Certificate for #16430 ⟨a, b | aba=ab, bbba=ab⟩

Back:⟨a, b | aba=ab, bbba=ab⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Referenced by [3].

[2] ab=bbba

Axiom: bbba=ab.

Flip LHS and RHS.

Defines rule #2.

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

[3] aba=bbba

Simplify [1] aba=ab.

Reduce RHS:

[2](ab)
⇒ bbba

Referenced by [4].

[4] bbbaa=bbba

Overlap of [3] aba=bbba with [2] ab=bbba:

aba ab

Critical pair: bbbaa=bbba.

Defines rule #3.

Referenced by [5].

[5] bbbbbbbbbbbba=bbbbbba

Overlap of [4] bbbaa=bbba with [2] ab=bbba:

bbba a ab

Critical pair: bbbabbba=bbbab.

Reduce LHS:

[2]bbb(ab)bba
[2]⇒ bbbbbb(ab)ba
[2]⇒ bbbbbbbbb(ab)a
[4]⇒ bbbbbbbbb(bbbaa)
⇒ bbbbbbbbbbbba

Reduce RHS:

[2]bbb(ab)
⇒ bbbbbba

Defines rule #1.