Certificate for #991 ⟨a, b | ababbba=ba⟩

Back:⟨a, b | ababbba=ba⟩

Completion settings:

[1] ababbba=ba

Axiom: ababbba=ba.

Referenced by [3].

[2] ababbb=c

Axiom: ababbb=c.

Referenced by [3], [4].

[3] ba=ca

Overlap of [1] ababbba=ba with [2] ababbb=c:

ababbba ababbb

Critical pair: ca=ba.

Flip LHS and RHS.

Defines rule #1.

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

[4] acabbb=c

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

a babbb ba

Critical pair: acabbb=c.

Defines rule #3.

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

[5] bc=cc

Overlap of [3] ba=ca with [4] acabbb=c:

b a acabbb

Critical pair: bc=cacabbb.

Reduce RHS:

[4]c(acabbb)
⇒ cc

Defines rule #2.

Referenced by [6], [7].

[6] acaccca=ca

Overlap of [4] acabbb=c with [3] ba=ca:

acabb b ba

Critical pair: acabbca=ca.

Reduce LHS:

[5]acab(bc)a
[5]⇒ aca(bc)ca
⇒ acaccca

Defines rule #4.

[7] acacccc=cc

Overlap of [4] acabbb=c with [5] bc=cc:

acabb b bc

Critical pair: acabbcc=cc.

Reduce LHS:

[5]acab(bc)c
[5]⇒ aca(bc)cc
⇒ acacccc

Defines rule #5.