Certificate for #2271 ⟨a, b | bb=aa, aaa=ab⟩

Back:⟨a, b | bb=aa, aaa=ab⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #4.

Referenced by [3], [4].

[2] ab=aaa

Axiom: aaa=ab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] baa=aaaa

Overlap of [1] bb=aa with [1] bb=aa:

b b bb

Critical pair: baa=aab.

Reduce RHS:

[2]a(ab)
⇒ aaaa

Defines rule #2.

[4] aaaaa=aaa

Overlap of [2] ab=aaa with [1] bb=aa:

a b bb

Critical pair: aaa=aaab.

Reduce RHS:

[2]aa(ab)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #1.