Certificate for #4378 ⟨a, b, c | aba=1, aaca=c⟩

Back:⟨a, b, c | aba=1, aaca=c⟩

Completion settings:

[1] aba=1

Axiom: aba=1.

Referenced by [3], [4], [5], [6].

[2] aaca=c

Axiom: aaca=c.

Referenced by [4], [5].

[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 #2.

Referenced by [4], [5], [6].

[4] aac=cab

Overlap of [2] aaca=c with [1] aba=1:

aac a aba

Critical pair: aac=cba.

Reduce RHS:

[3]c(ba)
⇒ cab

Defines rule #3.

[5] bc=ca

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

b a aaca

Critical pair: bc=abaca.

Reduce RHS:

[1](aba)ca
⇒ ca

Defines rule #1.

[6] aab=1

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

a ba ba

Critical pair: aab=1.

Defines rule #4.