Certificate for #1121 ⟨a, b | aa=1, abbba=b⟩

Back:⟨a, b | aa=1, abbba=b⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #3.

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

[2] abbba=b

Axiom: abbba=b.

Referenced by [3], [4].

[3] bbba=ab

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

a a abbba

Critical pair: ab=bbba.

Flip LHS and RHS.

Referenced by [5].

[4] ba=abbb

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

abbb a aa

Critical pair: abbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] abbbbbbbbb=ab

Simplify [3] bbba=ab.

Reduce LHS:

[4]bb(ba)
[4]⇒ b(ba)bbb
[4]⇒ (ba)bbbbbb
⇒ abbbbbbbbb

Referenced by [6].

[6] bbbbbbbbb=b

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

a a abbbbbbbbb

Critical pair: aab=bbbbbbbbb.

Reduce LHS:

[1](aa)b
⇒ b

Flip LHS and RHS.

Defines rule #1.