Certificate for #28181 ⟨a, b | aa=1, ababb=bbbb⟩

Back:⟨a, b | aa=1, ababb=bbbb⟩

Completion settings:

[1] aa=1

Axiom: aa=1.

Defines rule #3.

Referenced by [3].

[2] ababb=bbbb

Axiom: ababb=bbbb.

Referenced by [3], [4].

[3] babb=abbbb

Overlap of [1] aa=1 with [2] ababb=bbbb:

a a ababb

Critical pair: abbbb=babb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] bbbbbbbbbb=bbbbbbb

Overlap of [3] babb=abbbb with [3] babb=abbbb:

bab b babb

Critical pair: bababbbb=abbbbabb.

Reduce LHS:

[2]b(ababb)bb
⇒ bbbbbbb

Reduce RHS:

[3]abbb(babb)
[3]⇒ abb(babb)bb
[3]⇒ ab(babb)bbbb
[2]⇒ (ababb)bbbbbb
⇒ bbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.