Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
plus(plus(X,Y),Z) |
→ plus(X,plus(Y,Z)) |
| 2: |
|
times(X,s(Y)) |
→ plus(X,times(Y,X)) |
|
There are 4 dependency pairs:
|
| 3: |
|
PLUS(plus(X,Y),Z) |
→ PLUS(X,plus(Y,Z)) |
| 4: |
|
PLUS(plus(X,Y),Z) |
→ PLUS(Y,Z) |
| 5: |
|
TIMES(X,s(Y)) |
→ PLUS(X,times(Y,X)) |
| 6: |
|
TIMES(X,s(Y)) |
→ TIMES(Y,X) |
|
The approximated dependency graph contains 2 SCCs:
{3,4}
and {6}.
-
Consider the SCC {3,4}.
The usable rules are {1}.
By taking the AF π with
π(PLUS) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {1,3,4}
are strictly decreasing.
-
Consider the SCC {6}.
There are no usable rules.
The constraints could not be solved.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006