Tool CaT
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 4.31 |
|---|
stdout:
MAYBE
Problem:
purge(nil()) -> nil()
purge(.(x,y)) -> .(x,purge(remove(x,y)))
remove(x,nil()) -> nil()
remove(x,.(y,z)) -> if(=(x,y),remove(x,z),.(y,remove(x,z)))
Proof:
OpenTool IRC1
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 4.31 |
|---|
stdout:
MAYBE
Tool IRC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 4.31 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ purge(nil()) -> nil()
, purge(.(x, y)) -> .(x, purge(remove(x, y)))
, remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, 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: purge^#(nil()) -> c_0()
, 2: purge^#(.(x, y)) -> c_1(purge^#(remove(x, y)))
, 3: remove^#(x, nil()) -> c_2()
, 4: remove^#(x, .(y, z)) -> c_3(remove^#(x, z), remove^#(x, z))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ MAYBE ]
|
`->{3} [ NA ]
->{2} [ inherited ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{1}.
* Path {2}->{1}: NA
-----------------
The usable rules for this path are:
{ remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, z)))}
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 {4}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [0]
[0]
[0]
.(x1, x2) = [1 3 3] x1 + [0 0 0] x2 + [0]
[0 1 3] [0 0 0] [0]
[0 0 1] [0 0 0] [0]
remove(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]
if(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]
=(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]
purge^#(x1) = [0 0 0] x1 + [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]
remove^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules:
{remove^#(x, .(y, z)) -> c_3(remove^#(x, z), remove^#(x, z))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [0]
[0]
[0]
.(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]
remove(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]
if(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]
=(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]
purge^#(x1) = [0 0 0] x1 + [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]
remove^#(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_2() = [0]
[0]
[0]
c_3(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
[0 1 0] [0 1 0] [0]
[0 0 1] [0 0 1] [0]
We have not generated a proof for the resulting sub-problem.
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: purge^#(nil()) -> c_0()
, 2: purge^#(.(x, y)) -> c_1(purge^#(remove(x, y)))
, 3: remove^#(x, nil()) -> c_2()
, 4: remove^#(x, .(y, z)) -> c_3(remove^#(x, z), remove^#(x, z))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ MAYBE ]
|
`->{3} [ NA ]
->{2} [ inherited ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{1}.
* Path {2}->{1}: NA
-----------------
The usable rules for this path are:
{ remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, z)))}
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 {4}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [1 3] x1 + [0 0] x2 + [0]
[0 1] [0 0] [0]
remove(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
=(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
purge^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
remove^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[3 3] [3 3] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules:
{remove^#(x, .(y, z)) -> c_3(remove^#(x, z), remove^#(x, z))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
remove(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
=(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
purge^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1) = [0 0] x1 + [0]
[0 0] [0]
remove^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
[0 1] [0 1] [0]
We have not generated a proof for the resulting sub-problem.
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: purge^#(nil()) -> c_0()
, 2: purge^#(.(x, y)) -> c_1(purge^#(remove(x, y)))
, 3: remove^#(x, nil()) -> c_2()
, 4: remove^#(x, .(y, z)) -> c_3(remove^#(x, z), remove^#(x, z))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ MAYBE ]
|
`->{3} [ NA ]
->{2} [ inherited ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{1}.
* Path {2}->{1}: NA
-----------------
The usable rules for this path are:
{ remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, z)))}
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 {4}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [1] x1 + [0] x2 + [0]
remove(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
=(x1, x2) = [0] x1 + [0] x2 + [0]
purge^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
remove^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules:
{remove^#(x, .(y, z)) -> c_3(remove^#(x, z), remove^#(x, z))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {1, 2}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
remove(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
=(x1, x2) = [0] x1 + [0] x2 + [0]
purge^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
remove^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2) = [1] x1 + [1] x2 + [0]
We have not generated a proof for the resulting sub-problem.
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 4.31 |
|---|
stdout:
MAYBE
Tool RC2
| Execution Time | Unknown |
|---|
| Answer | MAYBE |
|---|
| Input | SK90 4.31 |
|---|
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ purge(nil()) -> nil()
, purge(.(x, y)) -> .(x, purge(remove(x, y)))
, remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, 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: purge^#(nil()) -> c_0()
, 2: purge^#(.(x, y)) -> c_1(x, purge^#(remove(x, y)))
, 3: remove^#(x, nil()) -> c_2()
, 4: remove^#(x, .(y, z)) ->
c_3(x, y, remove^#(x, z), y, remove^#(x, z))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ MAYBE ]
|
`->{3} [ NA ]
->{2} [ inherited ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{1}.
* Path {2}->{1}: NA
-----------------
The usable rules for this path are:
{ remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, z)))}
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 {4}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {3, 5}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [0]
[0]
[0]
.(x1, x2) = [1 3 3] x1 + [1 3 3] x2 + [0]
[0 1 3] [0 1 3] [0]
[0 0 1] [0 0 1] [0]
remove(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]
if(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]
=(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]
purge^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(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]
remove^#(x1, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[3 3 3] [3 3 3] [0]
[3 3 3] [3 3 3] [0]
c_2() = [0]
[0]
[0]
c_3(x1, x2, x3, x4, x5) = [0 0 0] x1 + [0 0 0] x2 + [1 0 0] x3 + [0 0 0] x4 + [1 0 0] x5 + [0]
[0 0 0] [0 0 0] [0 1 0] [0 0 0] [0 1 0] [0]
[0 0 0] [0 0 0] [0 0 1] [0 0 0] [0 0 1] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 3'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules:
{remove^#(x, .(y, z)) ->
c_3(x, y, remove^#(x, z), y, remove^#(x, z))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {3, 5}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
nil() = [0]
[0]
[0]
.(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]
remove(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]
if(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]
=(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]
purge^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_0() = [0]
[0]
[0]
c_1(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]
remove^#(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_2() = [0]
[0]
[0]
c_3(x1, x2, x3, x4, x5) = [0 0 0] x1 + [0 0 0] x2 + [1 0 0] x3 + [0 0 0] x4 + [1 0 0] x5 + [0]
[0 0 0] [0 0 0] [0 1 0] [0 0 0] [0 1 0] [0]
[0 0 0] [0 0 0] [0 0 1] [0 0 0] [0 0 1] [0]
We have not generated a proof for the resulting sub-problem.
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: purge^#(nil()) -> c_0()
, 2: purge^#(.(x, y)) -> c_1(x, purge^#(remove(x, y)))
, 3: remove^#(x, nil()) -> c_2()
, 4: remove^#(x, .(y, z)) ->
c_3(x, y, remove^#(x, z), y, remove^#(x, z))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ MAYBE ]
|
`->{3} [ NA ]
->{2} [ inherited ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{1}.
* Path {2}->{1}: NA
-----------------
The usable rules for this path are:
{ remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, z)))}
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 {4}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {3, 5}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [1 3] x1 + [1 3] x2 + [0]
[0 1] [0 1] [0]
remove(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
=(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
purge^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
remove^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[3 3] [3 3] [0]
c_2() = [0]
[0]
c_3(x1, x2, x3, x4, x5) = [0 0] x1 + [0 0] x2 + [1 0] x3 + [0 0] x4 + [1 0] x5 + [0]
[0 0] [0 0] [0 1] [0 0] [0 1] [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 2'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules:
{remove^#(x, .(y, z)) ->
c_3(x, y, remove^#(x, z), y, remove^#(x, z))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {3, 5}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0 0] x1 + [0]
[0 0] [0]
nil() = [0]
[0]
.(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
remove(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
if(x1, x2, x3) = [0 0] x1 + [0 0] x2 + [0 0] x3 + [0]
[0 0] [0 0] [0 0] [0]
=(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
purge^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_0() = [0]
[0]
c_1(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
remove^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_2() = [0]
[0]
c_3(x1, x2, x3, x4, x5) = [0 0] x1 + [0 0] x2 + [1 0] x3 + [0 0] x4 + [1 0] x5 + [0]
[0 0] [0 0] [0 1] [0 0] [0 1] [0]
We have not generated a proof for the resulting sub-problem.
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: purge^#(nil()) -> c_0()
, 2: purge^#(.(x, y)) -> c_1(x, purge^#(remove(x, y)))
, 3: remove^#(x, nil()) -> c_2()
, 4: remove^#(x, .(y, z)) ->
c_3(x, y, remove^#(x, z), y, remove^#(x, z))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{4} [ MAYBE ]
|
`->{3} [ NA ]
->{2} [ inherited ]
|
`->{1} [ NA ]
Sub-problems:
-------------
* Path {2}: inherited
-------------------
This path is subsumed by the proof of path {2}->{1}.
* Path {2}->{1}: NA
-----------------
The usable rules for this path are:
{ remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, z)))}
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 {4}: MAYBE
---------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {3, 5}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [1] x1 + [1] x2 + [0]
remove(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
=(x1, x2) = [0] x1 + [0] x2 + [0]
purge^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1, x2) = [0] x1 + [0] x2 + [0]
remove^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2, x3, x4, x5) = [0] x1 + [0] x2 + [1] x3 + [0] x4 + [1] x5 + [0]
We apply the sub-processor on the resulting sub-problem:
'matrix-interpretation of dimension 1'
--------------------------------------
Answer: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules:
{remove^#(x, .(y, z)) ->
c_3(x, y, remove^#(x, z), y, remove^#(x, z))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {4}->{3}: NA
-----------------
The usable rules of this path are empty.
The weightgap principle applies, using the following adequate RMI:
The following argument positions are usable:
Uargs(purge) = {}, Uargs(.) = {}, Uargs(remove) = {},
Uargs(if) = {}, Uargs(=) = {}, Uargs(purge^#) = {},
Uargs(c_1) = {}, Uargs(remove^#) = {}, Uargs(c_3) = {3, 5}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
purge(x1) = [0] x1 + [0]
nil() = [0]
.(x1, x2) = [0] x1 + [0] x2 + [0]
remove(x1, x2) = [0] x1 + [0] x2 + [0]
if(x1, x2, x3) = [0] x1 + [0] x2 + [0] x3 + [0]
=(x1, x2) = [0] x1 + [0] x2 + [0]
purge^#(x1) = [0] x1 + [0]
c_0() = [0]
c_1(x1, x2) = [0] x1 + [0] x2 + [0]
remove^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_2() = [0]
c_3(x1, x2, x3, x4, x5) = [0] x1 + [0] x2 + [1] x3 + [0] x4 + [1] x5 + [0]
We have not generated a proof for the resulting sub-problem.
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 pair1rc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 4.31 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ purge(nil()) -> nil()
, purge(.(x, y)) -> .(x, purge(remove(x, y)))
, remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, z)))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool pair3irc
| Execution Time | Unknown |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 4.31 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ purge(nil()) -> nil()
, purge(.(x, y)) -> .(x, purge(remove(x, y)))
, remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, 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 4.31 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ purge(nil()) -> nil()
, purge(.(x, y)) -> .(x, purge(remove(x, y)))
, remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, 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 | TIMEOUT |
|---|
| Input | SK90 4.31 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ purge(nil()) -> nil()
, purge(.(x, y)) -> .(x, purge(remove(x, y)))
, remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, z)))}
StartTerms: basic terms
Strategy: none
Certificate: TIMEOUT
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
Computation stopped due to timeout after 60.0 seconds
Arrrr..Tool tup3irc
| Execution Time | 60.307274ms |
|---|
| Answer | TIMEOUT |
|---|
| Input | SK90 4.31 |
|---|
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs:
{ purge(nil()) -> nil()
, purge(.(x, y)) -> .(x, purge(remove(x, y)))
, remove(x, nil()) -> nil()
, remove(x, .(y, z)) ->
if(=(x, y), remove(x, z), .(y, remove(x, 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..