Certificate for #13191 ⟨a, b | abb=aaa, bbb=ab⟩

Back:⟨a, b | abb=aaa, bbb=ab⟩

Completion settings:

[1] aaa=abb

Axiom: abb=aaa.

Flip LHS and RHS.

Referenced by [3].

[2] ab=bbb

Axiom: bbb=ab.

Flip LHS and RHS.

Defines rule #2.

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

[3] aaa=bbbb

Simplify [1] aaa=abb.

Reduce RHS:

[2](ab)b
⇒ bbbb

Defines rule #4.

Referenced by [4], [5].

[4] bbbba=bbbbbb

Overlap of [3] aaa=bbbb with [3] aaa=bbbb:

a aa aaa

Critical pair: abbbb=bbbba.

Reduce LHS:

[2](ab)bbb
⇒ bbbbbb

Flip LHS and RHS.

Defines rule #3.

[5] bbbbbbb=bbbbb

Overlap of [3] aaa=bbbb with [2] ab=bbb:

aa a ab

Critical pair: aabbb=bbbbb.

Reduce LHS:

[2]a(ab)bb
[2]⇒ (ab)bbbb
⇒ bbbbbbb

Defines rule #1.