Certificate for #21046 ⟨a, b | ab=aa, bbbb=bba⟩

Back:⟨a, b | ab=aa, bbbb=bba⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbbb=bba

Axiom: bbbb=bba.

Defines rule #3.

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

[3] aaaaa=aaaa

Overlap of [1] ab=aa with [2] bbbb=bba:

a b bbbb

Critical pair: abba=aabbb.

Reduce LHS:

[1](ab)ba
[1]⇒ a(ab)a
⇒ aaaa

Reduce RHS:

[1]a(ab)bb
[1]⇒ aa(ab)b
[1]⇒ aaa(ab)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.

[4] bbba=bbaa

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

b bbb bbbb

Critical pair: bbba=bbab.

Reduce RHS:

[1]bb(ab)
⇒ bbaa

Defines rule #2.

Referenced by [5].

[5] bbaaa=bbaa

Overlap of [2] bbbb=bba with [4] bbba=bbaa:

b bbb bbba

Critical pair: bbbaa=bbaa.

Reduce LHS:

[4](bbba)a
⇒ bbaaa

Defines rule #5.