Termination Proof Script
Consider the TRS R consisting of the rewrite rules
|
| 1: |
|
ack(0,y) |
→ s(y) |
| 2: |
|
ack(s(x),0) |
→ ack(x,s(0)) |
| 3: |
|
ack(s(x),s(y)) |
→ ack(x,ack(s(x),y)) |
| 4: |
|
f(s(x),y) |
→ f(x,s(x)) |
| 5: |
|
f(x,s(y)) |
→ f(y,x) |
| 6: |
|
f(x,y) |
→ ack(x,y) |
| 7: |
|
ack(s(x),y) |
→ f(x,x) |
|
There are 7 dependency pairs:
|
| 8: |
|
ACK(s(x),0) |
→ ACK(x,s(0)) |
| 9: |
|
ACK(s(x),s(y)) |
→ ACK(x,ack(s(x),y)) |
| 10: |
|
ACK(s(x),s(y)) |
→ ACK(s(x),y) |
| 11: |
|
F(s(x),y) |
→ F(x,s(x)) |
| 12: |
|
F(x,s(y)) |
→ F(y,x) |
| 13: |
|
F(x,y) |
→ ACK(x,y) |
| 14: |
|
ACK(s(x),y) |
→ F(x,x) |
|
Consider the SCC {8-14}.
The constraints could not be solved.
Tyrolean Termination Tool (0.02 seconds)
--- May 3, 2006