Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(x,c(y)) |
→ f(x,s(f(y,y))) |
| 2: |
|
f(s(x),s(y)) |
→ f(x,s(c(s(y)))) |
|
There are 3 dependency pairs:
|
| 3: |
|
F(x,c(y)) |
→ F(x,s(f(y,y))) |
| 4: |
|
F(x,c(y)) |
→ F(y,y) |
| 5: |
|
F(s(x),s(y)) |
→ F(x,s(c(s(y)))) |
|
The approximated dependency graph contains 2 SCCs:
{5}
and {4}.
-
Consider the SCC {5}.
There are no usable rules.
By taking the AF π with
π(F) = 1 together with
the lexicographic path order with
empty precedence,
rule 5
is strictly decreasing.
-
Consider the SCC {4}.
There are no usable rules.
By taking the AF π with
π(F) = 2 together with
the lexicographic path order with
empty precedence,
rule 4
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.02 seconds)
--- May 4, 2006