Certificate for #1602 ⟨a, b, c | aab=aa, bcb=1⟩

Back:⟨a, b, c | aab=aa, bcb=1⟩

Completion settings:

[1] aab=aa

Axiom: aab=aa.

Defines rule #2.

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 #1.

Referenced by [4], [5].

[4] aac=aa

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

aa b bcb

Critical pair: aa=aacb.

Reduce RHS:

[3]aa(cb)
[1]⇒ (aab)c
⇒ aac

Flip LHS and RHS.

Defines rule #3.

[5] bbc=1

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

b cb cb

Critical pair: bbc=1.

Defines rule #4.