Certificate for #3469 ⟨a, b, c | ba=ac, bcb=a⟩

Back:⟨a, b, c | ba=ac, bcb=a⟩

Completion settings:

[1] ac=ba

Axiom: ba=ac.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3], [4].

[2] bcb=a

Axiom: bcb=a.

Defines rule #2.

Referenced by [3], [4].

[3] bab=bca

Overlap of [2] bcb=a with [2] bcb=a:

bc b bcb

Critical pair: bca=acb.

Reduce RHS:

[1](ac)b
⇒ bab

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] aab=baa

Overlap of [2] bcb=a with [3] bab=bca:

bc b bab

Critical pair: bcbca=aab.

Reduce LHS:

[2](bcb)ca
[1]⇒ (ac)a
⇒ baa

Flip LHS and RHS.

Defines rule #4.