Certificate for #16042 ⟨a, b | aaa=ab, bbbb=ab⟩

Back:⟨a, b | aaa=ab, bbbb=ab⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [2], [3], [4].

[2] bbbb=aaa

Axiom: bbbb=ab.

Reduce RHS:

[1](ab)
⇒ aaa

Defines rule #4.

Referenced by [3], [4].

[3] aaaaaaaaa=aaaa

Overlap of [1] ab=aaa with [2] bbbb=aaa:

a b bbbb

Critical pair: aaaa=aaabbb.

Reduce RHS:

[1]aa(ab)bb
[1]⇒ aaaa(ab)b
[1]⇒ aaaaaa(ab)
⇒ aaaaaaaaa

Flip LHS and RHS.

Defines rule #1.

[4] baaa=aaaaa

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

b bbb bbbb

Critical pair: baaa=aaab.

Reduce RHS:

[1]aa(ab)
⇒ aaaaa

Defines rule #2.