Certificate for #25411 ⟨a, b | ab=a, aaaaa=bbb⟩

Back:⟨a, b | ab=a, aaaaa=bbb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] aaaaa=bbb

Axiom: aaaaa=bbb.

Defines rule #4.

Referenced by [3], [4].

[3] bbbb=bbb

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

aaaa a ab

Critical pair: aaaaa=bbbb.

Reduce LHS:

[2](aaaaa)
⇒ bbb

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[4] bbba=a

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

a aaaa aaaaa

Critical pair: abbb=bbba.

Reduce LHS:

[1](ab)bb
[1]⇒ (ab)b
[1]⇒ (ab)
⇒ a

Flip LHS and RHS.

Referenced by [5].

[5] ba=a

Overlap of [3] bbbb=bbb with [4] bbba=a:

b bbb bbba

Critical pair: ba=bbba.

Reduce RHS:

[4](bbba)
⇒ a

Defines rule #2.