Certificate for #18737 ⟨a, b | aaa=a, abbbba=b⟩

Completion settings:

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

[1] aaa=a

Axiom: aaa=a.

Defines rule #4.

Referenced by [3], [4].

[2] abbbba=b

Axiom: abbbba=b.

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

[3] aab=b

Overlap of [1] aaa=a with [2] abbbba=b:

aa a abbbba

Critical pair: aab=abbbba.

Reduce RHS:

[2]	(abbbba)
	⇒ b

Defines rule #3.

Referenced by [5], [8].

[4] baa=b

Overlap of [2] abbbba=b with [1] aaa=a:

abbbb a aaa

Critical pair: abbbba=baa.

Reduce LHS:

[2]	(abbbba)
	⇒ b

Flip LHS and RHS.

Referenced by [6].

[5] bbbba=ab

Overlap of [3] aab=b with [2] abbbba=b:

a ab abbbba

Critical pair: ab=bbbba.

Flip LHS and RHS.

Referenced by [7].

[6] ba=abbbb

Overlap of [2] abbbba=b with [4] baa=b:

abbb ba baa

Critical pair: abbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

[7] abbbbbbbbbbbbbbbb=ab

Simplify [5] bbbba=ab.

Reduce LHS:

[6]	bbb(ba)
[6]	⇒ bb(ba)bbbb
[6]	⇒ b(ba)bbbbbbbb
[6]	⇒ (ba)bbbbbbbbbbbb
	⇒ abbbbbbbbbbbbbbbb

Referenced by [8].

[8] bbbbbbbbbbbbbbbb=b

Overlap of [3] aab=b with [7] abbbbbbbbbbbbbbbb=ab:

a ab abbbbbbbbbbbbbbbb

Critical pair: aab=bbbbbbbbbbbbbbbb.

Reduce LHS:

[3]	(aab)
	⇒ b

Flip LHS and RHS.

Defines rule #1.