Term Rewriting System R:
[x, y, z]
rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))

Innermost Termination of R to be shown.



   R
Dependency Pair Analysis



R contains the following Dependency Pairs:

REV(++(x, y)) -> REV1(x, y)
REV(++(x, y)) -> REV2(x, y)
REV1(x, ++(y, z)) -> REV1(y, z)
REV2(x, ++(y, z)) -> REV(++(x, rev(rev2(y, z))))
REV2(x, ++(y, z)) -> REV(rev2(y, z))
REV2(x, ++(y, z)) -> REV2(y, z)

Furthermore, R contains two SCCs.


   R
DPs
       →DP Problem 1
Forward Instantiation Transformation
       →DP Problem 2
Nar


Dependency Pair:

REV1(x, ++(y, z)) -> REV1(y, z)


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

REV1(x, ++(y, z)) -> REV1(y, z)
one new Dependency Pair is created:

REV1(x, ++(y0, ++(y'', z''))) -> REV1(y0, ++(y'', z''))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
           →DP Problem 3
Forward Instantiation Transformation
       →DP Problem 2
Nar


Dependency Pair:

REV1(x, ++(y0, ++(y'', z''))) -> REV1(y0, ++(y'', z''))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

REV1(x, ++(y0, ++(y'', z''))) -> REV1(y0, ++(y'', z''))
one new Dependency Pair is created:

REV1(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV1(y0'', ++(y''0, ++(y'''', z'''')))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
           →DP Problem 3
FwdInst
             ...
               →DP Problem 4
Argument Filtering and Ordering
       →DP Problem 2
Nar


Dependency Pair:

REV1(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV1(y0'', ++(y''0, ++(y'''', z'''')))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




The following dependency pair can be strictly oriented:

REV1(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV1(y0'', ++(y''0, ++(y'''', z'''')))


There are no usable rules for innermost that need to be oriented.
Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System:
REV1(x1, x2) -> x2
++(x1, x2) -> ++(x1, x2)


   R
DPs
       →DP Problem 1
FwdInst
           →DP Problem 3
FwdInst
             ...
               →DP Problem 5
Dependency Graph
       →DP Problem 2
Nar


Dependency Pair:


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




Using the Dependency Graph resulted in no new DP problems.


   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Narrowing Transformation


Dependency Pairs:

REV2(x, ++(y, z)) -> REV2(y, z)
REV2(x, ++(y, z)) -> REV(rev2(y, z))
REV2(x, ++(y, z)) -> REV(++(x, rev(rev2(y, z))))
REV(++(x, y)) -> REV2(x, y)


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y, z)) -> REV(rev2(y, z))
two new Dependency Pairs are created:

REV2(x, ++(y', nil)) -> REV(nil)
REV2(x, ++(y0, ++(y'', z''))) -> REV(rev(++(y0, rev(rev2(y'', z'')))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y'', z''))) -> REV(rev(++(y0, rev(rev2(y'', z'')))))
REV(++(x, y)) -> REV2(x, y)
REV2(x, ++(y, z)) -> REV(++(x, rev(rev2(y, z))))
REV2(x, ++(y, z)) -> REV2(y, z)


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y'', z''))) -> REV(rev(++(y0, rev(rev2(y'', z'')))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 7
Forward Instantiation Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))
REV2(x, ++(y, z)) -> REV2(y, z)
REV2(x, ++(y, z)) -> REV(++(x, rev(rev2(y, z))))
REV(++(x, y)) -> REV2(x, y)


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

REV(++(x, y)) -> REV2(x, y)
two new Dependency Pairs are created:

REV(++(x'', ++(y'', z''))) -> REV2(x'', ++(y'', z''))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 8
Narrowing Transformation


Dependency Pairs:

REV2(x, ++(y, z)) -> REV2(y, z)
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y, z)) -> REV(++(x, rev(rev2(y, z))))
REV(++(x'', ++(y'', z''))) -> REV2(x'', ++(y'', z''))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y, z)) -> REV(++(x, rev(rev2(y, z))))
two new Dependency Pairs are created:

REV2(x, ++(y', nil)) -> REV(++(x, rev(nil)))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, rev(rev(++(y0, rev(rev2(y'', z'')))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 9
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, rev(rev(++(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y', nil)) -> REV(++(x, rev(nil)))
REV(++(x'', ++(y'', z''))) -> REV2(x'', ++(y'', z''))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))
REV2(x, ++(y, z)) -> REV2(y, z)


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y', nil)) -> REV(++(x, rev(nil)))
one new Dependency Pair is created:

REV2(x, ++(y', nil)) -> REV(++(x, nil))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 10
Rewriting Transformation


Dependency Pairs:

REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))
REV2(x, ++(y, z)) -> REV2(y, z)
REV(++(x'', ++(y'', z''))) -> REV2(x'', ++(y'', z''))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, rev(rev(++(y0, rev(rev2(y'', z'')))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, rev(rev(++(y0, rev(rev2(y'', z'')))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, rev(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 11
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, rev(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y'', z''))) -> REV2(x'', ++(y'', z''))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))
REV2(x, ++(y, z)) -> REV2(y, z)
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, rev(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 12
Forward Instantiation Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))
REV2(x, ++(y, z)) -> REV2(y, z)
REV(++(x'', ++(y'', z''))) -> REV2(x'', ++(y'', z''))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y, z)) -> REV2(y, z)
two new Dependency Pairs are created:

REV2(x, ++(y0, ++(y'', z''))) -> REV2(y0, ++(y'', z''))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 13
Forward Instantiation Transformation


Dependency Pairs:

REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV2(y0, ++(y'', z''))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))
REV(++(x'', ++(y'', z''))) -> REV2(x'', ++(y'', z''))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

REV(++(x'', ++(y'', z''))) -> REV2(x'', ++(y'', z''))
two new Dependency Pairs are created:

REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 14
Forward Instantiation Transformation


Dependency Pairs:

REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y'', z''))) -> REV2(y0, ++(y'', z''))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y'', z''))) -> REV2(y0, ++(y'', z''))
two new Dependency Pairs are created:

REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 15
Narrowing Transformation


Dependency Pairs:

REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))
four new Dependency Pairs are created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 16
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 17
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 18
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(nil)), rev2(y0, rev(nil))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 19
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(nil)), rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 20
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(nil)), rev2(y0, rev(nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(rev2(y''', nil)))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 21
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(rev2(y''', nil)))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(nil)), rev2(y0, rev(nil))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 22
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(nil)), rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(rev2(y''', nil)))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, rev(nil)), rev2(y0, rev(nil))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(nil))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 23
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(rev2(y''', nil)))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 24
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(rev2(y''', nil)))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(rev2(y''', nil)))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 25
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(nil))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 26
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(rev1(y0, nil), rev2(y0, rev(nil))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 27
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 28
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 29
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 30
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, rev(nil))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 31
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 32
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, nil))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 33
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, rev2(y0, nil)))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(y0, nil))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 34
Narrowing Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y'', z''))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))), rev2(rev1(y0, rev(rev2(y'', z''))), rev2(y0, rev(rev2(y'', z'')))))))
eight new Dependency Pairs are created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 35
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 36
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 37
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 38
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 39
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 40
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 41
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 42
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 43
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 44
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 45
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 46
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 47
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 48
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 49
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 50
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 51
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 52
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 53
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 54
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 55
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 56
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 57
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 58
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, rev(++(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 59
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 60
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 61
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 62
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 63
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 64
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(rev2(y''', nil)))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 65
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(y0, ++(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 66
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 67
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 68
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 69
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, rev(nil))), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 70
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 71
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 72
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 73
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, rev2(y0, nil)), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 74
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 75
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 76
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 77
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(rev1(y0, nil), rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 78
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 79
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 80
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 81
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(rev2(y''', nil))), rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 82
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 83
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 84
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 85
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, rev(nil)), rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 86
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 87
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 88
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(rev2(y''', nil)))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 89
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(rev1(y0, nil), rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 90
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 91
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 92
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 93
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, rev(nil))))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 94
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 95
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 96
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 97
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, rev2(y0, nil)))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 98
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, nil)))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 99
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, nil)))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 100
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, nil)))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 101
Rewriting Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, rev2(y0, nil))))
one new Dependency Pair is created:

REV2(x, ++(y0, ++(y''', nil))) -> REV(++(x, ++(y0, nil)))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 102
Forward Instantiation Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

REV(++(x'', ++(y0'', ++(y'''', z'''')))) -> REV2(x'', ++(y0'', ++(y'''', z'''')))
three new Dependency Pairs are created:

REV(++(x''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(x''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV(++(x''', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(x''', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV(++(x''', ++(y0''', ++(y'''''', ++(y''', z'''))))) -> REV2(x''', ++(y0''', ++(y'''''', ++(y''', z'''))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 103
Forward Instantiation Transformation


Dependency Pairs:

REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV(++(x''', ++(y0''', ++(y'''''', ++(y''', z'''))))) -> REV2(x''', ++(y0''', ++(y'''''', ++(y''', z'''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(x''', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(x''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y', ++(y0'', ++(y'''', z'''')))) -> REV2(y', ++(y0'', ++(y'''', z'''')))
four new Dependency Pairs are created:

REV2(x, ++(y''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(y''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y'', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(y'', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y'', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(y'', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y''', ++(y0''', ++(y'''''', ++(y''0, z'''))))) -> REV2(y''', ++(y0''', ++(y'''''', ++(y''0, z'''))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 104
Forward Instantiation Transformation


Dependency Pairs:

REV2(x, ++(y''', ++(y0''', ++(y'''''', ++(y''0, z'''))))) -> REV2(y''', ++(y0''', ++(y'''''', ++(y''0, z'''))))
REV2(x, ++(y'', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(y'', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y'', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(y'', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(y''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0''', ++(y'''''', ++(y''', z'''))))) -> REV2(x''', ++(y0''', ++(y'''''', ++(y''', z'''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(x''', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(x''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

REV(++(x''', ++(y''0, ++(y'''', z'''')))) -> REV2(x''', ++(y''0, ++(y'''', z'''')))
seven new Dependency Pairs are created:

REV(++(x'''', ++(y''0'', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(x'''', ++(y''0'', ++(y''''0, ++(y'''''', z''''''))))
REV(++(x'''', ++(y''0', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(x'''', ++(y''0', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV(++(x'''', ++(y''0', ++(y'''''', ++(y''', z'''))))) -> REV2(x'''', ++(y''0', ++(y'''''', ++(y''', z'''))))
REV(++(x'''', ++(y''0', ++(y'''''', ++(y''''0'', ++(y'''''''', z'''''''')))))) -> REV2(x'''', ++(y''0', ++(y'''''', ++(y''''0'', ++(y'''''''', z'''''''')))))
REV(++(x'''', ++(y''0', ++(y''''', ++(y''''0'', ++(y'''''''', z'''''''')))))) -> REV2(x'''', ++(y''0', ++(y''''', ++(y''''0'', ++(y'''''''', z'''''''')))))
REV(++(x'''', ++(y''0', ++(y''''', ++(y'''''''', ++(y0'''''''', ++(y'''''''''', z''''''''''))))))) -> REV2(x'''', ++(y''0', ++(y''''', ++(y'''''''', ++(y0'''''''', ++(y'''''''''', z''''''''''))))))
REV(++(x'''', ++(y''0'', ++(y'''''', ++(y'''''''', ++(y''0''', z'''''')))))) -> REV2(x'''', ++(y''0'', ++(y'''''', ++(y'''''''', ++(y''0''', z'''''')))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 105
Forward Instantiation Transformation


Dependency Pairs:

REV(++(x'''', ++(y''0'', ++(y'''''', ++(y'''''''', ++(y''0''', z'''''')))))) -> REV2(x'''', ++(y''0'', ++(y'''''', ++(y'''''''', ++(y''0''', z'''''')))))
REV(++(x'''', ++(y''0', ++(y''''', ++(y'''''''', ++(y0'''''''', ++(y'''''''''', z''''''''''))))))) -> REV2(x'''', ++(y''0', ++(y''''', ++(y'''''''', ++(y0'''''''', ++(y'''''''''', z''''''''''))))))
REV(++(x'''', ++(y''0', ++(y''''', ++(y''''0'', ++(y'''''''', z'''''''')))))) -> REV2(x'''', ++(y''0', ++(y''''', ++(y''''0'', ++(y'''''''', z'''''''')))))
REV(++(x'''', ++(y''0', ++(y'''''', ++(y''''0'', ++(y'''''''', z'''''''')))))) -> REV2(x'''', ++(y''0', ++(y'''''', ++(y''''0'', ++(y'''''''', z'''''''')))))
REV(++(x'''', ++(y''0', ++(y'''''', ++(y''', z'''))))) -> REV2(x'''', ++(y''0', ++(y'''''', ++(y''', z'''))))
REV2(x, ++(y'', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(y'', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y'', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(y'', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(y''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV(++(x'''', ++(y''0', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(x'''', ++(y''0', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV(++(x'''', ++(y''0'', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(x'''', ++(y''0'', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0''', ++(y'''''', ++(y''', z'''))))) -> REV2(x''', ++(y0''', ++(y'''''', ++(y''', z'''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(x''', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(x''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
REV2(x, ++(y''', ++(y0''', ++(y'''''', ++(y''0, z'''))))) -> REV2(y''', ++(y0''', ++(y'''''', ++(y''0, z'''))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost




On this DP problem, a Forward Instantiation SCC transformation can be performed.
As a result of transforming the rule

REV2(x, ++(y0'', ++(y''0, ++(y'''', z'''')))) -> REV2(y0'', ++(y''0, ++(y'''', z'''')))
seven new Dependency Pairs are created:

REV2(x, ++(y0'''', ++(y''0'', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(y0'''', ++(y''0'', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y0'''', ++(y''0', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(y0'''', ++(y''0', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0''', ++(y''0', ++(y'''''', ++(y''', z'''))))) -> REV2(y0''', ++(y''0', ++(y'''''', ++(y''', z'''))))
REV2(x, ++(y0''', ++(y''0', ++(y'''''', ++(y''''0'', ++(y'''''''', z'''''''')))))) -> REV2(y0''', ++(y''0', ++(y'''''', ++(y''''0'', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0''', ++(y''0', ++(y''''', ++(y''''0'', ++(y'''''''', z'''''''')))))) -> REV2(y0''', ++(y''0', ++(y''''', ++(y''''0'', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0''', ++(y''0', ++(y''''', ++(y'''''''', ++(y0'''''''', ++(y'''''''''', z''''''''''))))))) -> REV2(y0''', ++(y''0', ++(y''''', ++(y'''''''', ++(y0'''''''', ++(y'''''''''', z''''''''''))))))
REV2(x, ++(y0''', ++(y''0'', ++(y'''''', ++(y'''''''', ++(y''0''', z'''''')))))) -> REV2(y0''', ++(y''0'', ++(y'''''', ++(y'''''''', ++(y''0''', z'''''')))))

The transformation is resulting in one new DP problem:



   R
DPs
       →DP Problem 1
FwdInst
       →DP Problem 2
Nar
           →DP Problem 6
Rw
             ...
               →DP Problem 106
Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

REV(++(x'''', ++(y''0', ++(y''''', ++(y'''''''', ++(y0'''''''', ++(y'''''''''', z''''''''''))))))) -> REV2(x'''', ++(y''0', ++(y''''', ++(y'''''''', ++(y0'''''''', ++(y'''''''''', z''''''''''))))))
REV(++(x'''', ++(y''0', ++(y''''', ++(y''''0'', ++(y'''''''', z'''''''')))))) -> REV2(x'''', ++(y''0', ++(y''''', ++(y''''0'', ++(y'''''''', z'''''''')))))
REV(++(x'''', ++(y''0', ++(y'''''', ++(y''''0'', ++(y'''''''', z'''''''')))))) -> REV2(x'''', ++(y''0', ++(y'''''', ++(y''''0'', ++(y'''''''', z'''''''')))))
REV(++(x'''', ++(y''0', ++(y'''''', ++(y''', z'''))))) -> REV2(x'''', ++(y''0', ++(y'''''', ++(y''', z'''))))
REV2(x, ++(y0''', ++(y''0'', ++(y'''''', ++(y'''''''', ++(y''0''', z'''''')))))) -> REV2(y0''', ++(y''0'', ++(y'''''', ++(y'''''''', ++(y''0''', z'''''')))))
REV2(x, ++(y0''', ++(y''0', ++(y''''', ++(y'''''''', ++(y0'''''''', ++(y'''''''''', z''''''''''))))))) -> REV2(y0''', ++(y''0', ++(y''''', ++(y'''''''', ++(y0'''''''', ++(y'''''''''', z''''''''''))))))
REV2(x, ++(y0''', ++(y''0', ++(y''''', ++(y''''0'', ++(y'''''''', z'''''''')))))) -> REV2(y0''', ++(y''0', ++(y''''', ++(y''''0'', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0''', ++(y''0', ++(y'''''', ++(y''''0'', ++(y'''''''', z'''''''')))))) -> REV2(y0''', ++(y''0', ++(y'''''', ++(y''''0'', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0''', ++(y''0', ++(y'''''', ++(y''', z'''))))) -> REV2(y0''', ++(y''0', ++(y'''''', ++(y''', z'''))))
REV2(x, ++(y0'''', ++(y''0', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(y0'''', ++(y''0', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0'''', ++(y''0'', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(y0'''', ++(y''0'', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y''', ++(y0''', ++(y'''''', ++(y''0, z'''))))) -> REV2(y''', ++(y0''', ++(y'''''', ++(y''0, z'''))))
REV2(x, ++(y'', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(y'', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y'', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(y'', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(y''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV(++(x'''', ++(y''0', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(x'''', ++(y''0', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))))
REV(++(x'''', ++(y''0'', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(x'''', ++(y''0'', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev(++(y''', rev(rev2(y', z')))))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0''', ++(y'''''', ++(y''', z'''))))) -> REV2(x''', ++(y0''', ++(y'''''', ++(y''', z'''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))) -> REV2(x''', ++(y0'''', ++(y'''''', ++(y0'''''', ++(y'''''''', z'''''''')))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(x, ++(rev1(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev2(y''', ++(y', z'))))), rev2(rev1(y0, rev(rev2(y''', ++(y', z')))), rev2(y0, rev(rev2(y''', ++(y', z'))))))))
REV(++(x''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))) -> REV2(x''', ++(y0'''', ++(y''''0, ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV(++(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(x''', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV2(x, ++(y0, ++(y''', ++(y', z')))) -> REV(++(rev1(rev1(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z')))), rev2(rev1(y''', rev(rev2(y', z'))), rev2(y''', rev(rev2(y', z'))))), rev2(y0, rev(rev(++(y''', rev(rev2(y', z'))))))))
REV2(x, ++(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))) -> REV2(y0', ++(y'''', ++(y0'''', ++(y'''''', z''''''))))
REV(++(x'''', ++(y''0'', ++(y'''''', ++(y'''''''', ++(y''0''', z'''''')))))) -> REV2(x'''', ++(y''0'', ++(y'''''', ++(y'''''''', ++(y''0''', z'''''')))))


Rules:


rev(nil) -> nil
rev(++(x, y)) -> ++(rev1(x, y), rev2(x, y))
rev1(x, nil) -> x
rev1(x, ++(y, z)) -> rev1(y, z)
rev2(x, nil) -> nil
rev2(x, ++(y, z)) -> rev(++(x, rev(rev2(y, z))))


Strategy:

innermost



Innermost Termination of R could not be shown.
Duration:
0:35 minutes