Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
ackin(s(X),s(Y)) |
→ u21(ackin(s(X),Y),X) |
| 2: |
|
u21(ackout(X),Y) |
→ u22(ackin(Y,X)) |
|
There are 3 dependency pairs:
|
| 3: |
|
ACKIN(s(X),s(Y)) |
→ U21(ackin(s(X),Y),X) |
| 4: |
|
ACKIN(s(X),s(Y)) |
→ ACKIN(s(X),Y) |
| 5: |
|
U21(ackout(X),Y) |
→ ACKIN(Y,X) |
|
The approximated dependency graph contains one SCC:
{4}.
-
Consider the SCC {4}.
There are no usable rules.
By taking the AF π with
π(ACKIN) = 2 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 3, 2006