Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
1: |
|
del(x . (y . z)) |
→ f(x = y,x,y,z) |
2: |
|
f(true,x,y,z) |
→ del(y . z) |
3: |
|
f(false,x,y,z) |
→ x . del(y . z) |
4: |
|
nil = nil |
→ true |
5: |
|
(x . y) = nil |
→ false |
6: |
|
nil = (y . z) |
→ false |
7: |
|
(x . y) = (u . v) |
→ and(x = u,y = v) |
|
There are 6 dependency pairs:
|
8: |
|
DEL(x . (y . z)) |
→ F(x = y,x,y,z) |
9: |
|
DEL(x . (y . z)) |
→ x =# y |
10: |
|
F(true,x,y,z) |
→ DEL(y . z) |
11: |
|
F(false,x,y,z) |
→ DEL(y . z) |
12: |
|
(x . y) =# (u . v) |
→ x =# u |
13: |
|
(x . y) =# (u . v) |
→ y =# v |
|
The approximated dependency graph contains one SCC:
{8,10,11}.
-
Consider the SCC {8,10,11}.
The usable rules are {4-7}.
The constraints could not be solved.
Tyrolean Termination Tool (0.22 seconds)
--- May 3, 2006