Certificate for #330 ⟨a, b | aa=1, abba=b⟩

Back:⟨a, b | aa=1, abba=b⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #3.

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

[2] abba=b

Axiom: abba=b.

Referenced by [3], [4].

[3] bba=ab

Overlap of [1] aa=1 with [2] abba=b:

a a abba

Critical pair: ab=bba.

Flip LHS and RHS.

Referenced by [5].

[4] ba=abb

Overlap of [2] abba=b with [1] aa=1:

abb a aa

Critical pair: abb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] abbbb=ab

Simplify [3] bba=ab.

Reduce LHS:

[4]b(ba)
[4]⇒ (ba)bb
⇒ abbbb

Referenced by [6].

[6] bbbb=b

Overlap of [1] aa=1 with [5] abbbb=ab:

a a abbbb

Critical pair: aab=bbbb.

Reduce LHS:

[1](aa)b
⇒ b

Flip LHS and RHS.

Defines rule #1.