Certificate for #8777 ⟨a, b | ab=a, baaaaa=b⟩

Back:⟨a, b | ab=a, baaaaa=b⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] baaaaa=b

Axiom: baaaaa=b.

Defines rule #4.

Referenced by [3], [4].

[3] aaaaaa=a

Overlap of [1] ab=a with [2] baaaaa=b:

a b baaaaa

Critical pair: ab=aaaaaa.

Reduce LHS:

[1](ab)
⇒ a

Flip LHS and RHS.

Defines rule #3.

[4] bb=b

Overlap of [2] baaaaa=b with [1] ab=a:

baaaa a ab

Critical pair: baaaaa=bb.

Reduce LHS:

[2](baaaaa)
⇒ b

Flip LHS and RHS.

Defines rule #2.