Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
a__g(X) |
→ a__h(X) |
| 2: |
|
a__c |
→ d |
| 3: |
|
a__h(d) |
→ a__g(c) |
| 4: |
|
mark(g(X)) |
→ a__g(X) |
| 5: |
|
mark(h(X)) |
→ a__h(X) |
| 6: |
|
mark(c) |
→ a__c |
| 7: |
|
mark(d) |
→ d |
| 8: |
|
a__g(X) |
→ g(X) |
| 9: |
|
a__h(X) |
→ h(X) |
| 10: |
|
a__c |
→ c |
|
There are 5 dependency pairs:
|
| 11: |
|
A__G(X) |
→ A__H(X) |
| 12: |
|
A__H(d) |
→ A__G(c) |
| 13: |
|
MARK(g(X)) |
→ A__G(X) |
| 14: |
|
MARK(h(X)) |
→ A__H(X) |
| 15: |
|
MARK(c) |
→ A__C |
|
The approximated dependency graph contains one SCC:
{11,12}.
-
Consider the SCC {11,12}.
There are no usable rules.
By taking the AF π with
π(A__G) = π(A__H) = 1 together with
the lexicographic path order with
precedence d ≻ c,
rule 11
is weakly decreasing and
rule 12
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006