Certificate for #13115 ⟨a, b | bbb=aaa, aaba=b⟩

Completion settings:

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

[1] aaa=bbb

Axiom: bbb=aaa.

Flip LHS and RHS.

Defines rule #3.

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

[2] aaba=b

Axiom: aaba=b.

Referenced by [4], [6].

[3] abbb=bbba

Overlap of [1] aaa=bbb with [1] aaa=bbb:

a aa aaa

Critical pair: abbb=bbba.

Referenced by [5].

[4] ab=bbbba

Overlap of [1] aaa=bbb with [2] aaba=b:

a aa aaba

Critical pair: ab=bbbba.

Defines rule #2.

Referenced by [5], [6].

[5] bbbbbbbbbbbba=bbba

Simplify [3] abbb=bbba.

Reduce LHS:

[4]	(ab)bb
[4]	⇒ bbbb(ab)b
[4]	⇒ bbbbbbbb(ab)
	⇒ bbbbbbbbbbbba

Referenced by [6].

[6] bbbbbbbbbb=b

Overlap of [2] aaba=b with [4] ab=bbbba:

a aba ab

Critical pair: abbbbaa=b.

Reduce LHS:

[4]	(ab)bbbaa
[4]	⇒ bbbb(ab)bbaa
[4]	⇒ bbbbbbbb(ab)baa
[5]	⇒ (bbbbbbbbbbbba)baa
[4]	⇒ bbb(ab)aa
[1]	⇒ bbbbbbb(aaa)
	⇒ bbbbbbbbbb

Defines rule #1.