Certificate for #1979 ⟨a, b | aababbba=ba⟩

Back:⟨a, b | aababbba=ba⟩

Completion settings:

[1] aababbba=ba

Axiom: aababbba=ba.

Referenced by [3].

[2] aababbb=c

Axiom: aababbb=c.

Referenced by [3], [4].

[3] ba=ca

Overlap of [1] aababbba=ba with [2] aababbb=c:

aababbba aababbb

Critical pair: ca=ba.

Flip LHS and RHS.

Defines rule #1.

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

[4] aacabbb=c

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

aa babbb ba

Critical pair: aacabbb=c.

Defines rule #3.

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

[5] bc=cc

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

b a aacabbb

Critical pair: bc=caacabbb.

Reduce RHS:

[4]c(aacabbb)
⇒ cc

Defines rule #2.

Referenced by [6], [7].

[6] aacaccca=ca

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

aacabb b ba

Critical pair: aacabbca=ca.

Reduce LHS:

[5]aacab(bc)a
[5]⇒ aaca(bc)ca
⇒ aacaccca

Defines rule #4.

[7] aacacccc=cc

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

aacabb b bc

Critical pair: aacabbcc=cc.

Reduce LHS:

[5]aacab(bc)c
[5]⇒ aaca(bc)cc
⇒ aacacccc

Defines rule #5.