Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
quot(0,s(y),s(z)) |
→ 0 |
| 2: |
|
quot(s(x),s(y),z) |
→ quot(x,y,z) |
| 3: |
|
quot(x,0,s(z)) |
→ s(quot(x,s(z),s(z))) |
|
There are 2 dependency pairs:
|
| 4: |
|
QUOT(s(x),s(y),z) |
→ QUOT(x,y,z) |
| 5: |
|
QUOT(x,0,s(z)) |
→ QUOT(x,s(z),s(z)) |
|
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(QUOT) = 1 together with
the lexicographic path order with
empty precedence,
rule 5
is weakly decreasing and
rule 4
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006