) -> n__f(X)
, d(X) -> n__d(X)
, c(X) -> d(activate(X))
, c^#(X) -> c_1(d^#(activate(X)))
, h^#(X) -> c_2(c^#(n__d(X)))}
Details:
The given problem does not contain any strict rules
5) { activate^#(n__f(X)) -> c_5(f^#(X))
, f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))}
Weak Rules: {activate^#(n__f(X)) -> c_5(f^#(X))}
Details:
We apply the weight gap principle, strictly orienting the rules
{f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))}
and weakly orienting the rules
{activate^#(n__f(X)) -> c_5(f^#(X))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))}
Details:
Interpretation Functions:
f(x1) = [1] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [1] x1 + [0]
g(x1) = [1] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [1] x1 + [1]
c_0(x1) = [1] x1 + [0]
c^#(x1) = [1] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [1] x1 + [1]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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:
{ f^#(f(X)) -> c_0(c^#(n__f(g(n__f(X)))))
, activate^#(n__f(X)) -> c_5(f^#(X))}
Details:
The given problem does not contain any strict rules
6) {h^#(X) -> c_2(c^#(n__d(X)))}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {h^#(X) -> c_2(c^#(n__d(X)))}
Weak Rules: {}
Details:
We apply the weight gap principle, strictly orienting the rules
{h^#(X) -> c_2(c^#(n__d(X)))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{h^#(X) -> c_2(c^#(n__d(X)))}
Details:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [1] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [1] x1 + [8]
c_2(x1) = [1] x1 + [1]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {h^#(X) -> c_2(c^#(n__d(X)))}
Details:
The given problem does not contain any strict rules
7) { activate^#(n__f(X)) -> c_5(f^#(X))
, f^#(X) -> c_3()}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {f^#(X) -> c_3()}
Weak Rules: {activate^#(n__f(X)) -> c_5(f^#(X))}
Details:
We apply the weight gap principle, strictly orienting the rules
{f^#(X) -> c_3()}
and weakly orienting the rules
{activate^#(n__f(X)) -> c_5(f^#(X))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{f^#(X) -> c_3()}
Details:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [1] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [1] x1 + [1]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [1] x1 + [1]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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:
{ f^#(X) -> c_3()
, activate^#(n__f(X)) -> c_5(f^#(X))}
Details:
The given problem does not contain any strict rules
8) {activate^#(n__d(X)) -> c_6(d^#(X))}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {activate^#(n__d(X)) -> c_6(d^#(X))}
Weak Rules: {}
Details:
We apply the weight gap principle, strictly orienting the rules
{activate^#(n__d(X)) -> c_6(d^#(X))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{activate^#(n__d(X)) -> c_6(d^#(X))}
Details:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [1] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [1] x1 + [1]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [1] x1 + [0]
c_7() = [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: {activate^#(n__d(X)) -> c_6(d^#(X))}
Details:
The given problem does not contain any strict rules
9) {activate^#(n__f(X)) -> c_5(f^#(X))}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {activate^#(n__f(X)) -> c_5(f^#(X))}
Weak Rules: {}
Details:
We apply the weight gap principle, strictly orienting the rules
{activate^#(n__f(X)) -> c_5(f^#(X))}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{activate^#(n__f(X)) -> c_5(f^#(X))}
Details:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [1] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [1] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [1] x1 + [1]
c_5(x1) = [1] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {activate^#(n__f(X)) -> c_5(f^#(X))}
Details:
The given problem does not contain any strict rules
10)
{ activate^#(n__d(X)) -> c_6(d^#(X))
, d^#(X) -> c_4()}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {d^#(X) -> c_4()}
Weak Rules: {activate^#(n__d(X)) -> c_6(d^#(X))}
Details:
We apply the weight gap principle, strictly orienting the rules
{d^#(X) -> c_4()}
and weakly orienting the rules
{activate^#(n__d(X)) -> c_6(d^#(X))}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{d^#(X) -> c_4()}
Details:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [1] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [1] x1 + [1]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [1] x1 + [1]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [1] x1 + [0]
c_7() = [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:
{ d^#(X) -> c_4()
, activate^#(n__d(X)) -> c_6(d^#(X))}
Details:
The given problem does not contain any strict rules
11)
{activate^#(X) -> c_7()}
The usable rules for this path are empty.
We have oriented the usable rules with the following strongly linear interpretation:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [0] x1 + [0]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {activate^#(X) -> c_7()}
Weak Rules: {}
Details:
We apply the weight gap principle, strictly orienting the rules
{activate^#(X) -> c_7()}
and weakly orienting the rules
{}
using the following strongly linear interpretation:
Processor 'Matrix Interpretation' oriented the following rules strictly:
{activate^#(X) -> c_7()}
Details:
Interpretation Functions:
f(x1) = [0] x1 + [0]
c(x1) = [0] x1 + [0]
n__f(x1) = [0] x1 + [0]
g(x1) = [0] x1 + [0]
d(x1) = [0] x1 + [0]
activate(x1) = [0] x1 + [0]
h(x1) = [0] x1 + [0]
n__d(x1) = [0] x1 + [0]
f^#(x1) = [0] x1 + [0]
c_0(x1) = [0] x1 + [0]
c^#(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
d^#(x1) = [0] x1 + [0]
h^#(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
c_3() = [0]
c_4() = [0]
activate^#(x1) = [1] x1 + [4]
c_5(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [0]
c_7() = [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: {activate^#(X) -> c_7()}
Details:
The given problem does not contain any strict rules