Certificate for #1342 ⟨a, b, c | ab=1, baca=c⟩

Back:⟨a, b, c | ab=1, baca=c⟩

Completion settings:

[1] ab=1

Axiom: ab=1.

Defines rule #1.

Referenced by [3], [4].

[2] baca=c

Axiom: baca=c.

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

[3] aca=ac

Overlap of [1] ab=1 with [2] baca=c:

a b baca

Critical pair: ac=aca.

Flip LHS and RHS.

Referenced by [6].

[4] bac=cb

Overlap of [2] baca=c with [1] ab=1:

bac a ab

Critical pair: bac=cb.

Referenced by [5], [6], [8].

[5] cba=c

Overlap of [2] baca=c with [4] bac=cb:

baca bac

Critical pair: cba=c.

Referenced by [6], [7].

[6] cb=c

Overlap of [4] bac=cb with [3] aca=ac:

b ac aca

Critical pair: bac=cba.

Reduce LHS:

[4](bac)
⇒ cb

Reduce RHS:

[5](cba)
⇒ c

Defines rule #3.

Referenced by [7], [8].

[7] ca=c

Simplify [5] cba=c.

Reduce LHS:

[6](cb)a
⇒ ca

Defines rule #2.

[8] bac=c

Simplify [4] bac=cb.

Reduce RHS:

[6](cb)
⇒ c

Defines rule #4.