Certificate for #3030 ⟨a, b, c | aba=b, aca=b⟩

Back:⟨a, b, c | aba=b, aca=b⟩

Completion settings:

[1] aba=b

Axiom: aba=b.

Referenced by [3].

[2] b=aca

Axiom: aca=b.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] aba=aca

Simplify [1] aba=b.

Reduce RHS:

[2](b)
⇒ aca

Referenced by [4].

[4] aacaa=aca

Overlap of [3] aba=aca with [2] b=aca:

a ba b

Critical pair: aacaa=aca.

Defines rule #1.

Referenced by [5].

[5] acacaa=aacaca

Overlap of [4] aacaa=aca with [4] aacaa=aca:

aac aa aacaa

Critical pair: aacaca=acacaa.

Flip LHS and RHS.

Defines rule #2.