Term Rewriting System R:
[x, y]
minus(minus(x)) -> x
minus(h(x)) -> h(minus(x))
minus(f(x, y)) -> f(minus(y), minus(x))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
MINUS(h(x)) -> MINUS(x)
MINUS(f(x, y)) -> MINUS(y)
MINUS(f(x, y)) -> MINUS(x)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pairs:
MINUS(f(x, y)) -> MINUS(x)
MINUS(f(x, y)) -> MINUS(y)
MINUS(h(x)) -> MINUS(x)
Rules:
minus(minus(x)) -> x
minus(h(x)) -> h(minus(x))
minus(f(x, y)) -> f(minus(y), minus(x))
The following dependency pairs can be strictly oriented:
MINUS(f(x, y)) -> MINUS(x)
MINUS(f(x, y)) -> MINUS(y)
MINUS(h(x)) -> MINUS(x)
There are no usable rules using the Ce-refinement that need to be oriented.
Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System: MINUS(x1) -> MINUS(x1)
h(x1) -> h(x1)
f(x1, x2) -> f(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
minus(minus(x)) -> x
minus(h(x)) -> h(minus(x))
minus(f(x, y)) -> f(minus(y), minus(x))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes