Certificate for #7499 ⟨a, b, c | ab=1, bacc=ca⟩

Back:⟨a, b, c | ab=1, bacc=ca⟩

Completion settings:

[1] ab=1

Axiom: ab=1.

Defines rule #2.

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

[2] bacc=ca

Axiom: bacc=ca.

Referenced by [3], [5], [6].

[3] aca=acc

Overlap of [1] ab=1 with [2] bacc=ca:

a b bacc

Critical pair: aca=acc.

Referenced by [4].

[4] accb=ac

Overlap of [3] aca=acc with [1] ab=1:

ac a ab

Critical pair: ac=accb.

Flip LHS and RHS.

Referenced by [5], [7].

[5] bac=c

Overlap of [2] bacc=ca with [4] accb=ac:

b acc accb

Critical pair: bac=cab.

Reduce RHS:

[1]c(ab)
⇒ c

Defines rule #4.

Referenced by [6], [7].

[6] ca=cc

Overlap of [2] bacc=ca with [5] bac=c:

bacc bac

Critical pair: cc=ca.

Flip LHS and RHS.

Defines rule #1.

[7] ccb=c

Overlap of [5] bac=c with [4] accb=ac:

b ac accb

Critical pair: bac=ccb.

Reduce LHS:

[5](bac)
⇒ c

Flip LHS and RHS.

Defines rule #3.