Certificate for #4598 ⟨a, b | aabaaaba=aab⟩

Back:⟨a, b | aabaaaba=aab⟩

Completion settings:

[1] aabaaaba=aab

Axiom: aabaaaba=aab.

Referenced by [3].

[2] aab=c

Axiom: aab=c.

Defines rule #4.

Referenced by [3], [4], [5], [7].

[3] aabaaaba=c

Simplify [1] aabaaaba=aab.

Reduce RHS:

[2](aab)
⇒ c

Referenced by [4].

[4] caca=c

Overlap of [3] aabaaaba=c with [2] aab=c:

aabaaaba aab

Critical pair: caaaba=c.

Reduce LHS:

[2]ca(aab)a
⇒ caca

Defines rule #2.

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

[5] cab=cacc

Overlap of [4] caca=c with [2] aab=c:

cac a aab

Critical pair: cacc=cab.

Flip LHS and RHS.

Defines rule #5.

[6] cca=cac

Overlap of [4] caca=c with [4] caca=c:

ca ca caca

Critical pair: cac=cca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

[7] cb=ccc

Overlap of [6] cca=cac with [2] aab=c:

cc a aab

Critical pair: ccc=cacab.

Reduce RHS:

[4](caca)b
⇒ cb

Flip LHS and RHS.

Defines rule #3.