Term Rewriting System R:
[x, y, z]
*(x, *(y, z)) -> *(*(x, y), z)
*(x, x) -> x

Innermost Termination of R to be shown.

R
Dependency Pair Analysis

R contains the following Dependency Pairs:

*'(x, *(y, z)) -> *'(*(x, y), z)
*'(x, *(y, z)) -> *'(x, y)

Furthermore, R contains one SCC.

R
DPs
→DP Problem 1
Polynomial Ordering

Dependency Pair:

*'(x, *(y, z)) -> *'(x, y)

Rules:

*(x, *(y, z)) -> *(*(x, y), z)
*(x, x) -> x

Strategy:

innermost

The following dependency pair can be strictly oriented:

*'(x, *(y, z)) -> *'(x, y)

There are no usable rules for innermost w.r.t. to the implicit AFS that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:
 POL(*'(x1, x2)) =  x2 POL(*(x1, x2)) =  1 + x1

resulting in one new DP problem.

R
DPs
→DP Problem 1
Polo
→DP Problem 2
Dependency Graph

Dependency Pair:

Rules:

*(x, *(y, z)) -> *(*(x, y), z)
*(x, x) -> x

Strategy:

innermost

Using the Dependency Graph resulted in no new DP problems.

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