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 ACP @ CoCo 2022)

1 Non-Joinable Fork

The system is not confluent due to the following forking derivations.

t0 = gt(BIT1(c_1),BIT0(0))
ge(c_1,0)
= t1

t0 = gt(BIT1(c_1),BIT0(0))
gt(BIT1(c_1),0)
T
= t2

The two resulting terms cannot be joined for the following reason: