Certificate for #4765 ⟨a, b | abaaaaba=bab⟩

Back:⟨a, b | abaaaaba=bab⟩

Completion settings:

[1] abaaaaba=bab

Axiom: abaaaaba=bab.

Referenced by [3].

[2] bab=c

Axiom: bab=c.

Defines rule #5.

Referenced by [3], [4], [6], [7].

[3] abaaaaba=c

Simplify [1] abaaaaba=bab.

Reduce RHS:

[2](bab)
⇒ c

Defines rule #6.

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

[4] cab=bac

Overlap of [2] bab=c with [2] bab=c:

ba b bab

Critical pair: bac=cab.

Flip LHS and RHS.

Defines rule #2.

[5] caaaba=abaaac

Overlap of [3] abaaaaba=c with [3] abaaaaba=c:

abaaa aba abaaaaba

Critical pair: abaaac=caaaba.

Flip LHS and RHS.

Defines rule #3.

[6] cb=abaaaac

Overlap of [3] abaaaaba=c with [2] bab=c:

abaaaa ba bab

Critical pair: abaaaac=cb.

Flip LHS and RHS.

Defines rule #1.

[7] caaaaba=bc

Overlap of [2] bab=c with [3] abaaaaba=c:

b ab abaaaaba

Critical pair: bc=caaaaba.

Flip LHS and RHS.

Defines rule #4.