Term Rewriting System R:
[x, y]
dfib(s(s(x)), y) -> dfib(s(x), dfib(x, y))
Innermost Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
DFIB(s(s(x)), y) -> DFIB(s(x), dfib(x, y))
DFIB(s(s(x)), y) -> DFIB(x, y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pairs:
DFIB(s(s(x)), y) -> DFIB(x, y)
DFIB(s(s(x)), y) -> DFIB(s(x), dfib(x, y))
Rule:
dfib(s(s(x)), y) -> dfib(s(x), dfib(x, y))
Strategy:
innermost
The following dependency pairs can be strictly oriented:
DFIB(s(s(x)), y) -> DFIB(x, y)
DFIB(s(s(x)), y) -> DFIB(s(x), dfib(x, y))
The following usable rule for innermost w.r.t. to the AFS can be oriented:
dfib(s(s(x)), y) -> dfib(s(x), dfib(x, y))
Used ordering: Homeomorphic Embedding Order with EMB
resulting in one new DP problem.
Used Argument Filtering System: DFIB(x1, x2) -> DFIB(x1, x2)
s(x1) -> s(x1)
dfib(x1, x2) -> x2
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rule:
dfib(s(s(x)), y) -> dfib(s(x), dfib(x, y))
Strategy:
innermost
Using the Dependency Graph resulted in no new DP problems.
Innermost Termination of R successfully shown.
Duration:
0:00 minutes