Certificate for #474 ⟨a, b | ababab=ba⟩

Back:⟨a, b | ababab=ba⟩

Completion settings:

[1] ababab=ba

Axiom: ababab=ba.

Referenced by [3].

[2] ba=c

Axiom: ba=c.

Defines rule #3.

Referenced by [3], [4], [5], [6].

[3] ababab=c

Simplify [1] ababab=ba.

Reduce RHS:

[2](ba)
⇒ c

Referenced by [4].

[4] accb=c

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

a babab ba

Critical pair: acbab=c.

Reduce LHS:

[2]ac(ba)b
⇒ accb

Defines rule #2.

Referenced by [5], [6].

[5] cccb=bc

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

b a accb

Critical pair: bc=cccb.

Flip LHS and RHS.

Defines rule #1.

[6] ca=accc

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

acc b ba

Critical pair: accc=ca.

Flip LHS and RHS.

Defines rule #4.