Certificate for #434 ⟨a, b, c | ab=aa, bcb=1⟩

Back:⟨a, b, c | ab=aa, bcb=1⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [4].

[2] bcb=1

Axiom: bcb=1.

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

[3] cb=bc

Overlap of [2] bcb=1 with [2] bcb=1:

bc b bcb

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [4], [5].

[4] aaac=a

Overlap of [1] ab=aa with [2] bcb=1:

a b bcb

Critical pair: a=aacb.

Reduce RHS:

[3]aa(cb)
[1]⇒ a(ab)c
⇒ aaac

Flip LHS and RHS.

Defines rule #4.

[5] bbc=1

Overlap of [2] bcb=1 with [3] cb=bc:

b cb cb

Critical pair: bbc=1.

Defines rule #3.