Certificate for #20047 ⟨a, b | aab=a, bbbb=bbb⟩

Back:⟨a, b | aab=a, bbbb=bbb⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

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

[2] bbbb=bbb

Axiom: bbbb=bbb.

Defines rule #3.

Referenced by [3].

[3] abbb=abb

Overlap of [1] aab=a with [2] bbbb=bbb:

aa b bbbb

Critical pair: aabbb=abbb.

Reduce LHS:

[1](aab)bb
⇒ abb

Flip LHS and RHS.

Referenced by [4].

[4] abb=ab

Overlap of [1] aab=a with [3] abbb=abb:

a ab abbb

Critical pair: aabb=abb.

Reduce LHS:

[1](aab)b
⇒ ab

Flip LHS and RHS.

Referenced by [5].

[5] ab=a

Overlap of [1] aab=a with [4] abb=ab:

a ab abb

Critical pair: aab=ab.

Reduce LHS:

[1](aab)
⇒ a

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

[6] aa=a

Overlap of [1] aab=a with [5] ab=a:

a ab ab

Critical pair: aa=a.

Defines rule #1.