Certificate for #5111 ⟨a, b | aab=aa, baaa=b⟩

Back:⟨a, b | aab=aa, baaa=b⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #2.

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

[2] baaa=b

Axiom: baaa=b.

Defines rule #4.

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

[3] aaaaa=aa

Overlap of [1] aab=aa with [2] baaa=b:

aa b baaa

Critical pair: aab=aaaaa.

Reduce LHS:

[1](aab)
⇒ aa

Flip LHS and RHS.

Defines rule #5.

[4] bb=b

Overlap of [2] baaa=b with [1] aab=aa:

ba aa aab

Critical pair: baaa=bb.

Reduce LHS:

[2](baaa)
⇒ b

Flip LHS and RHS.

Defines rule #1.

[5] bab=ba

Overlap of [2] baaa=b with [1] aab=aa:

baa a aab

Critical pair: baaaa=bab.

Reduce LHS:

[2](baaa)a
⇒ ba

Flip LHS and RHS.

Defines rule #3.