Certificate for #25539 ⟨a, b | ab=a, baaaa=bbb⟩

Back:⟨a, b | ab=a, baaaa=bbb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3], [4].

[2] bbb=baaaa

Axiom: baaaa=bbb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[3] aaaaa=a

Overlap of [1] ab=a with [2] bbb=baaaa:

a b bbb

Critical pair: abaaaa=abb.

Reduce LHS:

[1](ab)aaaa
⇒ aaaaa

Reduce RHS:

[1](ab)b
[1]⇒ (ab)
⇒ a

Defines rule #1.

Referenced by [5].

[4] bbaaaa=baaaa

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

b bb bbb

Critical pair: bbaaaa=baaaab.

Reduce RHS:

[1]baaa(ab)
⇒ baaaa

Referenced by [5].

[5] bba=ba

Overlap of [4] bbaaaa=baaaa with [3] aaaaa=a:

bb aaaa aaaaa

Critical pair: bba=baaaaa.

Reduce RHS:

[3]b(aaaaa)
⇒ ba

Defines rule #3.