Tool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: innermost runtime-complexity with respect to
Rules:
{ app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))
, from(X) -> cons(X, from(s(X)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, prefix(L) -> cons(nil(), zWadr(L, prefix(L)))}
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: app^#(nil(), YS) -> c_0()
, 2: app^#(cons(X, XS), YS) -> c_1(app^#(XS, YS))
, 3: from^#(X) -> c_2(from^#(s(X)))
, 4: zWadr^#(nil(), YS) -> c_3()
, 5: zWadr^#(XS, nil()) -> c_4()
, 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
c_5(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
, 7: prefix^#(L) -> c_6(zWadr^#(L, prefix(L)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{7} [ inherited ]
|
|->{4} [ NA ]
|
|->{5} [ NA ]
|
`->{6} [ inherited ]
|
|->{1} [ NA ]
|
|->{2} [ inherited ]
| |
| `->{1} [ NA ]
|
|->{4} [ NA ]
|
`->{5} [ NA ]
->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: 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(app) = {}, Uargs(cons) = {}, Uargs(from) = {}, Uargs(s) = {},
Uargs(zWadr) = {}, Uargs(prefix) = {}, Uargs(app^#) = {},
Uargs(c_1) = {}, Uargs(from^#) = {}, Uargs(c_2) = {1},
Uargs(zWadr^#) = {}, Uargs(c_5) = {}, Uargs(prefix^#) = {},
Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
app(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]
nil() = [0]
[0]
[0]
cons(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]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s(x1) = [1 1 0] x1 + [0]
[0 0 1] [0]
[0 0 0] [0]
zWadr(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]
prefix(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
app^#(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]
from^#(x1) = [3 3 3] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_2(x1) = [1 0 0] x1 + [0]
[0 1 0] [0]
[0 0 1] [0]
zWadr^#(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_3() = [0]
[0]
[0]
c_4() = [0]
[0]
[0]
c_5(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]
prefix^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] 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: MAYBE
Input Problem: innermost DP runtime-complexity with respect to
Strict Rules: {from^#(X) -> c_2(from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {7}: inherited
-------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{4}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{5}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}: inherited
------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{1}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{2}: inherited
-----------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{2}->{1}: NA
---------------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{4}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{5}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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.
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: app^#(nil(), YS) -> c_0()
, 2: app^#(cons(X, XS), YS) -> c_1(app^#(XS, YS))
, 3: from^#(X) -> c_2(from^#(s(X)))
, 4: zWadr^#(nil(), YS) -> c_3()
, 5: zWadr^#(XS, nil()) -> c_4()
, 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
c_5(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
, 7: prefix^#(L) -> c_6(zWadr^#(L, prefix(L)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{7} [ inherited ]
|
|->{4} [ NA ]
|
|->{5} [ NA ]
|
`->{6} [ inherited ]
|
|->{1} [ NA ]
|
|->{2} [ inherited ]
| |
| `->{1} [ NA ]
|
|->{4} [ NA ]
|
`->{5} [ NA ]
->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: 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(app) = {}, Uargs(cons) = {}, Uargs(from) = {}, Uargs(s) = {},
Uargs(zWadr) = {}, Uargs(prefix) = {}, Uargs(app^#) = {},
Uargs(c_1) = {}, Uargs(from^#) = {}, Uargs(c_2) = {1},
Uargs(zWadr^#) = {}, Uargs(c_5) = {}, Uargs(prefix^#) = {},
Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
s(x1) = [1 0] x1 + [0]
[0 1] [0]
zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
prefix(x1) = [0 0] x1 + [0]
[0 0] [0]
app^#(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]
from^#(x1) = [3 3] x1 + [0]
[3 3] [0]
c_2(x1) = [1 0] x1 + [0]
[0 1] [0]
zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3() = [0]
[0]
c_4() = [0]
[0]
c_5(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
prefix^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [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: {from^#(X) -> c_2(from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {7}: inherited
-------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{4}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{5}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}: inherited
------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{1}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{2}: inherited
-----------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{2}->{1}: NA
---------------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{4}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{5}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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.
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: app^#(nil(), YS) -> c_0()
, 2: app^#(cons(X, XS), YS) -> c_1(app^#(XS, YS))
, 3: from^#(X) -> c_2(from^#(s(X)))
, 4: zWadr^#(nil(), YS) -> c_3()
, 5: zWadr^#(XS, nil()) -> c_4()
, 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
c_5(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
, 7: prefix^#(L) -> c_6(zWadr^#(L, prefix(L)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{7} [ inherited ]
|
|->{4} [ NA ]
|
|->{5} [ NA ]
|
`->{6} [ inherited ]
|
|->{1} [ NA ]
|
|->{2} [ inherited ]
| |
| `->{1} [ NA ]
|
|->{4} [ NA ]
|
`->{5} [ NA ]
->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: 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(app) = {}, Uargs(cons) = {}, Uargs(from) = {}, Uargs(s) = {},
Uargs(zWadr) = {}, Uargs(prefix) = {}, Uargs(app^#) = {},
Uargs(c_1) = {}, Uargs(from^#) = {}, Uargs(c_2) = {1},
Uargs(zWadr^#) = {}, Uargs(c_5) = {}, Uargs(prefix^#) = {},
Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
app(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
s(x1) = [0] x1 + [0]
zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
prefix(x1) = [0] x1 + [0]
app^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0() = [0]
c_1(x1) = [0] x1 + [0]
from^#(x1) = [3] x1 + [0]
c_2(x1) = [1] x1 + [0]
zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3() = [0]
c_4() = [0]
c_5(x1, x2) = [0] x1 + [0] x2 + [0]
prefix^#(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [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: {from^#(X) -> c_2(from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {7}: inherited
-------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{4}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{5}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}: inherited
------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{1}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{2}: inherited
-----------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{2}->{1}: NA
---------------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{4}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{5}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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.
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
stdout:
MAYBE
Tool RC2
stdout:
MAYBE
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: MAYBE
Input Problem: runtime-complexity with respect to
Rules:
{ app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))
, from(X) -> cons(X, from(s(X)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, prefix(L) -> cons(nil(), zWadr(L, prefix(L)))}
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: app^#(nil(), YS) -> c_0(YS)
, 2: app^#(cons(X, XS), YS) -> c_1(X, app^#(XS, YS))
, 3: from^#(X) -> c_2(X, from^#(s(X)))
, 4: zWadr^#(nil(), YS) -> c_3()
, 5: zWadr^#(XS, nil()) -> c_4()
, 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
c_5(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
, 7: prefix^#(L) -> c_6(zWadr^#(L, prefix(L)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{7} [ inherited ]
|
|->{4} [ NA ]
|
|->{5} [ NA ]
|
`->{6} [ inherited ]
|
|->{1} [ NA ]
|
|->{2} [ inherited ]
| |
| `->{1} [ NA ]
|
|->{4} [ NA ]
|
`->{5} [ NA ]
->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: 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(app) = {}, Uargs(cons) = {}, Uargs(from) = {}, Uargs(s) = {},
Uargs(zWadr) = {}, Uargs(prefix) = {}, Uargs(app^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(from^#) = {},
Uargs(c_2) = {2}, Uargs(zWadr^#) = {}, Uargs(c_5) = {},
Uargs(prefix^#) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
app(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]
nil() = [0]
[0]
[0]
cons(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]
from(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
s(x1) = [0 1 0] x1 + [0]
[0 0 0] [0]
[0 0 1] [0]
zWadr(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]
prefix(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
app^#(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, x2) = [0 0 0] x1 + [0 0 0] x2 + [0]
[0 0 0] [0 0 0] [0]
[0 0 0] [0 0 0] [0]
from^#(x1) = [1 3 3] x1 + [0]
[3 3 3] [0]
[3 3 3] [0]
c_2(x1, x2) = [0 1 0] x1 + [1 0 0] x2 + [0]
[0 0 0] [0 1 0] [0]
[0 0 0] [0 0 1] [0]
zWadr^#(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_3() = [0]
[0]
[0]
c_4() = [0]
[0]
[0]
c_5(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]
prefix^#(x1) = [0 0 0] x1 + [0]
[0 0 0] [0]
[0 0 0] [0]
c_6(x1) = [0 0 0] 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: MAYBE
Input Problem: DP runtime-complexity with respect to
Strict Rules: {from^#(X) -> c_2(X, from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {7}: inherited
-------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{4}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{5}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}: inherited
------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{1}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{2}: inherited
-----------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{2}->{1}: NA
---------------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{4}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{5}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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.
2) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: app^#(nil(), YS) -> c_0(YS)
, 2: app^#(cons(X, XS), YS) -> c_1(X, app^#(XS, YS))
, 3: from^#(X) -> c_2(X, from^#(s(X)))
, 4: zWadr^#(nil(), YS) -> c_3()
, 5: zWadr^#(XS, nil()) -> c_4()
, 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
c_5(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
, 7: prefix^#(L) -> c_6(zWadr^#(L, prefix(L)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{7} [ inherited ]
|
|->{4} [ NA ]
|
|->{5} [ NA ]
|
`->{6} [ inherited ]
|
|->{1} [ NA ]
|
|->{2} [ inherited ]
| |
| `->{1} [ NA ]
|
|->{4} [ NA ]
|
`->{5} [ NA ]
->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: 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(app) = {}, Uargs(cons) = {}, Uargs(from) = {}, Uargs(s) = {},
Uargs(zWadr) = {}, Uargs(prefix) = {}, Uargs(app^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(from^#) = {},
Uargs(c_2) = {2}, Uargs(zWadr^#) = {}, Uargs(c_5) = {},
Uargs(prefix^#) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
app(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
nil() = [0]
[0]
cons(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from(x1) = [0 0] x1 + [0]
[0 0] [0]
s(x1) = [1 1] x1 + [0]
[0 0] [0]
zWadr(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
prefix(x1) = [0 0] x1 + [0]
[0 0] [0]
app^#(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, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
from^#(x1) = [1 3] x1 + [0]
[3 3] [0]
c_2(x1, x2) = [0 1] x1 + [1 0] x2 + [0]
[0 0] [0 1] [0]
zWadr^#(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
c_3() = [0]
[0]
c_4() = [0]
[0]
c_5(x1, x2) = [0 0] x1 + [0 0] x2 + [0]
[0 0] [0 0] [0]
prefix^#(x1) = [0 0] x1 + [0]
[0 0] [0]
c_6(x1) = [0 0] x1 + [0]
[0 0] [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: {from^#(X) -> c_2(X, from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {7}: inherited
-------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{4}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{5}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}: inherited
------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{1}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{2}: inherited
-----------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{2}->{1}: NA
---------------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{4}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{5}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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.
3) 'wdg' failed due to the following reason:
Transformation Details:
-----------------------
We have computed the following set of weak (innermost) dependency pairs:
{ 1: app^#(nil(), YS) -> c_0(YS)
, 2: app^#(cons(X, XS), YS) -> c_1(X, app^#(XS, YS))
, 3: from^#(X) -> c_2(X, from^#(s(X)))
, 4: zWadr^#(nil(), YS) -> c_3()
, 5: zWadr^#(XS, nil()) -> c_4()
, 6: zWadr^#(cons(X, XS), cons(Y, YS)) ->
c_5(app^#(Y, cons(X, nil())), zWadr^#(XS, YS))
, 7: prefix^#(L) -> c_6(zWadr^#(L, prefix(L)))}
Following Dependency Graph (modulo SCCs) was computed. (Answers to
subproofs are indicated to the right.)
->{7} [ inherited ]
|
|->{4} [ NA ]
|
|->{5} [ NA ]
|
`->{6} [ inherited ]
|
|->{1} [ NA ]
|
|->{2} [ inherited ]
| |
| `->{1} [ NA ]
|
|->{4} [ NA ]
|
`->{5} [ NA ]
->{3} [ MAYBE ]
Sub-problems:
-------------
* Path {3}: 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(app) = {}, Uargs(cons) = {}, Uargs(from) = {}, Uargs(s) = {},
Uargs(zWadr) = {}, Uargs(prefix) = {}, Uargs(app^#) = {},
Uargs(c_0) = {}, Uargs(c_1) = {}, Uargs(from^#) = {},
Uargs(c_2) = {2}, Uargs(zWadr^#) = {}, Uargs(c_5) = {},
Uargs(prefix^#) = {}, Uargs(c_6) = {}
We have the following constructor-restricted matrix interpretation:
Interpretation Functions:
app(x1, x2) = [0] x1 + [0] x2 + [0]
nil() = [0]
cons(x1, x2) = [0] x1 + [0] x2 + [0]
from(x1) = [0] x1 + [0]
s(x1) = [0] x1 + [0]
zWadr(x1, x2) = [0] x1 + [0] x2 + [0]
prefix(x1) = [0] x1 + [0]
app^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_0(x1) = [0] x1 + [0]
c_1(x1, x2) = [0] x1 + [0] x2 + [0]
from^#(x1) = [3] x1 + [0]
c_2(x1, x2) = [2] x1 + [1] x2 + [0]
zWadr^#(x1, x2) = [0] x1 + [0] x2 + [0]
c_3() = [0]
c_4() = [0]
c_5(x1, x2) = [0] x1 + [0] x2 + [0]
prefix^#(x1) = [0] x1 + [0]
c_6(x1) = [0] x1 + [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: {from^#(X) -> c_2(X, from^#(s(X)))}
Weak Rules: {}
Proof Output:
The input cannot be shown compatible
* Path {7}: inherited
-------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{4}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{5}: NA
-----------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}: inherited
------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{1}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{2}: inherited
-----------------------------
This path is subsumed by the proof of path {7}->{6}->{2}->{1}.
* Path {7}->{6}->{2}->{1}: NA
---------------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{4}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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 {7}->{6}->{5}: NA
----------------------
The usable rules for this path are:
{ prefix(L) -> cons(nil(), zWadr(L, prefix(L)))
, zWadr(nil(), YS) -> nil()
, zWadr(XS, nil()) -> nil()
, zWadr(cons(X, XS), cons(Y, YS)) ->
cons(app(Y, cons(X, nil())), zWadr(XS, YS))
, app(nil(), YS) -> YS
, app(cons(X, XS), YS) -> cons(X, app(XS, YS))}
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.
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.