Certificate for #16073 ⟨a, b | aaa=bb, baab=bb⟩

Completion settings:

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

[1] aaa=bb

Axiom: aaa=bb.

Defines rule #6.

Referenced by [3], [5], [6], [7].

[2] baab=bb

Axiom: baab=bb.

Defines rule #5.

Referenced by [4], [5].

[3] bba=abb

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

a aa aaa

Critical pair: abb=bba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5], [7].

[4] aabbb=bbb

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

baa b baab

Critical pair: baabb=bbaab.

Reduce LHS:

[2]	(baab)b
	⇒ bbb

Reduce RHS:

[3]	(bba)ab
[3]	⇒ a(bba)b
	⇒ aabbb

Flip LHS and RHS.

Referenced by [6], [7].

[5] babb=bbbbb

Overlap of [2] baab=bb with [3] bba=abb:

baa b bba

Critical pair: baaabb=bbba.

Reduce LHS:

[1]	b(aaa)bb
	⇒ bbbbb

Reduce RHS:

[3]	b(bba)
	⇒ babb

Flip LHS and RHS.

Defines rule #3.

[6] abbb=bbbbb

Overlap of [1] aaa=bb with [4] aabbb=bbb:

a aa aabbb

Critical pair: abbb=bbbbb.

Defines rule #2.

Referenced by [7].

[7] bbbbbbb=bbb

Overlap of [1] aaa=bb with [4] aabbb=bbb:

aa a aabbb

Critical pair: aabbb=bbabbb.

Reduce LHS:

[4]	(aabbb)
	⇒ bbb

Reduce RHS:

[3]	(bba)bbb
[6]	⇒ (abbb)bb
	⇒ bbbbbbb

Flip LHS and RHS.

Defines rule #1.