Term Rewriting System R:
[x, y, z]
+(-(x, y), z) -> -(+(x, z), y)
-(+(x, y), y) -> x

Termination of R to be shown.

R
Dependency Pair Analysis

R contains the following Dependency Pairs:

+'(-(x, y), z) -> -'(+(x, z), y)
+'(-(x, y), z) -> +'(x, z)

Furthermore, R contains one SCC.

R
DPs
→DP Problem 1
Argument Filtering and Ordering

Dependency Pair:

+'(-(x, y), z) -> +'(x, z)

Rules:

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

The following dependency pair can be strictly oriented:

+'(-(x, y), z) -> +'(x, z)

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:
+'(x1, x2) -> +'(x1, x2)
-(x1, x2) -> -(x1, x2)

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

Dependency Pair:

Rules:

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

Using the Dependency Graph resulted in no new DP problems.

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