Term Rewriting System R:
[x, y]
bin(x, 0) -> s(0)
bin(0, s(y)) -> 0
bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y))
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
BIN(s(x), s(y)) -> BIN(x, s(y))
BIN(s(x), s(y)) -> BIN(x, y)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
Dependency Pairs:
BIN(s(x), s(y)) -> BIN(x, y)
BIN(s(x), s(y)) -> BIN(x, s(y))
Rules:
bin(x, 0) -> s(0)
bin(0, s(y)) -> 0
bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y))
The following dependency pairs can be strictly oriented:
BIN(s(x), s(y)) -> BIN(x, y)
BIN(s(x), s(y)) -> BIN(x, s(y))
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: BIN(x1, x2) -> BIN(x1, x2)
s(x1) -> s(x1)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rules:
bin(x, 0) -> s(0)
bin(0, s(y)) -> 0
bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes