Certificate for #7592 ⟨a, b, c | ab=1, cacc=ba⟩

Back:⟨a, b, c | ab=1, cacc=ba⟩

Completion settings:

[1] ab=1

Axiom: ab=1.

Defines rule #1.

Referenced by [4], [6].

[2] cacc=ba

Axiom: cacc=ba.

Defines rule #4.

Referenced by [3].

[3] baacc=cacba

Overlap of [2] cacc=ba with [2] cacc=ba:

cac c cacc

Critical pair: cacba=baacc.

Flip LHS and RHS.

Referenced by [4], [5].

[4] aacc=acacba

Overlap of [1] ab=1 with [3] baacc=cacba:

a b baacc

Critical pair: acacba=aacc.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] bacacba=cacba

Overlap of [3] baacc=cacba with [4] aacc=acacba:

b aacc aacc

Critical pair: bacacba=cacba.

Referenced by [6].

[6] bacacb=cacb

Overlap of [5] bacacba=cacba with [1] ab=1:

bacacb a ab

Critical pair: bacacb=cacbab.

Reduce RHS:

[1]cacb(ab)
⇒ cacb

Defines rule #3.