Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(0,y) |
→ 0 |
| 2: |
|
f(s(x),y) |
→ f(f(x,y),y) |
|
There are 2 dependency pairs:
|
| 3: |
|
F(s(x),y) |
→ F(f(x,y),y) |
| 4: |
|
F(s(x),y) |
→ F(x,y) |
|
The approximated dependency graph contains one SCC:
{4}.
-
Consider the SCC {4}.
There are no usable rules.
By taking the AF π with
π(F) = 1 together with
the lexicographic path order with
empty precedence,
rule 4
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006