Termination Proof using AProVE

Term Rewriting System R:
[X, Y, L]
rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Innermost Termination of R to be shown.

     ↳Dependency Pair Analysis

R contains the following Dependency Pairs:

REV1(X, cons(Y, L)) -> REV1(Y, L)
REV(cons(X, L)) -> REV1(X, L)
REV(cons(X, L)) -> REV2(X, L)
REV2(X, cons(Y, L)) -> REV(cons(X, rev(rev2(Y, L))))
REV2(X, cons(Y, L)) -> REV(rev2(Y, L))
REV2(X, cons(Y, L)) -> REV2(Y, L)

Furthermore, R contains two SCCs.

     ↳DPs

       →DP Problem 1

         ↳Forward Instantiation Transformation

       →DP Problem 2

         ↳Nar

Dependency Pair:

REV1(X, cons(Y, L)) -> REV1(Y, L)

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV1(X, cons(Y, L)) -> REV1(Y, L)

one new Dependency Pair is created:

REV1(X, cons(Y0, cons(Y'', L''))) -> REV1(Y0, cons(Y'', L''))

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, cons(Y0, cons(Y'', L''))) -> REV1(Y0, cons(Y'', L''))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV1(X, cons(Y0, cons(Y'', L''))) -> REV1(Y0, cons(Y'', L''))

one new Dependency Pair is created:

REV1(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV1(Y0'', cons(Y''0, cons(Y'''', L'''')))

The transformation is resulting in one new DP problem:

     ↳DPs

       →DP Problem 1

         ↳FwdInst

           →DP Problem 3

             ↳FwdInst

...

               →DP Problem 4

                 ↳Argument Filtering and Ordering

       →DP Problem 2

         ↳Nar

Dependency Pair:

REV1(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV1(Y0'', cons(Y''0, cons(Y'''', L'''')))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

The following dependency pair can be strictly oriented:

REV1(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV1(Y0'', cons(Y''0, cons(Y'''', L'''')))

There are no usable rules for innermost that need to be oriented.
Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System:

REV1(x₁, x₂) -> x₂
cons(x₁, x₂) -> cons(x₁, x₂)

     ↳DPs

       →DP Problem 1

         ↳FwdInst

           →DP Problem 3

             ↳FwdInst

...

               →DP Problem 5

                 ↳Dependency Graph

       →DP Problem 2

         ↳Nar

Dependency Pair:

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

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, cons(Y, L)) -> REV2(Y, L)
REV2(X, cons(Y, L)) -> REV(rev2(Y, L))
REV2(X, cons(Y, L)) -> REV(cons(X, rev(rev2(Y, L))))
REV(cons(X, L)) -> REV2(X, L)

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y, L)) -> REV(rev2(Y, L))

two new Dependency Pairs are created:

REV2(X, cons(Y', nil)) -> REV(nil)
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(rev(cons(Y0, rev(rev2(Y'', L'')))))

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, cons(Y0, cons(Y'', L''))) -> REV(rev(cons(Y0, rev(rev2(Y'', L'')))))
REV(cons(X, L)) -> REV2(X, L)
REV2(X, cons(Y, L)) -> REV(cons(X, rev(rev2(Y, L))))
REV2(X, cons(Y, L)) -> REV2(Y, L)

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y'', L''))) -> REV(rev(cons(Y0, rev(rev2(Y'', L'')))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))

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, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))
REV2(X, cons(Y, L)) -> REV2(Y, L)
REV2(X, cons(Y, L)) -> REV(cons(X, rev(rev2(Y, L))))
REV(cons(X, L)) -> REV2(X, L)

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV(cons(X, L)) -> REV2(X, L)

two new Dependency Pairs are created:

REV(cons(X'', cons(Y'', L''))) -> REV2(X'', cons(Y'', L''))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))

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, cons(Y, L)) -> REV2(Y, L)
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y, L)) -> REV(cons(X, rev(rev2(Y, L))))
REV(cons(X'', cons(Y'', L''))) -> REV2(X'', cons(Y'', L''))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y, L)) -> REV(cons(X, rev(rev2(Y, L))))

two new Dependency Pairs are created:

REV2(X, cons(Y', nil)) -> REV(cons(X, rev(nil)))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, rev(rev(cons(Y0, rev(rev2(Y'', L'')))))))

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, cons(Y0, cons(Y'', L''))) -> REV(cons(X, rev(rev(cons(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y', nil)) -> REV(cons(X, rev(nil)))
REV(cons(X'', cons(Y'', L''))) -> REV2(X'', cons(Y'', L''))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))
REV2(X, cons(Y, L)) -> REV2(Y, L)

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y', nil)) -> REV(cons(X, rev(nil)))

one new Dependency Pair is created:

REV2(X, cons(Y', nil)) -> REV(cons(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(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))
REV2(X, cons(Y, L)) -> REV2(Y, L)
REV(cons(X'', cons(Y'', L''))) -> REV2(X'', cons(Y'', L''))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, rev(rev(cons(Y0, rev(rev2(Y'', L'')))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, rev(rev(cons(Y0, rev(rev2(Y'', L'')))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, rev(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))

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, cons(Y0, cons(Y'', L''))) -> REV(cons(X, rev(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y'', L''))) -> REV2(X'', cons(Y'', L''))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))
REV2(X, cons(Y, L)) -> REV2(Y, L)
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, rev(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))

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, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))
REV2(X, cons(Y, L)) -> REV2(Y, L)
REV(cons(X'', cons(Y'', L''))) -> REV2(X'', cons(Y'', L''))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y, L)) -> REV2(Y, L)

two new Dependency Pairs are created:

REV2(X, cons(Y0, cons(Y'', L''))) -> REV2(Y0, cons(Y'', L''))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))

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, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV2(Y0, cons(Y'', L''))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))
REV(cons(X'', cons(Y'', L''))) -> REV2(X'', cons(Y'', L''))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV(cons(X'', cons(Y'', L''))) -> REV2(X'', cons(Y'', L''))

two new Dependency Pairs are created:

REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))

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(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV2(Y0, cons(Y'', L''))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y'', L''))) -> REV2(Y0, cons(Y'', L''))

two new Dependency Pairs are created:

REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))

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, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))

four new Dependency Pairs are created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(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 21

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(nil))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(nil))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(nil))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(nil))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(nil))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(nil))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(nil))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), 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 25

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, nil)))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(nil))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(nil))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, nil)))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, rev(nil))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), 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 27

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, nil)))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, nil)))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, nil)))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, nil)))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, nil)))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), 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, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, nil)))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, nil)))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), rev2(Y0, nil)))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(rev1(Y0, nil), 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:

REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

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

                 ↳Narrowing Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y'', L''))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))), rev2(rev1(Y0, rev(rev2(Y'', L''))), rev2(Y0, rev(rev2(Y'', L'')))))))

eight new Dependency Pairs are created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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 34

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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 36

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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 38

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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 40

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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 42

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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 44

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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 46

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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 48

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 50

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 52

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 54

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 56

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, rev(cons(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 58

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 59

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 61

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, rev(nil))), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 63

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(Y0, cons(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 65

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 66

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 67

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), rev2(Y0, nil)), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), 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 68

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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 69

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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 70

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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 71

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(rev2(Y''', nil))), rev2(Y0, rev(nil))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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 72

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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 73

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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 74

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(rev2(Y''', nil)))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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 75

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, rev(nil)), rev2(Y0, rev(nil))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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 76

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), 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 77

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), 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 78

                 ↳Rewriting Transformation

Dependency Pairs:

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), 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 79

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, rev(nil))))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), 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 80

                 ↳Rewriting Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), 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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), 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:

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), 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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), rev2(Y0, nil)))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), 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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), rev2(rev1(Y0, nil), nil))))

one new Dependency Pair is created:

REV2(X, cons(Y0, cons(Y''', nil))) -> REV(cons(X, cons(rev1(rev1(Y0, nil), nil), 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

                 ↳Forward Instantiation Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV(cons(X'', cons(Y0'', cons(Y'''', L'''')))) -> REV2(X'', cons(Y0'', cons(Y'''', L'''')))

three new Dependency Pairs are created:

REV(cons(X''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(X''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV(cons(X''', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(X''', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV(cons(X''', cons(Y0''', cons(Y'''''', cons(Y''', L'''))))) -> REV2(X''', cons(Y0''', cons(Y'''''', cons(Y''', L'''))))

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

                 ↳Forward Instantiation Transformation

Dependency Pairs:

REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV(cons(X''', cons(Y0''', cons(Y'''''', cons(Y''', L'''))))) -> REV2(X''', cons(Y0''', cons(Y'''''', cons(Y''', L'''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(X''', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(X''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y', cons(Y0'', cons(Y'''', L'''')))) -> REV2(Y', cons(Y0'', cons(Y'''', L'''')))

four new Dependency Pairs are created:

REV2(X, cons(Y''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(Y''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y'', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(Y'', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y'', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(Y'', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y'0, cons(Y0''', cons(Y'''''', cons(Y''', L'''))))) -> REV2(Y'0, cons(Y0''', cons(Y'''''', cons(Y''', L'''))))

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

                 ↳Forward Instantiation Transformation

Dependency Pairs:

REV2(X, cons(Y'0, cons(Y0''', cons(Y'''''', cons(Y''', L'''))))) -> REV2(Y'0, cons(Y0''', cons(Y'''''', cons(Y''', L'''))))
REV2(X, cons(Y'', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(Y'', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y'', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(Y'', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(Y''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0''', cons(Y'''''', cons(Y''', L'''))))) -> REV2(X''', cons(Y0''', cons(Y'''''', cons(Y''', L'''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(X''', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(X''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV(cons(X''', cons(Y''0, cons(Y'''', L'''')))) -> REV2(X''', cons(Y''0, cons(Y'''', L'''')))

seven new Dependency Pairs are created:

REV(cons(X'''', cons(Y''0'', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(X'''', cons(Y''0'', cons(Y'''''', cons(Y''''''', L''''''))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y''', L'''))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y''', L'''))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))
REV(cons(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))) -> REV2(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))
REV(cons(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''', cons(Y0'''''''', cons(Y'''''''''', L''''''''''))))))) -> REV2(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''', cons(Y0'''''''', cons(Y'''''''''', L''''''''''))))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''', cons(Y'''''0, L'''''')))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''', cons(Y'''''0, L'''''')))))

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

                 ↳Forward Instantiation Transformation

Dependency Pairs:

REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''', cons(Y'''''0, L'''''')))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''', cons(Y'''''0, L'''''')))))
REV(cons(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''', cons(Y0'''''''', cons(Y'''''''''', L''''''''''))))))) -> REV2(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''', cons(Y0'''''''', cons(Y'''''''''', L''''''''''))))))
REV(cons(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))) -> REV2(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y''', L'''))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y''', L'''))))
REV2(X, cons(Y'', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(Y'', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y'', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(Y'', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(Y''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV(cons(X'''', cons(Y''0'', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(X'''', cons(Y''0'', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0''', cons(Y'''''', cons(Y''', L'''))))) -> REV2(X''', cons(Y0''', cons(Y'''''', cons(Y''', L'''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(X''', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(X''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))
REV2(X, cons(Y'0, cons(Y0''', cons(Y'''''', cons(Y''', L'''))))) -> REV2(Y'0, cons(Y0''', cons(Y'''''', cons(Y''', L'''))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

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

REV2(X, cons(Y0'', cons(Y''0, cons(Y'''', L'''')))) -> REV2(Y0'', cons(Y''0, cons(Y'''', L'''')))

seven new Dependency Pairs are created:

REV2(X, cons(Y0'''', cons(Y''0'', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(Y0'''', cons(Y''0'', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y0'''', cons(Y''0', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(Y0'''', cons(Y''0', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y0''', cons(Y''0', cons(Y'''''', cons(Y''', L'''))))) -> REV2(Y0''', cons(Y''0', cons(Y'''''', cons(Y''', L'''))))
REV2(X, cons(Y0''', cons(Y''0', cons(Y'''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))) -> REV2(Y0''', cons(Y''0', cons(Y'''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))
REV2(X, cons(Y0''', cons(Y''0', cons(Y''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))) -> REV2(Y0''', cons(Y''0', cons(Y''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))
REV2(X, cons(Y0''', cons(Y''0', cons(Y''''', cons(Y'''''''', cons(Y0'''''''', cons(Y'''''''''', L''''''''''))))))) -> REV2(Y0''', cons(Y''0', cons(Y''''', cons(Y'''''''', cons(Y0'''''''', cons(Y'''''''''', L''''''''''))))))
REV2(X, cons(Y0''', cons(Y''0', cons(Y'''''', cons(Y'''''''', cons(Y'''''0, L'''''')))))) -> REV2(Y0''', cons(Y''0', cons(Y'''''', cons(Y'''''''', cons(Y'''''0, L'''''')))))

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

                 ↳Remaining Obligation(s)

The following remains to be proven:
Dependency Pairs:

REV(cons(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''', cons(Y0'''''''', cons(Y'''''''''', L''''''''''))))))) -> REV2(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''', cons(Y0'''''''', cons(Y'''''''''', L''''''''''))))))
REV(cons(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))) -> REV2(X'''', cons(Y''0', cons(Y''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y''', L'''))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y''', L'''))))
REV2(X, cons(Y0''', cons(Y''0', cons(Y'''''', cons(Y'''''''', cons(Y'''''0, L'''''')))))) -> REV2(Y0''', cons(Y''0', cons(Y'''''', cons(Y'''''''', cons(Y'''''0, L'''''')))))
REV2(X, cons(Y0''', cons(Y''0', cons(Y''''', cons(Y'''''''', cons(Y0'''''''', cons(Y'''''''''', L''''''''''))))))) -> REV2(Y0''', cons(Y''0', cons(Y''''', cons(Y'''''''', cons(Y0'''''''', cons(Y'''''''''', L''''''''''))))))
REV2(X, cons(Y0''', cons(Y''0', cons(Y''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))) -> REV2(Y0''', cons(Y''0', cons(Y''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))
REV2(X, cons(Y0''', cons(Y''0', cons(Y'''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))) -> REV2(Y0''', cons(Y''0', cons(Y'''''', cons(Y'''''''''', cons(Y''''''''''', L'''''''')))))
REV2(X, cons(Y0''', cons(Y''0', cons(Y'''''', cons(Y''', L'''))))) -> REV2(Y0''', cons(Y''0', cons(Y'''''', cons(Y''', L'''))))
REV2(X, cons(Y0'''', cons(Y''0', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(Y0'''', cons(Y''0', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y0'''', cons(Y''0'', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(Y0'''', cons(Y''0'', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y'0, cons(Y0''', cons(Y'''''', cons(Y''', L'''))))) -> REV2(Y'0, cons(Y0''', cons(Y'''''', cons(Y''', L'''))))
REV2(X, cons(Y'', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(Y'', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y'', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(Y'', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(Y''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))))
REV(cons(X'''', cons(Y''0'', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(X'''', cons(Y''0'', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev(cons(Y''', rev(rev2(Y', L')))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0''', cons(Y'''''', cons(Y''', L'''))))) -> REV2(X''', cons(Y0''', cons(Y'''''', cons(Y''', L'''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))) -> REV2(X''', cons(Y0'''', cons(Y'''''', cons(Y0'''''', cons(Y'''''''', L'''''''')))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(X, cons(rev1(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))), rev2(rev1(Y0, rev(rev2(Y''', cons(Y', L')))), rev2(Y0, rev(rev2(Y''', cons(Y', L'))))))))
REV(cons(X''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))) -> REV2(X''', cons(Y0'''', cons(Y'''''', cons(Y''''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV(cons(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(X''', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV2(X, cons(Y0, cons(Y''', cons(Y', L')))) -> REV(cons(rev1(rev1(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L')))), rev2(rev1(Y''', rev(rev2(Y', L'))), rev2(Y''', rev(rev2(Y', L'))))), rev2(Y0, rev(rev(cons(Y''', rev(rev2(Y', L'))))))))
REV2(X, cons(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))) -> REV2(Y0', cons(Y'''', cons(Y0'''', cons(Y'''''', L''''''))))
REV(cons(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''', cons(Y'''''0, L'''''')))))) -> REV2(X'''', cons(Y''0', cons(Y'''''', cons(Y'''''''', cons(Y'''''0, L'''''')))))

Rules:

rev1(0, nil) -> 0
rev1(s(X), nil) -> s(X)
rev1(X, cons(Y, L)) -> rev1(Y, L)
rev(nil) -> nil
rev(cons(X, L)) -> cons(rev1(X, L), rev2(X, L))
rev2(X, nil) -> nil
rev2(X, cons(Y, L)) -> rev(cons(X, rev(rev2(Y, L))))

Strategy:

innermost

Innermost Termination of R could not be shown.
Duration:
0:38 minutes