Certificate for #976 ⟨a, b | abaabab=ba⟩

Back:⟨a, b | abaabab=ba⟩

Completion settings:

[1] abaabab=ba

Axiom: abaabab=ba.

Referenced by [3].

[2] ba=c

Axiom: ba=c.

Defines rule #3.

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

[3] abaabab=c

Simplify [1] abaabab=ba.

Reduce RHS:

[2](ba)
⇒ c

Referenced by [4].

[4] acacb=c

Overlap of [3] abaabab=c with [2] ba=c:

a baabab ba

Critical pair: acabab=c.

Reduce LHS:

[2]aca(ba)b
⇒ acacb

Defines rule #2.

Referenced by [5], [6].

[5] bc=ccacb

Overlap of [2] ba=c with [4] acacb=c:

b a acacb

Critical pair: bc=ccacb.

Defines rule #4.

[6] acacc=ca

Overlap of [4] acacb=c with [2] ba=c:

acac b ba

Critical pair: acacc=ca.

Defines rule #1.