Certificate for #16322 ⟨a, b | aab=bb, bbaa=ab⟩

Completion settings:

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

[1] aab=bb

Axiom: aab=bb.

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

[2] bbaa=ab

Axiom: bbaa=ab.

Referenced by [3], [4], [6], [7], [8].

[3] bab=abb

Overlap of [1] aab=bb with [2] bbaa=ab:

aa b bbaa

Critical pair: aaab=bbbaa.

Reduce LHS:

[1]	a(aab)
	⇒ abb

Reduce RHS:

[2]	b(bbaa)
	⇒ bab

Flip LHS and RHS.

Referenced by [5].

[4] abb=bbbb

Overlap of [2] bbaa=ab with [1] aab=bb:

bb aa aab

Critical pair: bbbb=abb.

Flip LHS and RHS.

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

[5] bab=bbbb

Simplify [3] bab=abb.

Reduce RHS:

[4]	(abb)
	⇒ bbbb

Referenced by [6], [7].

[6] bbbbb=bb

Overlap of [4] abb=bbbb with [2] bbaa=ab:

a bb bbaa

Critical pair: aab=bbbbaa.

Reduce LHS:

[1]	(aab)
	⇒ bb

Reduce RHS:

[2]	bb(bbaa)
[5]	⇒ b(bab)
	⇒ bbbbb

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

[7] ab=bbb

Overlap of [4] abb=bbbb with [2] bbaa=ab:

ab b bbaa

Critical pair: abab=bbbbbaa.

Reduce LHS:

[5]	a(bab)
[4]	⇒ (abb)bb
[6]	⇒ (bbbbb)b
	⇒ bbb

Reduce RHS:

[6]	(bbbbb)aa
[2]	⇒ (bbaa)
	⇒ ab

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

[8] bbaa=bbb

Simplify [2] bbaa=ab.

Reduce RHS:

[7]	(ab)
	⇒ bbb

Defines rule #3.