Certificate for #16084 ⟨a, b | aab=aa, aaaa=bb⟩

Back:⟨a, b | aab=aa, aaaa=bb⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #3.

Referenced by [3], [4].

[2] bb=aaaa

Axiom: aaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[3] aaaaaa=aa

Overlap of [1] aab=aa with [2] bb=aaaa:

aa b bb

Critical pair: aaaaaa=aab.

Reduce RHS:

[1](aab)
⇒ aa

Defines rule #1.

Referenced by [5].

[4] baaaa=aaaa

Overlap of [2] bb=aaaa with [2] bb=aaaa:

b b bb

Critical pair: baaaa=aaaab.

Reduce RHS:

[1]aa(aab)
⇒ aaaa

Referenced by [5].

[5] baa=aa

Overlap of [4] baaaa=aaaa with [3] aaaaaa=aa:

b aaaa aaaaaa

Critical pair: baa=aaaaaa.

Reduce RHS:

[3](aaaaaa)
⇒ aa

Defines rule #2.