Certificate for #5066 ⟨a, b | aaa=ab, bbaa=a⟩

Back:⟨a, b | aaa=ab, bbaa=a⟩

Completion settings:

[1] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[2] bbaa=a

Axiom: bbaa=a.

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

[3] aaaaaaa=aa

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

a b bbaa

Critical pair: aa=aaabaa.

Reduce RHS:

[1]aa(ab)aa
⇒ aaaaaaa

Flip LHS and RHS.

Referenced by [4].

[4] aaaaaa=a

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

bb aa aaaaaaa

Critical pair: bbaa=aaaaaa.

Reduce LHS:

[2](bbaa)
⇒ a

Flip LHS and RHS.

Defines rule #1.

Referenced by [5].

[5] bba=aaaaa

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

bb aa aaaaaa

Critical pair: bba=aaaaa.

Defines rule #3.