Certificate for #10942 ⟨a, b | aabb=bba, bbbb=1⟩

Back:⟨a, b | aabb=bba, bbbb=1⟩

Completion settings:

[1] aabb=bba

Axiom: aabb=bba.

Referenced by [3], [4].

[2] bbbb=1

Axiom: bbbb=1.

Defines rule #3.

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

[3] bbabb=aa

Overlap of [1] aabb=bba with [2] bbbb=1:

aa bb bbbb

Critical pair: aa=bbabb.

Flip LHS and RHS.

Referenced by [4], [5].

[4] aaaa=a

Overlap of [1] aabb=bba with [3] bbabb=aa:

aa bb bbabb

Critical pair: aaaa=bbaabb.

Reduce RHS:

[1]bb(aabb)
[2]⇒ (bbbb)a
⇒ a

Defines rule #1.

[5] abb=bbaa

Overlap of [2] bbbb=1 with [3] bbabb=aa:

bb bb bbabb

Critical pair: bbaa=abb.

Flip LHS and RHS.

Defines rule #2.