Certificate for #24145 ⟨a, b | aa=a, abbbbba=b⟩

Back:⟨a, b | aa=a, abbbbba=b⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #1.

Referenced by [3], [4].

[2] abbbbba=b

Axiom: abbbbba=b.

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

[3] ab=b

Overlap of [1] aa=a with [2] abbbbba=b:

a a abbbbba

Critical pair: ab=abbbbba.

Reduce RHS:

[2](abbbbba)
⇒ b

Defines rule #2.

Referenced by [4], [5].

[4] bbbbba=ba

Overlap of [2] abbbbba=b with [1] aa=a:

abbbbb a aa

Critical pair: abbbbba=ba.

Reduce LHS:

[3](ab)bbbba
⇒ bbbbba

Referenced by [5], [6].

[5] ba=b

Overlap of [2] abbbbba=b with [3] ab=b:

abbbbba ab

Critical pair: bbbbba=b.

Reduce LHS:

[4](bbbbba)
⇒ ba

Defines rule #3.

Referenced by [6].

[6] bbbbb=b

Simplify [4] bbbbba=ba.

Reduce LHS:

[5]bbbb(ba)
⇒ bbbbb

Reduce RHS:

[5](ba)
⇒ b

Defines rule #4.