Termination Proof Script
Consider the TRS R consisting of the rewrite rule
|
| 1: |
|
dfib(s(s(x)),y) |
→ dfib(s(x),dfib(x,y)) |
|
There are 2 dependency pairs:
|
| 2: |
|
DFIB(s(s(x)),y) |
→ DFIB(s(x),dfib(x,y)) |
| 3: |
|
DFIB(s(s(x)),y) |
→ DFIB(x,y) |
|
Consider the SCC {2,3}.
By taking the AF π with
π(dfib) = π(DFIB) = 1 together with
the lexicographic path order with
empty precedence,
the rules in {1-3}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006