Certificate for #4234 ⟨a, b | abaaaabab=ba⟩

Back:⟨a, b | abaaaabab=ba⟩

Completion settings:

[1] abaaaabab=ba

Axiom: abaaaabab=ba.

Referenced by [3].

[2] ba=c

Axiom: ba=c.

Defines rule #3.

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

[3] abaaaabab=c

Simplify [1] abaaaabab=ba.

Reduce RHS:

[2](ba)
⇒ c

Referenced by [4].

[4] acaaacb=c

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

a baaaabab ba

Critical pair: acaaabab=c.

Reduce LHS:

[2]acaaa(ba)b
⇒ acaaacb

Defines rule #2.

Referenced by [5], [6].

[5] bc=ccaaacb

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

b a acaaacb

Critical pair: bc=ccaaacb.

Defines rule #4.

[6] acaaacc=ca

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

acaaac b ba

Critical pair: acaaacc=ca.

Defines rule #1.