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 w.r.t. to the implicit AFS 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