Certificate for #847 ⟨a, b | ababaaab=b⟩

Back:⟨a, b | ababaaab=b⟩

Completion settings:

[1] ababaaab=b

Axiom: ababaaab=b.

Referenced by [3].

[2] ab=c

Axiom: ab=c.

Referenced by [3], [4].

[3] b=ccaac

Overlap of [1] ababaaab=b with [2] ab=c:

ababaaab ab

Critical pair: cabaaab=b.

Reduce LHS:

[2]c(ab)aaab
[2]⇒ ccaa(ab)
⇒ ccaac

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] accaac=c

Overlap of [2] ab=c with [3] b=ccaac:

a b b

Critical pair: accaac=c.

Defines rule #3.

Referenced by [5], [6].

[5] accac=ccaac

Overlap of [4] accaac=c with [4] accaac=c:

acca ac accaac

Critical pair: accac=ccaac.

Defines rule #2.

Referenced by [6].

[6] accc=ccac

Overlap of [5] accac=ccaac with [4] accaac=c:

acc ac accaac

Critical pair: accc=ccaaccaac.

Reduce RHS:

[4]cca(accaac)
⇒ ccac

Defines rule #1.