Tool CaT
Execution Time | Unknown |
---|
Answer | MAYBE |
---|
Input | SK90 4.42 |
---|
stdout:
MAYBE
Problem:
f(a(),g(y)) -> g(g(y))
f(g(x),a()) -> f(x,g(a()))
f(g(x),g(y)) -> h(g(y),x,g(y))
h(g(x),y,z) -> f(y,h(x,y,z))
h(a(),y,z) -> z
Proof:
OpenTool IRC1
Execution Time | Unknown |
---|
Answer | MAYBE |
---|
Input | SK90 4.42 |
---|
stdout:
MAYBE
Tool IRC2
Execution Time | Unknown |
---|
Answer | MAYBE |
---|
Input | SK90 4.42 |
---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z}
Proof Output:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(a(), g(y)) -> c_0()
, 2: f^#(g(x), a()) -> c_1(f^#(x, g(a())))
, 3: f^#(g(x), g(y)) -> c_2(h^#(g(y), x, g(y)))
, 4: h^#(g(x), y, z) -> c_3(f^#(y, h(x, y, z)))
, 5: h^#(a(), y, z) -> c_4()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{5} [ YES(?,O(1)) ]
->{2,4,3} [ inherited ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2,4,3}: inherited
-----------------------
This path is subsumed by the proof of path {2,4,3}->{1}.
* Path {2,4,3}->{1}: NA
---------------------
The usable rules for this path are:
{ h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z
, f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {5}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {}, Uargs(h) = {}, Uargs(f^#) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(h^#) = {}, Uargs(c_3) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
a() = [0]
[0]
[0]
g(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
h(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0 0 0] [0]
f^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_2(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
h^#(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0 0 0] [0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4() = [0]
[0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {h^#(a(), y, z) -> c_4()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(h^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
a() = [2]
[2]
[2]
h^#(x1, x2, x3) = [0 2 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [7]
[2 2 0] [0 0 0] [0 0 0] [3]
[2 2 2] [0 0 0] [0 0 0] [3]
c_4() = [0]
[1]
[1]
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(a(), g(y)) -> c_0()
, 2: f^#(g(x), a()) -> c_1(f^#(x, g(a())))
, 3: f^#(g(x), g(y)) -> c_2(h^#(g(y), x, g(y)))
, 4: h^#(g(x), y, z) -> c_3(f^#(y, h(x, y, z)))
, 5: h^#(a(), y, z) -> c_4()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{5} [ YES(?,O(1)) ]
->{2,4,3} [ inherited ]
|
`->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {2,4,3}: inherited
-----------------------
This path is subsumed by the proof of path {2,4,3}->{1}.
* Path {2,4,3}->{1}: MAYBE
------------------------
The usable rules for this path are:
{ h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z
, f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f^#(g(x), a()) -> c_1(f^#(x, g(a())))
, h^#(g(x), y, z) -> c_3(f^#(y, h(x, y, z)))
, f^#(g(x), g(y)) -> c_2(h^#(g(y), x, g(y)))
, f^#(a(), g(y)) -> c_0()
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z
, f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))}
Proof Output:
The input cannot be shown compatible
* Path {5}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {}, Uargs(h) = {}, Uargs(f^#) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(h^#) = {}, Uargs(c_3) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
a() = [0]
[0]
g(x1) = [0 0] x1 + [0]
[0 0] [0]
h(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
f^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
h^#(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4() = [0]
[0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {h^#(a(), y, z) -> c_4()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(h^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
a() = [2]
[2]
h^#(x1, x2, x3) = [2 0] x1 + [0 0] x2 + [0 0] x3 + [7]
[2 2] [0 0] [0 0] [7]
c_4() = [0]
[1]
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(a(), g(y)) -> c_0()
, 2: f^#(g(x), a()) -> c_1(f^#(x, g(a())))
, 3: f^#(g(x), g(y)) -> c_2(h^#(g(y), x, g(y)))
, 4: h^#(g(x), y, z) -> c_3(f^#(y, h(x, y, z)))
, 5: h^#(a(), y, z) -> c_4()}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{5} [ YES(?,O(1)) ]
->{2,4,3} [ inherited ]
|
`->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {2,4,3}: inherited
-----------------------
This path is subsumed by the proof of path {2,4,3}->{1}.
* Path {2,4,3}->{1}: MAYBE
------------------------
The usable rules for this path are:
{ h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z
, f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ f^#(g(x), a()) -> c_1(f^#(x, g(a())))
, h^#(g(x), y, z) -> c_3(f^#(y, h(x, y, z)))
, f^#(g(x), g(y)) -> c_2(h^#(g(y), x, g(y)))
, f^#(a(), g(y)) -> c_0()
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z
, f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))}
Proof Output:
The input cannot be shown compatible
* Path {5}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {}, Uargs(h) = {}, Uargs(f^#) = {},
Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(h^#) = {}, Uargs(c_3) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0] x1 + [0] x2 + [0]
a() = [0]
g(x1) = [0] x1 + [0]
h(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
f^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
h^#(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
c_3(x1) = [0] x1 + [0]
c_4() = [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {h^#(a(), y, z) -> c_4()}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(h^#) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
a() = [7]
h^#(x1, x2, x3) = [1] x1 + [0] x2 + [0] x3 + [7]
c_4() = [1]
4) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
Tool RC1
Execution Time | Unknown |
---|
Answer | MAYBE |
---|
Input | SK90 4.42 |
---|
stdout:
MAYBE
Tool RC2
Execution Time | Unknown |
---|
Answer | MAYBE |
---|
Input | SK90 4.42 |
---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z}
Proof Output:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(a(), g(y)) -> c_0(y)
, 2: f^#(g(x), a()) -> c_1(f^#(x, g(a())))
, 3: f^#(g(x), g(y)) -> c_2(h^#(g(y), x, g(y)))
, 4: h^#(g(x), y, z) -> c_3(f^#(y, h(x, y, z)))
, 5: h^#(a(), y, z) -> c_4(z)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{5} [ YES(?,O(1)) ]
->{2,4,3} [ inherited ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2,4,3}: inherited
-----------------------
This path is subsumed by the proof of path {2,4,3}->{1}.
* Path {2,4,3}->{1}: NA
---------------------
The usable rules for this path are:
{ h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z
, f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We have not generated a proof for the resulting sub-problem.
* Path {5}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {}, Uargs(h) = {}, Uargs(f^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(h^#) = {},
Uargs(c_3) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
a() = [0]
[0]
[0]
g(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
h(x1, x2, x3) = [0 0 0] x1 + [0 0 0] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0 0 0] [0]
f^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
c_0(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_1(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_2(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
h^#(x1, x2, x3) = [0 0 0] x1 + [3 3 3] x2 + [0 0 0] x3 + [0]
[0 0 0] [0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0 0 0] [0]
c_3(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_4(x1) = [1 1 1] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {h^#(a(), y, z) -> c_4(z)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(h^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
a() = [2]
[0]
[2]
h^#(x1, x2, x3) = [2 0 2] x1 + [0 0 0] x2 + [7 7 7] x3 + [7]
[2 0 2] [0 0 0] [7 7 7] [7]
[2 0 2] [0 0 0] [7 7 7] [7]
c_4(x1) = [1 3 3] x1 + [0]
[1 1 1] [1]
[1 1 1] [1]
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(a(), g(y)) -> c_0(y)
, 2: f^#(g(x), a()) -> c_1(f^#(x, g(a())))
, 3: f^#(g(x), g(y)) -> c_2(h^#(g(y), x, g(y)))
, 4: h^#(g(x), y, z) -> c_3(f^#(y, h(x, y, z)))
, 5: h^#(a(), y, z) -> c_4(z)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{5} [ YES(?,O(1)) ]
->{2,4,3} [ inherited ]
|
`->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {2,4,3}: inherited
-----------------------
This path is subsumed by the proof of path {2,4,3}->{1}.
* Path {2,4,3}->{1}: MAYBE
------------------------
The usable rules for this path are:
{ h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z
, f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ f^#(g(x), a()) -> c_1(f^#(x, g(a())))
, h^#(g(x), y, z) -> c_3(f^#(y, h(x, y, z)))
, f^#(g(x), g(y)) -> c_2(h^#(g(y), x, g(y)))
, f^#(a(), g(y)) -> c_0(y)
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z
, f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))}
Proof Output:
The input cannot be shown compatible
* Path {5}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {}, Uargs(h) = {}, Uargs(f^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(h^#) = {},
Uargs(c_3) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
a() = [0]
[0]
g(x1) = [0 0] x1 + [0]
[0 0] [0]
h(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
f^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_0(x1) = [0 0] x1 + [0]
[0 0] [0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
c_2(x1) = [0 0] x1 + [0]
[0 0] [0]
h^#(x1, x2, x3) = [0 0] x1 + [3 3] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
c_3(x1) = [0 0] x1 + [0]
[0 0] [0]
c_4(x1) = [1 1] x1 + [0]
[0 0] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {h^#(a(), y, z) -> c_4(z)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(h^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
a() = [2]
[2]
h^#(x1, x2, x3) = [2 2] x1 + [0 0] x2 + [7 7] x3 + [7]
[2 2] [0 0] [7 7] [3]
c_4(x1) = [1 3] x1 + [0]
[1 1] [1]
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: f^#(a(), g(y)) -> c_0(y)
, 2: f^#(g(x), a()) -> c_1(f^#(x, g(a())))
, 3: f^#(g(x), g(y)) -> c_2(h^#(g(y), x, g(y)))
, 4: h^#(g(x), y, z) -> c_3(f^#(y, h(x, y, z)))
, 5: h^#(a(), y, z) -> c_4(z)}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{5} [ YES(?,O(1)) ]
->{2,4,3} [ inherited ]
|
`->{1} [ MAYBE ]
Sub-problems:
-------------
* Path {2,4,3}: inherited
-----------------------
This path is subsumed by the proof of path {2,4,3}->{1}.
* Path {2,4,3}->{1}: MAYBE
------------------------
The usable rules for this path are:
{ h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z
, f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))}
The weight gap principle does not apply:
The input cannot be shown compatible
Complexity induced by the adequate RMI: MAYBE
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ f^#(g(x), a()) -> c_1(f^#(x, g(a())))
, h^#(g(x), y, z) -> c_3(f^#(y, h(x, y, z)))
, f^#(g(x), g(y)) -> c_2(h^#(g(y), x, g(y)))
, f^#(a(), g(y)) -> c_0(y)
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z
, f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))}
Proof Output:
The input cannot be shown compatible
* Path {5}: YES(?,O(1))
---------------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(f) = {}, Uargs(g) = {}, Uargs(h) = {}, Uargs(f^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(c_2) = {}, Uargs(h^#) = {},
Uargs(c_3) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
f(x1, x2) = [0] x1 + [0] x2 + [0]
a() = [0]
g(x1) = [0] x1 + [0]
h(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
f^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1) = [0] x1 + [0]
c_2(x1) = [0] x1 + [0]
h^#(x1, x2, x3) = [0] x1 + [3] x2 + [0] x3 + [0]
c_3(x1) = [0] x1 + [0]
c_4(x1) = [1] x1 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: YES(?,O(1))
Input Problem: DP runtime-complexity with respect to
Strict Rules: {h^#(a(), y, z) -> c_4(z)}
Weak Rules: {}
Proof Output:
The following argument positions are usable:
Uargs(h^#) = {}, Uargs(c_4) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
a() = [5]
h^#(x1, x2, x3) = [3] x1 + [0] x2 + [7] x3 + [0]
c_4(x1) = [1] x1 + [0]
4) 'matrix-interpretation of dimension 1' failed due to the following reason:
The input cannot be shown compatible
5) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
6) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason:
match-boundness of the problem could not be verified.
Tool pair2rc
Execution Time | Unknown |
---|
Answer | TIMEOUT |
---|
Input | SK90 4.42 |
---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair3irc
Execution Time | Unknown |
---|
Answer | TIMEOUT |
---|
Input | SK90 4.42 |
---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair3rc
Execution Time | Unknown |
---|
Answer | TIMEOUT |
---|
Input | SK90 4.42 |
---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool rc
Execution Time | Unknown |
---|
Answer | MAYBE |
---|
Input | SK90 4.42 |
---|
stdout:
MAYBE
We consider the following Problem:
Strict Trs:
{ f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z}
StartTerms: basic terms
Strategy: none
Certificate: MAYBE
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Fastest' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Sequentially' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
Empty strict component of the problem is NOT empty.
2) 'Fastest' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'matrix-interpretation of dimension 4 (timeout of 100.0 seconds)' failed due to the following reason:
The input cannot be shown compatible
2) 'matrix-interpretation of dimension 3 (timeout of 100.0 seconds)' failed due to the following reason:
The input cannot be shown compatible
3) 'matrix-interpretation of dimension 2 (timeout of 100.0 seconds)' failed due to the following reason:
The input cannot be shown compatible
2) 'Fastest' failed due to the following reason:
None of the processors succeeded.
Details of failed attempt(s):
-----------------------------
1) 'Bounds with minimal-enrichment and initial automaton 'match' (timeout of 100.0 seconds)' failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'Bounds with perSymbol-enrichment and initial automaton 'match' (timeout of 5.0 seconds)' failed due to the following reason:
match-boundness of the problem could not be verified.
2) 'dp' failed due to the following reason:
We have computed the following dependency pairs
Strict Dependency Pairs:
{ f^#(a(), g(y)) -> c_1(y)
, f^#(g(x), a()) -> c_2(f^#(x, g(a())))
, f^#(g(x), g(y)) -> c_3(h^#(g(y), x, g(y)))
, h^#(g(x), y, z) -> c_4(f^#(y, h(x, y, z)))
, h^#(a(), y, z) -> c_5(z)}
We consider the following Problem:
Strict DPs:
{ f^#(a(), g(y)) -> c_1(y)
, f^#(g(x), a()) -> c_2(f^#(x, g(a())))
, f^#(g(x), g(y)) -> c_3(h^#(g(y), x, g(y)))
, h^#(g(x), y, z) -> c_4(f^#(y, h(x, y, z)))
, h^#(a(), y, z) -> c_5(z)}
Strict Trs:
{ f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z}
StartTerms: basic terms
Strategy: none
Certificate: MAYBE
Application of 'usablerules':
-----------------------------
All rules are usable.
No subproblems were generated.
Arrrr..Tool tup3irc
Execution Time | 61.71491ms |
---|
Answer | TIMEOUT |
---|
Input | SK90 4.42 |
---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ f(a(), g(y)) -> g(g(y))
, f(g(x), a()) -> f(x, g(a()))
, f(g(x), g(y)) -> h(g(y), x, g(y))
, h(g(x), y, z) -> f(y, h(x, y, z))
, h(a(), y, z) -> z}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..