Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
a__f(X) |
→ g(h(f(X))) |
| 2: |
|
mark(f(X)) |
→ a__f(mark(X)) |
| 3: |
|
mark(g(X)) |
→ g(X) |
| 4: |
|
mark(h(X)) |
→ h(mark(X)) |
| 5: |
|
a__f(X) |
→ f(X) |
|
There are 3 dependency pairs:
|
| 6: |
|
MARK(f(X)) |
→ A__F(mark(X)) |
| 7: |
|
MARK(f(X)) |
→ MARK(X) |
| 8: |
|
MARK(h(X)) |
→ MARK(X) |
|
The approximated dependency graph contains one SCC:
{7,8}.
-
Consider the SCC {7,8}.
There are no usable rules.
By taking the AF π with
π(f) = π(MARK) = 1 together with
the lexicographic path order with
empty precedence,
rule 7
is weakly decreasing and
rule 8
is strictly decreasing.
There is one new SCC.
-
Consider the SCC {7}.
By taking the AF π with
π(MARK) = 1 together with
the lexicographic path order with
empty precedence,
rule 7
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006