Certificate for #2355 ⟨a, b | abbabba=bab⟩

Back:⟨a, b | abbabba=bab⟩

Completion settings:

[1] abbabba=bab

Axiom: abbabba=bab.

Referenced by [3].

[2] bab=c

Axiom: bab=c.

Defines rule #5.

Referenced by [3], [4], [5], [6], [7].

[3] abbabba=c

Simplify [1] abbabba=bab.

Reduce RHS:

[2](bab)
⇒ c

Referenced by [4].

[4] abcba=c

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

ab babba bab

Critical pair: abcba=c.

Referenced by [6], [7].

[5] cab=bac

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

ba b bab

Critical pair: bac=cab.

Flip LHS and RHS.

Defines rule #4.

[6] cb=abcc

Overlap of [4] abcba=c with [2] bab=c:

abc ba bab

Critical pair: abcc=cb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

[7] accca=c

Overlap of [4] abcba=c with [6] cb=abcc:

ab cba cb

Critical pair: ababcca=c.

Reduce LHS:

[2]a(bab)cca
⇒ accca

Defines rule #1.

Referenced by [8].

[8] cccca=acccc

Overlap of [7] accca=c with [7] accca=c:

accc a accca

Critical pair: acccc=cccca.

Flip LHS and RHS.

Defines rule #2.