Certificate for #21046 ⟨a, b | ab=aa, bbbb=bba⟩

Back:⟨a, b | ab=aa, bbbb=bba⟩

Completion settings:

[1] aa=ab

Axiom: ab=aa.

Flip LHS and RHS.

Defines rule #4.

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

[2] bba=bbbb

Axiom: bbbb=bba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

[3] aba=abb

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

a a aa

Critical pair: aab=aba.

Reduce LHS:

[1](aa)b
⇒ abb

Flip LHS and RHS.

Defines rule #5.

Referenced by [4].

[4] abbbb=abbb

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

a a aba

Critical pair: aabb=abba.

Reduce LHS:

[1](aa)bb
⇒ abbb

Reduce RHS:

[2]a(bba)
⇒ abbbb

Flip LHS and RHS.

Defines rule #2.

[5] bbbbbb=bbbbb

Overlap of [2] bba=bbbb with [1] aa=ab:

bb a aa

Critical pair: bbab=bbbba.

Reduce LHS:

[2](bba)b
⇒ bbbbb

Reduce RHS:

[2]bb(bba)
⇒ bbbbbb

Flip LHS and RHS.

Defines rule #1.