Certificate for #568 ⟨a, b | abab=aaba⟩

Back:⟨a, b | abab=aaba⟩

Completion settings:

[1] abab=aaba

Axiom: abab=aaba.

Referenced by [3].

[2] ab=c

Axiom: ab=c.

Defines rule #1.

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

[3] abab=aca

Simplify [1] abab=aaba.

Reduce RHS:

[2]a(ab)a
⇒ aca

Referenced by [4].

[4] aca=cc

Overlap of [3] abab=aca with [2] ab=c:

abab ab

Critical pair: cab=aca.

Reduce LHS:

[2]c(ab)
⇒ cc

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6].

[5] ccb=acc

Overlap of [4] aca=cc with [2] ab=c:

ac a ab

Critical pair: acc=ccb.

Flip LHS and RHS.

Defines rule #3.

[6] ccca=accc

Overlap of [4] aca=cc with [4] aca=cc:

ac a aca

Critical pair: accc=ccca.

Flip LHS and RHS.

Defines rule #4.