Certificate for #1941 ⟨a, b, c | abc=ab, bcc=1⟩

Completion settings:

[1] abc=ab

Axiom: abc=ab.

Referenced by [3], [4].

[2] bcc=1

Axiom: bcc=1.

Defines rule #3.

Referenced by [3].

[3] ab=a

Overlap of [1] abc=ab with [2] bcc=1:

a bc bcc

Critical pair: a=abc.

Reduce RHS:

[1](abc)
⇒ ab

Flip LHS and RHS.

Defines rule #1.

Referenced by [4].

[4] ac=a

Overlap of [1] abc=ab with [3] ab=a:

abc ab

Critical pair: ac=ab.

Reduce RHS:

[3](ab)
⇒ a

Defines rule #2.