Certificate for #4265 ⟨a, b | abaababab=ba⟩

Back:⟨a, b | abaababab=ba⟩

Completion settings:

[1] abaababab=ba

Axiom: abaababab=ba.

Referenced by [3].

[2] ba=c

Axiom: ba=c.

Defines rule #3.

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

[3] abaababab=c

Simplify [1] abaababab=ba.

Reduce RHS:

[2](ba)
⇒ c

Referenced by [4].

[4] acaccb=c

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

a baababab ba

Critical pair: acababab=c.

Reduce LHS:

[2]aca(ba)bab
[2]⇒ acac(ba)b
⇒ acaccb

Defines rule #2.

Referenced by [5], [6].

[5] bc=ccaccb

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

b a acaccb

Critical pair: bc=ccaccb.

Defines rule #4.

[6] acaccc=ca

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

acacc b ba

Critical pair: acaccc=ca.

Defines rule #1.