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