Certificate for #25905 ⟨a, b | ab=a, bbbb=baaa⟩

Back:⟨a, b | ab=a, bbbb=baaa⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bbbb=baaa

Axiom: bbbb=baaa.

Defines rule #4.

Referenced by [3], [4].

[3] aaaa=a

Overlap of [1] ab=a with [2] bbbb=baaa:

a b bbbb

Critical pair: abaaa=abbb.

Reduce LHS:

[1](ab)aaa
⇒ aaaa

Reduce RHS:

[1](ab)bb
[1]⇒ (ab)b
[1]⇒ (ab)
⇒ a

Defines rule #3.

Referenced by [5].

[4] bbaaa=baaa

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

b bbb bbbb

Critical pair: bbaaa=baaab.

Reduce RHS:

[1]baa(ab)
⇒ baaa

Referenced by [5].

[5] bba=ba

Overlap of [4] bbaaa=baaa with [3] aaaa=a:

bb aaa aaaa

Critical pair: bba=baaaa.

Reduce RHS:

[3]b(aaaa)
⇒ ba

Defines rule #2.