Termination Proof Script
Consider the TRS R consisting of the rewrite rule
|
| 1: |
|
x * (y + z) |
→ (x * y) + (x * z) |
|
There are 2 dependency pairs:
|
| 2: |
|
x *# (y + z) |
→ x *# y |
| 3: |
|
x *# (y + z) |
→ x *# z |
|
The approximated dependency graph contains one SCC:
{2,3}.
-
Consider the SCC {2,3}.
There are no usable rules.
By taking the AF π with
π(*#) = 2 together with
the lexicographic path order with
empty precedence,
the rules in {2,3}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006