Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
g(f(x),y) |
→ f(h(x,y)) |
| 2: |
|
h(x,y) |
→ g(x,f(y)) |
|
There are 2 dependency pairs:
|
| 3: |
|
G(f(x),y) |
→ H(x,y) |
| 4: |
|
H(x,y) |
→ G(x,f(y)) |
|
The approximated dependency graph contains one SCC:
{3,4}.
-
Consider the SCC {3,4}.
There are no usable rules.
By taking the AF π with
π(G) = π(H) = 1 together with
the lexicographic path order with
empty precedence,
rule 4
is weakly decreasing and
rule 3
is strictly decreasing.
Hence the TRS is terminating.
Tyrolean Termination Tool (0.01 seconds)
--- May 4, 2006