Certificate for #6795 ⟨a, b | aba=b, bbbb=aa⟩

Back:⟨a, b | aba=b, bbbb=aa⟩

Completion settings:

[1] aba=b

Axiom: aba=b.

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

[2] aa=bbbb

Axiom: bbbb=aa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

[3] bba=abb

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

ab a aba

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [5], [6].

[4] ba=abbbbb

Overlap of [1] aba=b with [2] aa=bbbb:

ab a aa

Critical pair: abbbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] abbbbbbbbb=ab

Overlap of [2] aa=bbbb with [1] aba=b:

a a aba

Critical pair: ab=bbbbba.

Reduce RHS:

[3]bbb(bba)
[3]⇒ b(bba)bb
[4]⇒ (ba)bbbb
⇒ abbbbbbbbb

Flip LHS and RHS.

Referenced by [6].

[6] bbbbbbbbb=b

Overlap of [5] abbbbbbbbb=ab with [3] bba=abb:

abbbbbbb bb bba

Critical pair: abbbbbbbabb=aba.

Reduce LHS:

[3]abbbbb(bba)bb
[3]⇒ abbb(bba)bbbb
[3]⇒ ab(bba)bbbbbb
[1]⇒ (aba)bbbbbbbb
⇒ bbbbbbbbb

Reduce RHS:

[1](aba)
⇒ b

Defines rule #1.