Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
div(X,e) |
→ i(X) |
| 2: |
|
i(div(X,Y)) |
→ div(Y,X) |
| 3: |
|
div(div(X,Y),Z) |
→ div(Y,div(i(X),Z)) |
|
There are 5 dependency pairs:
|
| 4: |
|
DIV(X,e) |
→ I(X) |
| 5: |
|
I(div(X,Y)) |
→ DIV(Y,X) |
| 6: |
|
DIV(div(X,Y),Z) |
→ DIV(Y,div(i(X),Z)) |
| 7: |
|
DIV(div(X,Y),Z) |
→ DIV(i(X),Z) |
| 8: |
|
DIV(div(X,Y),Z) |
→ I(X) |
|
Consider the SCC {4-8}.
By taking the AF π with
π(DIV) = π(I) = 1 together with
the lexicographic path order with
precedence div ≈ i,
rule 4
is weakly decreasing and
the rules in {1-3,5-8}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.02 seconds)
--- May 4, 2006