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 2023)

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: