Certificate for #9162 ⟨a, b | aa=a, abbb=bba⟩

Back:⟨a, b | aa=a, abbb=bba⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #3.

Referenced by [3], [4].

[2] bba=abbb

Axiom: abbb=bba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] ababbb=abbb

Overlap of [2] bba=abbb with [1] aa=a:

bb a aa

Critical pair: bba=abbba.

Reduce LHS:

[2](bba)
⇒ abbb

Reduce RHS:

[2]ab(bba)
⇒ ababbb

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] abbbbbbbbb=abbbbbb

Overlap of [2] bba=abbb with [3] ababbb=abbb:

bb a ababbb

Critical pair: bbabbb=abbbbabbb.

Reduce LHS:

[2](bba)bbb
⇒ abbbbbb

Reduce RHS:

[2]abb(bba)bbb
[2]⇒ a(bba)bbbbbb
[1]⇒ (aa)bbbbbbbbb
⇒ abbbbbbbbb

Flip LHS and RHS.

Defines rule #1.