Certificate for #20295 ⟨a, b | aba=b, abbb=abb⟩

Back:⟨a, b | aba=b, abbb=abb⟩

Completion settings:

[1] aba=b

Axiom: aba=b.

Defines rule #1.

Referenced by [3], [4], [5], [6].

[2] abbb=abb

Axiom: abbb=abb.

Defines rule #4.

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

[3] bba=abb

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

ab a aba

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] aabb=bbb

Overlap of [3] bba=abb with [1] aba=b:

bb a aba

Critical pair: bbb=abbba.

Reduce RHS:

[2](abbb)a
[3]⇒ a(bba)
⇒ aabb

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] babb=abb

Overlap of [1] aba=b with [4] aabb=bbb:

ab a aabb

Critical pair: abbbb=babb.

Reduce LHS:

[2](abbb)b
[2]⇒ (abbb)
⇒ abb

Flip LHS and RHS.

Defines rule #5.

[6] bbbb=bbb

Overlap of [1] aba=b with [2] abbb=abb:

ab a abbb

Critical pair: ababb=bbbb.

Reduce LHS:

[1](aba)bb
⇒ bbb

Flip LHS and RHS.

Defines rule #6.