Certificate for #2892 ⟨a, b | aa=a, bbabb=a⟩

Back:⟨a, b | aa=a, bbabb=a⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #1.

Referenced by [3].

[2] bbabb=a

Axiom: bbabb=a.

Referenced by [3], [4].

[3] bba=abb

Overlap of [2] bbabb=a with [2] bbabb=a:

bba bb bbabb

Critical pair: bbaa=aabb.

Reduce LHS:

[1]bb(aa)
⇒ bba

Reduce RHS:

[1](aa)bb
⇒ abb

Defines rule #2.

Referenced by [4].

[4] abbbb=a

Overlap of [2] bbabb=a with [3] bba=abb:

bbabb bba

Critical pair: abbbb=a.

Defines rule #3.