Certificate for #4870 ⟨a, b | abbabaab=baa⟩

Back:⟨a, b | abbabaab=baa⟩

Completion settings:

[1] abbabaab=baa

Axiom: abbabaab=baa.

Referenced by [3].

[2] ba=c

Axiom: ba=c.

Defines rule #1.

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

[3] abbabaab=ca

Simplify [1] abbabaab=baa.

Reduce RHS:

[2](ba)a
⇒ ca

Referenced by [4].

[4] abccab=ca

Overlap of [3] abbabaab=ca with [2] ba=c:

ab babaab ba

Critical pair: abcbaab=ca.

Reduce LHS:

[2]abc(ba)ab
⇒ abccab

Defines rule #3.

Referenced by [5], [6], [7].

[5] cbccab=bca

Overlap of [2] ba=c with [4] abccab=ca:

b a abccab

Critical pair: bca=cbccab.

Flip LHS and RHS.

Defines rule #2.

[6] caa=abccac

Overlap of [4] abccab=ca with [2] ba=c:

abcca b ba

Critical pair: abccac=caa.

Flip LHS and RHS.

Defines rule #4.

[7] caccab=abccca

Overlap of [4] abccab=ca with [4] abccab=ca:

abcc ab abccab

Critical pair: abccca=caccab.

Flip LHS and RHS.

Defines rule #5.