Certificate for #2200 ⟨a, b | ab=aa, bbaa=a⟩

Back:⟨a, b | ab=aa, bbaa=a⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] bbaa=a

Axiom: bbaa=a.

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

[3] aaaaa=aa

Overlap of [1] ab=aa with [2] bbaa=a:

a b bbaa

Critical pair: aa=aabaa.

Reduce RHS:

[1]a(ab)aa
⇒ aaaaa

Flip LHS and RHS.

Referenced by [4].

[4] aaaa=a

Overlap of [2] bbaa=a with [3] aaaaa=aa:

bb aa aaaaa

Critical pair: bbaa=aaaa.

Reduce LHS:

[2](bbaa)
⇒ a

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] bba=aaa

Overlap of [2] bbaa=a with [4] aaaa=a:

bb aa aaaa

Critical pair: bba=aaa.

Defines rule #2.