Certificate for #16043 ⟨a, b | aaa=ab, bbbb=ba⟩

Back:⟨a, b | aaa=ab, bbbb=ba⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[2] bbbb=ba

Axiom: bbbb=ba.

Defines rule #5.

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

[3] aaaaaaaaa=aaaa

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

a b bbbb

Critical pair: aba=aaabbb.

Reduce LHS:

[1](ab)a
⇒ aaaa

Reduce RHS:

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

Flip LHS and RHS.

Defines rule #1.

[4] bba=baaa

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

b bbb bbbb

Critical pair: bba=bab.

Reduce RHS:

[1]b(ab)
⇒ baaa

Defines rule #4.

Referenced by [5].

[5] baaaaaaa=baa

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

bb bb bba

Critical pair: bbbaaa=baa.

Reduce LHS:

[4]b(bba)aa
[4]⇒ (bba)aaaa
⇒ baaaaaaa

Defines rule #2.