Certificate for #16404 ⟨a, b | aba=ab, abbb=bb⟩

Back:⟨a, b | aba=ab, abbb=bb⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #1.

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

[2] abbb=bb

Axiom: abbb=bb.

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

[3] abba=abb

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

ab a aba

Critical pair: abab=abba.

Reduce LHS:

[1](aba)b
⇒ abb

Flip LHS and RHS.

Referenced by [5].

[4] bbb=bb

Overlap of [1] aba=ab with [2] abbb=bb:

ab a abbb

Critical pair: abbb=abbbb.

Reduce LHS:

[2](abbb)
⇒ bb

Reduce RHS:

[2](abbb)b
⇒ bbb

Flip LHS and RHS.

Defines rule #4.

Referenced by [6].

[5] bba=bb

Overlap of [1] aba=ab with [3] abba=abb:

ab a abba

Critical pair: ababb=abbba.

Reduce LHS:

[1](aba)bb
[2]⇒ (abbb)
⇒ bb

Reduce RHS:

[2](abbb)a
⇒ bba

Flip LHS and RHS.

Defines rule #3.

[6] abb=bb

Overlap of [2] abbb=bb with [4] bbb=bb:

a bbb bbb

Critical pair: abb=bb.

Defines rule #2.