Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
a(a(x)) |
→ b(b(x)) |
| 2: |
|
b(b(a(x))) |
→ a(b(b(x))) |
|
There are 5 dependency pairs:
|
| 3: |
|
A(a(x)) |
→ B(b(x)) |
| 4: |
|
A(a(x)) |
→ B(x) |
| 5: |
|
B(b(a(x))) |
→ A(b(b(x))) |
| 6: |
|
B(b(a(x))) |
→ B(b(x)) |
| 7: |
|
B(b(a(x))) |
→ B(x) |
|
Consider the SCC {3-7}.
By taking the AF π with
π(A) = π(b) = π(B) = 1 together with
the lexicographic path order with
empty precedence,
rule 2
is weakly decreasing and
the rules in {1,3-7}
are strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 3, 2006