Certificate for #19618 ⟨a, b | aab=b, bbbaa=ba⟩

Completion settings:

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

[1] aab=b

Axiom: aab=b.

Defines rule #4.

Referenced by [3], [4].

[2] bbbaa=ba

Axiom: bbbaa=ba.

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

[3] bab=bbbb

Overlap of [2] bbbaa=ba with [1] aab=b:

bbb aa aab

Critical pair: bbbb=bab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] bbbbbb=bb

Overlap of [2] bbbaa=ba with [1] aab=b:

bbba a aab

Critical pair: bbbab=baab.

Reduce LHS:

[3]	bb(bab)
	⇒ bbbbbb

Reduce RHS:

[1]	b(aab)
	⇒ bb

Defines rule #1.

Referenced by [5], [6].

[5] bbaa=bbbba

Overlap of [3] bab=bbbb with [2] bbbaa=ba:

ba b bbbaa

Critical pair: baba=bbbbbbaa.

Reduce LHS:

[3]	(bab)a
	⇒ bbbba

Reduce RHS:

[4]	(bbbbbb)aa
	⇒ bbaa

Flip LHS and RHS.

Referenced by [6].

[6] bbbbba=ba

Overlap of [4] bbbbbb=bb with [5] bbaa=bbbba:

bbbbb b bbaa

Critical pair: bbbbbbbbba=bbbaa.

Reduce LHS:

[4]	(bbbbbb)bbba
	⇒ bbbbba

Reduce RHS:

[2]	(bbbaa)
	⇒ ba

Defines rule #3.

Referenced by [7].

[7] baa=bbba

Overlap of [6] bbbbba=ba with [2] bbbaa=ba:

bb bbba bbbaa

Critical pair: bbba=baa.

Flip LHS and RHS.

Defines rule #5.