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