Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
intlist(nil) |
→ nil |
| 2: |
|
int(s(x),0) |
→ nil |
| 3: |
|
int(x,x) |
→ cons(x,nil) |
| 4: |
|
intlist(cons(x,y)) |
→ cons(s(x),intlist(y)) |
| 5: |
|
int(s(x),s(y)) |
→ intlist(int(x,y)) |
| 6: |
|
int(0,s(y)) |
→ cons(0,int(s(0),s(y))) |
| 7: |
|
intlist(cons(x,nil)) |
→ cons(s(x),nil) |
|
There are 4 dependency pairs:
|
| 8: |
|
INTLIST(cons(x,y)) |
→ INTLIST(y) |
| 9: |
|
INT(s(x),s(y)) |
→ INTLIST(int(x,y)) |
| 10: |
|
INT(s(x),s(y)) |
→ INT(x,y) |
| 11: |
|
INT(0,s(y)) |
→ INT(s(0),s(y)) |
|
The approximated dependency graph contains 2 SCCs:
{8}
and {10,11}.
-
Consider the SCC {8}.
There are no usable rules.
By taking the AF π with
π(INTLIST) = 1
and π(cons) = [2] together with
the lexicographic path order with
empty precedence,
rule 8
is strictly decreasing.
-
Consider the SCC {10,11}.
There are no usable rules.
By taking the AF π with
π(INT) = 2 together with
the lexicographic path order with
empty precedence,
rule 11
is weakly decreasing and
rule 10
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006