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