Certificate for #3441 ⟨a, b, c | ba=ac, aac=b⟩

Back:⟨a, b, c | ba=ac, aac=b⟩

Completion settings:

[1] ac=ba

Axiom: ba=ac.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [4].

[2] aba=b

Axiom: aac=b.

Reduce LHS:

[1]a(ac)
⇒ aba

Defines rule #1.

Referenced by [3], [4].

[3] bba=abb

Overlap of [2] aba=b with [2] aba=b:

ab a aba

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] bc=aabb

Overlap of [2] aba=b with [1] ac=ba:

ab a ac

Critical pair: abba=bc.

Reduce LHS:

[3]a(bba)
⇒ aabb

Flip LHS and RHS.

Defines rule #4.