Certificate for #15520 ⟨a, b | aaa=bb, aabbb=b⟩

Back:⟨a, b | aaa=bb, aabbb=b⟩

Completion settings:

[1] aaa=bb

Axiom: aaa=bb.

Defines rule #2.

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

[2] aabbb=b

Axiom: aabbb=b.

Defines rule #3.

Referenced by [4], [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 [7].

[4] bbbbb=ab

Overlap of [1] aaa=bb with [2] aabbb=b:

a aa aabbb

Critical pair: ab=bbbbb.

Flip LHS and RHS.

Defines rule #4.

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

[5] bab=abb

Overlap of [4] bbbbb=ab with [4] bbbbb=ab:

b bbbb bbbbb

Critical pair: bab=abb.

Referenced by [6].

[6] baab=aabb

Overlap of [5] bab=abb with [4] bbbbb=ab:

ba b bbbbb

Critical pair: baab=abbbbbb.

Reduce RHS:

[4]a(bbbbb)b
⇒ aabb

Referenced by [7].

[7] ba=ab

Overlap of [6] baab=aabb with [3] bba=abb:

baa b bba

Critical pair: baaabb=aabbba.

Reduce LHS:

[1]b(aaa)bb
[4]⇒ (bbbbb)
⇒ ab

Reduce RHS:

[2](aabbb)a
⇒ ba

Flip LHS and RHS.

Defines rule #1.