Certificate for #28179 ⟨a, b | aa=1, ababb=bbab⟩

Back:⟨a, b | aa=1, ababb=bbab⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [4].

[2] bbab=ababb

Axiom: ababb=bbab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[3] ababababb=bababbb

Overlap of [2] bbab=ababb with [2] bbab=ababb:

bba b bbab

Critical pair: bbaababb=ababbbab.

Reduce LHS:

[1]bb(aa)babb
[2]⇒ b(bbab)b
⇒ bababbb

Reduce RHS:

[2]abab(bbab)
⇒ ababababb

Flip LHS and RHS.

Referenced by [4].

[4] babababb=abababbb

Overlap of [1] aa=1 with [3] ababababb=bababbb:

a a ababababb

Critical pair: abababbb=babababb.

Flip LHS and RHS.

Defines rule #3.