Certificate for #5337 ⟨a, b | aaa=ab, bbb=ba⟩

Back:⟨a, b | aaa=ab, bbb=ba⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[2] bbb=ba

Axiom: bbb=ba.

Defines rule #5.

Referenced by [3], [4], [5].

[3] aaaaaaa=aaaa

Overlap of [1] ab=aaa with [2] bbb=ba:

a b bbb

Critical pair: aba=aaabb.

Reduce LHS:

[1](ab)a
⇒ aaaa

Reduce RHS:

[1]aa(ab)b
[1]⇒ aaaa(ab)
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #1.

[4] bba=baaa

Overlap of [2] bbb=ba with [2] bbb=ba:

b bb bbb

Critical pair: bba=bab.

Reduce RHS:

[1]b(ab)
⇒ baaa

Defines rule #4.

Referenced by [5].

[5] baaaaa=baa

Overlap of [2] bbb=ba with [4] bba=baaa:

b bb bba

Critical pair: bbaaa=baa.

Reduce LHS:

[4](bba)aa
⇒ baaaaa

Defines rule #2.