Certificate for #7834 ⟨a, b, c | ab=1, cac=baa⟩

Back:⟨a, b, c | ab=1, cac=baa⟩

Completion settings:

[1] ab=1

Axiom: ab=1.

Defines rule #1.

Referenced by [3], [4], [6], [7].

[2] cac=baa

Axiom: cac=baa.

Defines rule #3.

Referenced by [3].

[3] baaac=caa

Overlap of [2] cac=baa with [2] cac=baa:

ca c cac

Critical pair: cabaa=baaac.

Reduce LHS:

[1]c(ab)aa
⇒ caa

Flip LHS and RHS.

Referenced by [4], [5].

[4] aaac=acaa

Overlap of [1] ab=1 with [3] baaac=caa:

a b baaac

Critical pair: acaa=aaac.

Flip LHS and RHS.

Defines rule #4.

Referenced by [5].

[5] bacaa=caa

Overlap of [3] baaac=caa with [4] aaac=acaa:

b aaac aaac

Critical pair: bacaa=caa.

Referenced by [6].

[6] baca=ca

Overlap of [5] bacaa=caa with [1] ab=1:

baca a ab

Critical pair: baca=caab.

Reduce RHS:

[1]ca(ab)
⇒ ca

Referenced by [7].

[7] bac=c

Overlap of [6] baca=ca with [1] ab=1:

bac a ab

Critical pair: bac=cab.

Reduce RHS:

[1]c(ab)
⇒ c

Defines rule #2.