Certificate for #20819 ⟨a, b | ab=aa, bbaaa=bb⟩

Back:⟨a, b | ab=aa, bbaaa=bb⟩

Completion settings:

[1] aa=ab

Axiom: ab=aa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [2], [3], [4].

[2] bbaba=bb

Axiom: bbaaa=bb.

Reduce LHS:

[1]bb(aa)a
⇒ bbaba

Referenced by [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 #3.

Referenced by [4], [5].

[4] abba=abbb

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

a a aba

Critical pair: aabb=abba.

Reduce LHS:

[1](aa)bb
⇒ abbb

Flip LHS and RHS.

Referenced by [6].

[5] bbabb=bb

Simplify [2] bbaba=bb.

Reduce LHS:

[3]bb(aba)
⇒ bbabb

Referenced by [6], [7].

[6] bba=bbb

Overlap of [5] bbabb=bb with [4] abba=abbb:

bb abb abba

Critical pair: bbabbb=bba.

Reduce LHS:

[5](bbabb)b
⇒ bbb

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

[7] bbbbb=bb

Overlap of [5] bbabb=bb with [6] bba=bbb:

bbabb bba

Critical pair: bbbbb=bb.

Defines rule #4.