Term Rewriting System R:
[x, y]
rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)

Termination of R to be shown.

R
Dependency Pair Analysis

R contains the following Dependency Pairs:

REV(++(x, y)) -> REV(y)
REV(++(x, y)) -> REV(x)
REV(++(x, x)) -> REV(x)

Furthermore, R contains one SCC.

R
DPs
→DP Problem 1
Argument Filtering and Ordering

Dependency Pairs:

REV(++(x, x)) -> REV(x)
REV(++(x, y)) -> REV(x)
REV(++(x, y)) -> REV(y)

Rules:

rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)

The following dependency pairs can be strictly oriented:

REV(++(x, x)) -> REV(x)
REV(++(x, y)) -> REV(x)
REV(++(x, y)) -> REV(y)

The following rules can be oriented:

rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
rev > ++

resulting in one new DP problem.
Used Argument Filtering System:
REV(x1) -> REV(x1)
++(x1, x2) -> ++(x1, x2)
rev(x1) -> rev(x1)

R
DPs
→DP Problem 1
AFS
→DP Problem 2
Dependency Graph

Dependency Pair:

Rules:

rev(a) -> a
rev(b) -> b
rev(++(x, y)) -> ++(rev(y), rev(x))
rev(++(x, x)) -> rev(x)

Using the Dependency Graph resulted in no new DP problems.

Termination of R successfully shown.
Duration:
0:00 minutes