Certificate for #16142 ⟨a, b | aab=aa, bbbb=ab⟩

Back:⟨a, b | aab=aa, bbbb=ab⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Referenced by [3].

[2] ab=bbbb

Axiom: bbbb=ab.

Flip LHS and RHS.

Defines rule #2.

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

[3] aa=bbbbbbb

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

a ab ab

Critical pair: abbbb=aa.

Reduce LHS:

[2](ab)bbb
⇒ bbbbbbb

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

[4] bbbbbbbb=bbbbbbb

Overlap of [3] aa=bbbbbbb with [2] ab=bbbb:

a a ab

Critical pair: abbbb=bbbbbbbb.

Reduce LHS:

[2](ab)bbb
⇒ bbbbbbb

Flip LHS and RHS.

Defines rule #1.

Referenced by [5].

[5] bbbbbbba=bbbbbbb

Overlap of [3] aa=bbbbbbb with [3] aa=bbbbbbb:

a a aa

Critical pair: abbbbbbb=bbbbbbba.

Reduce LHS:

[2](ab)bbbbbb
[4]⇒ (bbbbbbbb)bb
[4]⇒ (bbbbbbbb)b
[4]⇒ (bbbbbbbb)
⇒ bbbbbbb

Flip LHS and RHS.

Defines rule #3.