Certificate for #24182 ⟨a, b | aa=a, bbabbbb=a⟩

Back:⟨a, b | aa=a, bbabbbb=a⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #3.

Referenced by [3], [4].

[2] bbabbbb=a

Axiom: bbabbbb=a.

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

[3] bbabba=abbbb

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

bbabb bb bbabbbb

Critical pair: bbabba=aabbbb.

Reduce RHS:

[1](aa)bbbb
⇒ abbbb

Referenced by [4].

[4] bba=abbbbbbbb

Overlap of [3] bbabba=abbbb with [2] bbabbbb=a:

bba bba bbabbbb

Critical pair: bbaa=abbbbbbbb.

Reduce LHS:

[1]bb(aa)
⇒ bba

Defines rule #2.

Referenced by [5].

[5] abbbbbbbbbbbb=a

Overlap of [2] bbabbbb=a with [4] bba=abbbbbbbb:

bbabbbb bba

Critical pair: abbbbbbbbbbbb=a.

Defines rule #1.