Certificate for #5338 ⟨a, b | aaa=bb, aab=aa⟩

Back:⟨a, b | aaa=bb, aab=aa⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4].

[2] aab=aa

Axiom: aab=aa.

Defines rule #3.

Referenced by [3], [4].

[3] baaa=aaa

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

b b bb

Critical pair: baaa=aaab.

Reduce RHS:

[2]a(aab)
⇒ aaa

Referenced by [5].

[4] aaaaa=aa

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

aa b bb

Critical pair: aaaaa=aab.

Reduce RHS:

[2](aab)
⇒ aa

Defines rule #1.

Referenced by [5].

[5] baa=aa

Overlap of [3] baaa=aaa with [4] aaaaa=aa:

b aaa aaaaa

Critical pair: baa=aaaaa.

Reduce RHS:

[4](aaaaa)
⇒ aa

Defines rule #2.