Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
g(x,y) |
→ x |
| 2: |
|
g(x,y) |
→ y |
| 3: |
|
f(0,1,x) |
→ f(s(x),x,x) |
| 4: |
|
f(x,y,s(z)) |
→ s(f(0,1,z)) |
|
There are 2 dependency pairs:
|
| 5: |
|
F(0,1,x) |
→ F(s(x),x,x) |
| 6: |
|
F(x,y,s(z)) |
→ F(0,1,z) |
|
The approximated dependency graph contains one SCC:
{5,6}.
-
Consider the SCC {5,6}.
There are no usable rules.
By taking the AF π with
π(F) = 3 together with
the lexicographic path order with
empty precedence,
rule 5
is weakly decreasing and
rule 6
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006