Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
bin(x,0) |
→ s(0) |
| 2: |
|
bin(0,s(y)) |
→ 0 |
| 3: |
|
bin(s(x),s(y)) |
→ bin(x,s(y)) + bin(x,y) |
|
There are 2 dependency pairs:
|
| 4: |
|
BIN(s(x),s(y)) |
→ BIN(x,s(y)) |
| 5: |
|
BIN(s(x),s(y)) |
→ BIN(x,y) |
|
The approximated dependency graph contains one SCC:
{4,5}.
-
Consider the SCC {4,5}.
There are no usable rules.
By taking the AF π with
π(BIN) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {4,5}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006