Certificate for #16370 ⟨a, b | aba=aa, bbbb=aa⟩

Completion settings:

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

[1] aba=aa

Axiom: aba=aa.

Referenced by [3].

[2] aa=bbbb

Axiom: bbbb=aa.

Flip LHS and RHS.

Defines rule #5.

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

[3] aba=bbbb

Simplify [1] aba=aa.

Reduce RHS:

[2]	(aa)
	⇒ bbbb

Defines rule #6.

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

[4] bbbba=abbbb

Overlap of [2] aa=bbbb with [2] aa=bbbb:

a a aa

Critical pair: abbbb=bbbba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [5], [6].

[5] babbbb=abbbbb

Overlap of [3] aba=bbbb with [3] aba=bbbb:

ab a aba

Critical pair: abbbbb=bbbbba.

Reduce RHS:

[4]	b(bbbba)
	⇒ babbbb

Flip LHS and RHS.

Referenced by [7], [8].

[6] abbbbb=abbbb

Overlap of [3] aba=bbbb with [2] aa=bbbb:

ab a aa

Critical pair: abbbbb=bbbba.

Reduce RHS:

[4]	(bbbba)
	⇒ abbbb

Defines rule #2.

Referenced by [7], [8].

[7] bbbbbbbbb=bbbbbbbb

Overlap of [3] aba=bbbb with [6] abbbbb=abbbb:

ab a abbbbb

Critical pair: ababbbb=bbbbbbbbb.

Reduce LHS:

[5]	a(babbbb)
[6]	⇒ a(abbbbb)
[2]	⇒ (aa)bbbb
	⇒ bbbbbbbb

Flip LHS and RHS.

Defines rule #1.

[8] babbbb=abbbb

Simplify [5] babbbb=abbbbb.

Reduce RHS:

[6]	(abbbbb)
	⇒ abbbb

Defines rule #3.