Certification Problem
Input (COPS 1124)
We consider the TRS containing the following rules:
There are 108 ruless (increase limit for explicit display).
The underlying signature is as follows:
{NUMERAL/1, 0/0, BIT0/1, SUC/1, BIT1/1, PRE/1, if/3, eq/2, plus/2, mult/2, exp/2, EVEN/1, T/0, F/0, ODD/1, le/2, lt/2, ge/2, gt/2, minus/2}Property / Task
Prove or disprove confluence.Answer / Result
No.Proof (by csi @ CoCo 2020)
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
plus(NUMERAL(0),NUMERAL(n)) |
|
→
|
plus(0,NUMERAL(n)) |
|
= |
t1
|
| t0
|
= |
plus(NUMERAL(0),NUMERAL(n)) |
|
→
|
NUMERAL(plus(0,n)) |
|
= |
t1
|
The two resulting terms cannot be joined for the following reason:
- When applying the cap-function on both terms (where variables may be treated like constants)
then the resulting terms do not unify.