Certificate for #13215 ⟨a, b | abb=aba, bba=ab⟩

Back:⟨a, b | abb=aba, bba=ab⟩

Completion settings:

[1] aba=abb

Axiom: abb=aba.

Flip LHS and RHS.

Referenced by [3].

[2] ab=bba

Axiom: bba=ab.

Flip LHS and RHS.

Defines rule #2.

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

[3] aba=bbbba

Simplify [1] aba=abb.

Reduce RHS:

[2](ab)b
[2]⇒ bb(ab)
⇒ bbbba

Referenced by [4].

[4] bbaa=bbbba

Overlap of [3] aba=bbbba with [2] ab=bba:

aba ab

Critical pair: bbaa=bbbba.

Defines rule #3.

Referenced by [5].

[5] bbbbbbbba=bbbbbba

Overlap of [4] bbaa=bbbba with [2] ab=bba:

bba a ab

Critical pair: bbabba=bbbbab.

Reduce LHS:

[2]bb(ab)ba
[2]⇒ bbbb(ab)a
[4]⇒ bbbb(bbaa)
⇒ bbbbbbbba

Reduce RHS:

[2]bbbb(ab)
⇒ bbbbbba

Defines rule #1.