Certificate for #16420 ⟨a, b | aba=ab, babb=bb⟩

Back:⟨a, b | aba=ab, babb=bb⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #1.

Referenced by [3], [4].

[2] babb=bb

Axiom: babb=bb.

Defines rule #4.

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] abbb=abb

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

a ba babb

Critical pair: abb=abbb.

Flip LHS and RHS.

Referenced by [6].

[5] bba=bb

Overlap of [2] babb=bb with [3] abba=abb:

b abb abba

Critical pair: babb=bba.

Reduce LHS:

[2](babb)
⇒ bb

Flip LHS and RHS.

Defines rule #2.

[6] bbb=bb

Overlap of [2] babb=bb with [4] abbb=abb:

b abb abbb

Critical pair: babb=bbb.

Reduce LHS:

[2](babb)
⇒ bb

Flip LHS and RHS.

Defines rule #3.