Certificate for #15426 ⟨a, b | aaa=aa, abbba=b⟩

Back:⟨a, b | aaa=aa, abbba=b⟩

Completion settings:

[1] aaa=aa

Axiom: aaa=aa.

Defines rule #3.

Referenced by [3], [4].

[2] abbba=b

Axiom: abbba=b.

Referenced by [3], [4], [5], [6], [7].

[3] aab=ab

Overlap of [1] aaa=aa with [2] abbba=b:

aa a abbba

Critical pair: aab=aabbba.

Reduce RHS:

[2]a(abbba)
⇒ ab

Referenced by [5].

[4] baa=ba

Overlap of [2] abbba=b with [1] aaa=aa:

abbb a aaa

Critical pair: abbbaa=baa.

Reduce LHS:

[2](abbba)a
⇒ ba

Flip LHS and RHS.

Referenced by [7].

[5] ab=b

Overlap of [3] aab=ab with [2] abbba=b:

a ab abbba

Critical pair: ab=abbba.

Reduce RHS:

[2](abbba)
⇒ b

Defines rule #1.

Referenced by [6], [7].

[6] bbba=b

Overlap of [2] abbba=b with [5] ab=b:

abbba ab

Critical pair: bbba=b.

Referenced by [7], [8].

[7] ba=b

Overlap of [2] abbba=b with [4] baa=ba:

abb ba baa

Critical pair: abbba=ba.

Reduce LHS:

[5](ab)bba
[6]⇒ (bbba)
⇒ b

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[8] bbb=b

Simplify [6] bbba=b.

Reduce LHS:

[7]bb(ba)
⇒ bbb

Defines rule #4.