Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
h(X,Z) |
→ f(X,s(X),Z) |
| 2: |
|
f(X,Y,g(X,Y)) |
→ h(0,g(X,Y)) |
| 3: |
|
g(0,Y) |
→ 0 |
| 4: |
|
g(X,s(Y)) |
→ g(X,Y) |
|
There are 3 dependency pairs:
|
| 5: |
|
H(X,Z) |
→ F(X,s(X),Z) |
| 6: |
|
F(X,Y,g(X,Y)) |
→ H(0,g(X,Y)) |
| 7: |
|
G(X,s(Y)) |
→ G(X,Y) |
|
The approximated dependency graph contains 2 SCCs:
{7}
and {5,6}.
-
Consider the SCC {7}.
There are no usable rules.
By taking the AF π with
π(G) = 2 together with
the lexicographic path order with
empty precedence,
rule 7
is strictly decreasing.
-
Consider the SCC {5,6}.
The usable rules are {3,4}.
The constraints could not be solved.
Tyrolean Termination Tool (0.04 seconds)
--- May 3, 2006