Certificate for #2426 ⟨a, b, c | aab=b, acba=1⟩

Back:⟨a, b, c | aab=b, acba=1⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #1.

Referenced by [4].

[2] acba=1

Axiom: acba=1.

Referenced by [3], [4], [5].

[3] cba=acb

Overlap of [2] acba=1 with [2] acba=1:

acb a acba

Critical pair: acb=cba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] cbb=b

Overlap of [3] cba=acb with [1] aab=b:

cb a aab

Critical pair: cbb=acbab.

Reduce RHS:

[2](acba)b
⇒ b

Defines rule #3.

[5] aacb=1

Overlap of [2] acba=1 with [3] cba=acb:

a cba cba

Critical pair: aacb=1.

Defines rule #4.