Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
or(true,y) |
→ true |
| 2: |
|
or(x,true) |
→ true |
| 3: |
|
or(false,false) |
→ false |
| 4: |
|
mem(x,nil) |
→ false |
| 5: |
|
mem(x,set(y)) |
→ x = y |
| 6: |
|
mem(x,union(y,z)) |
→ or(mem(x,y),mem(x,z)) |
|
There are 3 dependency pairs:
|
| 7: |
|
MEM(x,union(y,z)) |
→ OR(mem(x,y),mem(x,z)) |
| 8: |
|
MEM(x,union(y,z)) |
→ MEM(x,y) |
| 9: |
|
MEM(x,union(y,z)) |
→ MEM(x,z) |
|
The approximated dependency graph contains one SCC:
{8,9}.
-
Consider the SCC {8,9}.
There are no usable rules.
By taking the AF π with
π(MEM) = 2 together with
the lexicographic path order with
empty precedence,
the rules in {8,9}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006