Certificate for #3913 ⟨a, b | aaaababaa=ba⟩

Back:⟨a, b | aaaababaa=ba⟩

Completion settings:

[1] aaaababaa=ba

Axiom: aaaababaa=ba.

Referenced by [3].

[2] ba=c

Axiom: ba=c.

Defines rule #4.

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

[3] aaaababaa=c

Simplify [1] aaaababaa=ba.

Reduce RHS:

[2](ba)
⇒ c

Referenced by [4].

[4] aaaacca=c

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

aaaa babaa ba

Critical pair: aaaacbaa=c.

Reduce LHS:

[2]aaaac(ba)a
⇒ aaaacca

Defines rule #2.

Referenced by [5], [6].

[5] bc=caaacca

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

b a aaaacca

Critical pair: bc=caaacca.

Defines rule #3.

[6] aaaaccc=caaacca

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

aaaacc a aaaacca

Critical pair: aaaaccc=caaacca.

Defines rule #1.