Certificate for #20914 ⟨a, b | bb=aa, ababa=aa⟩

Completion settings:

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

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [4], [6], [7].

[2] ababa=bb

Axiom: ababa=aa.

Reduce RHS:

[1]	(aa)
	⇒ bb

Defines rule #5.

Referenced by [4], [5].

[3] bba=abb

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

a a aa

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [4], [5], [6], [8].

[4] bababb=abb

Overlap of [1] aa=bb with [2] ababa=bb:

a a ababa

Critical pair: abb=bbbaba.

Reduce RHS:

[3]	b(bba)ba
[3]	⇒ bab(bba)
	⇒ bababb

Flip LHS and RHS.

Referenced by [6].

[5] babb=abbb

Overlap of [2] ababa=bb with [2] ababa=bb:

ab aba ababa

Critical pair: abbb=bbba.

Reduce RHS:

[3]	b(bba)
	⇒ babb

Flip LHS and RHS.

Referenced by [6].

[6] abb=bbbbbb

Overlap of [5] babb=abbb with [3] bba=abb:

bab b bba

Critical pair: bababb=abbbba.

Reduce LHS:

[4]	(bababb)
	⇒ abb

Reduce RHS:

[3]	abb(bba)
[3]	⇒ a(bba)bb
[1]	⇒ (aa)bbbb
	⇒ bbbbbb

Defines rule #2.

Referenced by [7], [8].

[7] bbbbbbbbbb=bbbb

Overlap of [1] aa=bb with [6] abb=bbbbbb:

a a abb

Critical pair: abbbbbb=bbbb.

Reduce LHS:

[6]	(abb)bbbb
	⇒ bbbbbbbbbb

Defines rule #1.

[8] bba=bbbbbb

Simplify [3] bba=abb.

Reduce RHS:

[6]	(abb)
	⇒ bbbbbb

Defines rule #3.