Term Rewriting System R:
[x, y, z]
and(not(not(x)), y, not(z)) -> and(y, band(x, z), x)

Innermost 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`
`         ↳Argument Filtering and 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)

Strategy:

innermost

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 for innermost w.r.t. to the AFS that need to be oriented.
Used ordering: Polynomial ordering with Polynomial interpretation:
 POL(not(x1)) =  1 + x1 POL(AND(x1, x2, x3)) =  1 + x1 + x2 + x3

resulting in one new DP problem.
Used Argument Filtering System:
AND(x1, x2, x3) -> AND(x1, x2, x3)
not(x1) -> not(x1)
band(x1, x2) -> x2

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳AFS`
`           →DP Problem 2`
`             ↳Dependency Graph`

Dependency Pair:

Rule:

and(not(not(x)), y, not(z)) -> and(y, band(x, z), x)

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

Innermost Termination of R successfully shown.
Duration:
0:00 minutes