Termination Proof using AProVE

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.

     ↳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.

     ↳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:

     ↳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:

     ↳DPs

       →DP Problem 1

         ↳FwdInst

           →DP Problem 3

             ↳FwdInst

...

               →DP Problem 4

                 ↳Polynomial 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: Polynomial ordering with Polynomial interpretation:

POL(REV1(x₁, x₂)) = x₂

POL(++(x₁, x₂)) = 1 + x₂

resulting in one new DP problem.

     ↳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.

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳DPs

       →DP Problem 1

         ↳FwdInst

       →DP Problem 2

         ↳Nar

           →DP Problem 6

             ↳Rw

...

               →DP Problem 92

                 ↳Rewriting Transformation

Dependency Pairs:

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:

     ↳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:

     ↳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:

     ↳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:

     ↳DPs

       →DP Problem 1

         ↳FwdInst

       →DP Problem 2

         ↳Nar

           →DP Problem 6

             ↳Rw

...

               →DP Problem 96

                 ↳Rewriting Transformation

Dependency Pairs:

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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:

     ↳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:
0:37 minutes

POL(REV1(x₁, x₂))	= x₂
POL(++(x₁, x₂))	= 1 + x₂