Term Rewriting System R:
[x, y]
merge(x, nil) -> x
merge(nil, y) -> y
merge(++(x, y), ++(u, v)) -> ++(x, merge(y, ++(u, v)))
merge(++(x, y), ++(u, v)) -> ++(u, merge(++(x, y), v))

Termination of R to be shown.

R
Dependency Pair Analysis

R contains the following Dependency Pairs:

MERGE(++(x, y), ++(u, v)) -> MERGE(y, ++(u, v))
MERGE(++(x, y), ++(u, v)) -> MERGE(++(x, y), v)

Furthermore, R contains one SCC.

R
DPs
→DP Problem 1
Argument Filtering and Ordering

Dependency Pair:

MERGE(++(x, y), ++(u, v)) -> MERGE(y, ++(u, v))

Rules:

merge(x, nil) -> x
merge(nil, y) -> y
merge(++(x, y), ++(u, v)) -> ++(x, merge(y, ++(u, v)))
merge(++(x, y), ++(u, v)) -> ++(u, merge(++(x, y), v))

The following dependency pair can be strictly oriented:

MERGE(++(x, y), ++(u, v)) -> MERGE(y, ++(u, v))

There are no usable rules using the Ce-refinement that need to be oriented.
Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:
trivial

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

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

Dependency Pair:

Rules:

merge(x, nil) -> x
merge(nil, y) -> y
merge(++(x, y), ++(u, v)) -> ++(x, merge(y, ++(u, v)))
merge(++(x, y), ++(u, v)) -> ++(u, merge(++(x, y), v))

Using the Dependency Graph resulted in no new DP problems.

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