Certificate for #3383 ⟨a, b | aa=1, abbbab=b⟩

Back:⟨a, b | aa=1, abbbab=b⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [5].

[2] abbbab=b

Axiom: abbbab=b.

Referenced by [3], [4].

[3] bbbab=ab

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

a a abbbab

Critical pair: ab=bbbab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] abbbb=ab

Overlap of [2] abbbab=b with [2] abbbab=b:

abbb ab abbbab

Critical pair: abbbb=bbbab.

Reduce RHS:

[3](bbbab)
⇒ ab

Referenced by [5].

[5] bbbb=b

Overlap of [1] aa=1 with [4] abbbb=ab:

a a abbbb

Critical pair: aab=bbbb.

Reduce LHS:

[1](aa)b
⇒ b

Flip LHS and RHS.

Defines rule #2.