Certificate for #4370 ⟨a, b, c | aba=1, aaac=c⟩

Back:⟨a, b, c | aba=1, aaac=c⟩

Completion settings:

[1] aba=1

Axiom: aba=1.

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

[2] aaac=c

Axiom: aaac=c.

Defines rule #4.

Referenced by [4].

[3] ba=ab

Overlap of [1] aba=1 with [1] aba=1:

ab a aba

Critical pair: ab=ba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [5].

[4] bc=ac

Overlap of [3] ba=ab with [2] aaac=c:

b a aaac

Critical pair: bc=abaac.

Reduce RHS:

[1](aba)ac
⇒ ac

Defines rule #2.

[5] aab=1

Overlap of [1] aba=1 with [3] ba=ab:

a ba ba

Critical pair: aab=1.

Defines rule #3.