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