Term Rewriting System R:
[x, y, z]
+(-(x, y), z) -> -(+(x, z), y)
-(+(x, y), y) -> x
Innermost 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
Strategy:
innermost
The following dependency pair can be strictly oriented:
+'(-(x, y), z) -> +'(x, z)
There are no usable rules for innermost 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: +'(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
Strategy:
innermost
Using the Dependency Graph resulted in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes