Certificate for #16070 ⟨a, b | aaa=bb, abbb=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 #4.

Referenced by [3], [4].

[2] abbb=bb

Axiom: abbb=bb.

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

[3] bba=abb

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

a aa aaa

Critical pair: abb=bba.

Flip LHS and RHS.

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

[4] aabb=bbbbb

Overlap of [1] aaa=bb with [2] abbb=bb:

aa a abbb

Critical pair: aabb=bbbbb.

Referenced by [6].

[5] babb=bb

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

abb b bba

Critical pair: abbabb=bbba.

Reduce LHS:

[3]	a(bba)bb
[2]	⇒ a(abbb)b
[2]	⇒ (abbb)
	⇒ bb

Reduce RHS:

[3]	b(bba)
	⇒ babb

Flip LHS and RHS.

Referenced by [6].

[6] abb=bbbbbb

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

ba bb bba

Critical pair: baabb=bba.

Reduce LHS:

[4]	b(aabb)
	⇒ bbbbbb

Reduce RHS:

[3]	(bba)
	⇒ abb

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8].

[7] bbbbbbb=bb

Overlap of [2] abbb=bb with [6] abb=bbbbbb:

abbb abb

Critical pair: bbbbbbb=bb.

Defines rule #1.

[8] bba=bbbbbb

Simplify [3] bba=abb.

Reduce RHS:

[6]	(abb)
	⇒ bbbbbb

Defines rule #3.