Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
f(0,y) |
→ y |
| 2: |
|
f(x,0) |
→ x |
| 3: |
|
f(i(x),y) |
→ i(x) |
| 4: |
|
f(f(x,y),z) |
→ f(x,f(y,z)) |
| 5: |
|
f(g(x,y),z) |
→ g(f(x,z),f(y,z)) |
| 6: |
|
f(1,g(x,y)) |
→ x |
| 7: |
|
f(2,g(x,y)) |
→ y |
|
There are 4 dependency pairs:
|
| 8: |
|
F(f(x,y),z) |
→ F(x,f(y,z)) |
| 9: |
|
F(f(x,y),z) |
→ F(y,z) |
| 10: |
|
F(g(x,y),z) |
→ F(x,z) |
| 11: |
|
F(g(x,y),z) |
→ F(y,z) |
|
Consider the SCC {8-11}.
By taking the AF π with
π(F) = π(i) = 1 together with
the lexicographic path order with
precedence f ≻ g,
the rules in {1-11}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006