Term Rewriting System R:
[x, y, z]
and(not(not(x)), y, not(z)) -> and(y, band(x, z), x)
Termination of R to be shown.
R
↳Dependency Pair Analysis
R contains the following Dependency Pairs:
AND(not(not(x)), y, not(z)) -> AND(y, band(x, z), x)
Furthermore, R contains one SCC.
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
Dependency Pair:
AND(not(not(x)), y, not(z)) -> AND(y, band(x, z), x)
Rule:
and(not(not(x)), y, not(z)) -> and(y, band(x, z), x)
The following dependency pair can be strictly oriented:
AND(not(not(x)), y, not(z)) -> AND(y, band(x, z), x)
There are no usable rules using the Ce-refinement that need to be oriented.
Used ordering: Polynomial ordering with Polynomial interpretation:
POL(band(x1, x2)) | = 0 |
POL(not(x1)) | = 1 |
POL(AND(x1, x2, x3)) | = 1 + x1 + x2 |
resulting in one new DP problem.
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Dependency Graph
Dependency Pair:
Rule:
and(not(not(x)), y, not(z)) -> and(y, band(x, z), x)
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes