Certificate for #461 ⟨a, b, c | ba=ab, aca=1⟩

Back:⟨a, b, c | ba=ab, aca=1⟩

Completion settings:

[1] ba=ab

Axiom: ba=ab.

Defines rule #2.

Referenced by [4].

[2] aca=1

Axiom: aca=1.

Referenced by [3], [4], [5], [6].

[3] ca=ac

Overlap of [2] aca=1 with [2] aca=1:

ac a aca

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [5], [6].

[4] aabc=b

Overlap of [1] ba=ab with [2] aca=1:

b a aca

Critical pair: b=abca.

Reduce RHS:

[3]ab(ca)
[1]⇒ a(ba)c
⇒ aabc

Flip LHS and RHS.

Referenced by [5].

[5] bc=cb

Overlap of [3] ca=ac with [4] aabc=b:

c a aabc

Critical pair: cb=acabc.

Reduce RHS:

[2](aca)bc
⇒ bc

Flip LHS and RHS.

Defines rule #3.

[6] aac=1

Overlap of [2] aca=1 with [3] ca=ac:

a ca ca

Critical pair: aac=1.

Defines rule #4.