Certificate for #5287 ⟨a, b | aba=bb, abbb=b⟩

Completion settings:

Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1

[1] aba=bb

Axiom: aba=bb.

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

[2] abbb=b

Axiom: abbb=b.

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

[3] bbba=b

Overlap of [1] aba=bb with [1] aba=bb:

ab a aba

Critical pair: abbb=bbba.

Reduce LHS:

[2]	(abbb)
	⇒ b

Flip LHS and RHS.

Referenced by [5], [6].

[4] abb=bbbbb

Overlap of [1] aba=bb with [2] abbb=b:

ab a abbb

Critical pair: abb=bbbbb.

Referenced by [6].

[5] ba=ab

Overlap of [2] abbb=b with [3] bbba=b:

a bbb bbba

Critical pair: ab=ba.

Flip LHS and RHS.

Referenced by [7], [8].

[6] bbbbbb=b

Overlap of [2] abbb=b with [3] bbba=b:

abb b bbba

Critical pair: abbb=bbba.

Reduce LHS:

[4]	(abb)b
	⇒ bbbbbb

Reduce RHS:

[3]	(bbba)
	⇒ b

Defines rule #1.

[7] ab=bbbb

Overlap of [2] abbb=b with [5] ba=ab:

abb b ba

Critical pair: abbab=ba.

Reduce LHS:

[5]	ab(ba)b
[1]	⇒ (aba)bb
	⇒ bbbb

Reduce RHS:

[5]	(ba)
	⇒ ab

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[8] ba=bbbb

Simplify [5] ba=ab.

Reduce RHS:

[7]	(ab)
	⇒ bbbb

Defines rule #3.