Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(x,c(x),c(y)) |
→ f(y,y,f(y,x,y)) |
| 2: |
|
f(s(x),y,z) |
→ f(x,s(c(y)),c(z)) |
| 3: |
|
f(c(x),x,y) |
→ c(y) |
| 4: |
|
g(x,y) |
→ x |
| 5: |
|
g(x,y) |
→ y |
|
There are 3 dependency pairs:
|
| 6: |
|
F(x,c(x),c(y)) |
→ F(y,y,f(y,x,y)) |
| 7: |
|
F(x,c(x),c(y)) |
→ F(y,x,y) |
| 8: |
|
F(s(x),y,z) |
→ F(x,s(c(y)),c(z)) |
|
The approximated dependency graph contains 2 SCCs:
{8}
and {6,7}.
-
Consider the SCC {8}.
There are no usable rules.
By taking the AF π with
π(F) = 1 together with
the lexicographic path order with
empty precedence,
rule 8
is strictly decreasing.
-
Consider the SCC {6,7}.
The usable rules are {1-3}.
The constraints could not be solved.
Tyrolean Termination Tool (0.03 seconds)
--- May 4, 2006