Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(x,0) |
→ s(0) |
| 2: |
|
f(s(x),s(y)) |
→ s(f(x,y)) |
| 3: |
|
g(0,x) |
→ g(f(x,x),x) |
|
There are 3 dependency pairs:
|
| 4: |
|
F(s(x),s(y)) |
→ F(x,y) |
| 5: |
|
G(0,x) |
→ G(f(x,x),x) |
| 6: |
|
G(0,x) |
→ F(x,x) |
|
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