Certificate for #1895 ⟨a, b | aaababaa=ba⟩

Back:⟨a, b | aaababaa=ba⟩

Completion settings:

[1] aaababaa=ba

Axiom: aaababaa=ba.

Referenced by [3].

[2] ba=c

Axiom: ba=c.

Defines rule #4.

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

[3] aaababaa=c

Simplify [1] aaababaa=ba.

Reduce RHS:

[2](ba)
⇒ c

Referenced by [4].

[4] aaacca=c

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

aaa babaa ba

Critical pair: aaacbaa=c.

Reduce LHS:

[2]aaac(ba)a
⇒ aaacca

Defines rule #2.

Referenced by [5], [6].

[5] bc=caacca

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

b a aaacca

Critical pair: bc=caacca.

Defines rule #3.

[6] aaaccc=caacca

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

aaacc a aaacca

Critical pair: aaaccc=caacca.

Defines rule #1.