Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
(x : y) : z |
→ x : (y : z) |
| 2: |
|
(x + y) : z |
→ (x : z) + (y : z) |
| 3: |
|
z : (x + f(y)) |
→ g(z,y) : (x + a) |
|
There are 5 dependency pairs:
|
| 4: |
|
(x : y) :# z |
→ x :# (y : z) |
| 5: |
|
(x : y) :# z |
→ y :# z |
| 6: |
|
(x + y) :# z |
→ x :# z |
| 7: |
|
(x + y) :# z |
→ y :# z |
| 8: |
|
z :# (x + f(y)) |
→ g(z,y) :# (x + a) |
|
The approximated dependency graph contains one SCC:
{4-7}.
-
Consider the SCC {4-7}.
By taking the AF π with
π(:#) = π(g) = 1
and π(f) = [ ] together with
the lexicographic path order with
precedence : ≻ +
and f ≻ a,
the rules in {1-7}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.07 seconds)
--- May 3, 2006