Certificate for #3534 ⟨a, b, c | bb=ac, bca=b⟩

Back:⟨a, b, c | bb=ac, bca=b⟩

Completion settings:

[1] ac=bb

Axiom: bb=ac.

Flip LHS and RHS.

Referenced by [5], [6].

[2] bca=b

Axiom: bca=b.

Referenced by [4].

[3] bc=d

Axiom: bc=d.

Referenced by [4], [5].

[4] b=da

Overlap of [2] bca=b with [3] bc=d:

bca bc

Critical pair: da=b.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6].

[5] ddada=d

Overlap of [3] bc=d with [4] b=da:

bc b

Critical pair: dac=d.

Reduce LHS:

[1]d(ac)
[4]⇒ d(b)b
[4]⇒ dda(b)
⇒ ddada

Defines rule #1.

Referenced by [7].

[6] ac=dada

Simplify [1] ac=bb.

Reduce RHS:

[4](b)b
[4]⇒ da(b)
⇒ dada

Defines rule #3.

Referenced by [7].

[7] dc=ddad

Overlap of [5] ddada=d with [6] ac=dada:

ddad a ac

Critical pair: ddaddada=dc.

Reduce LHS:

[5]dda(ddada)
⇒ ddad

Flip LHS and RHS.

Defines rule #4.