Certificate for #4067 ⟨a, b | aabaaaaba=ba⟩

Back:⟨a, b | aabaaaaba=ba⟩

Completion settings:

[1] aabaaaaba=ba

Axiom: aabaaaaba=ba.

Referenced by [3].

[2] ba=c

Axiom: ba=c.

Defines rule #3.

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

[3] aabaaaaba=c

Simplify [1] aabaaaaba=ba.

Reduce RHS:

[2](ba)
⇒ c

Referenced by [4].

[4] aacaaac=c

Overlap of [3] aabaaaaba=c with [2] ba=c:

aa baaaaba ba

Critical pair: aacaaaba=c.

Reduce LHS:

[2]aacaaa(ba)
⇒ aacaaac

Referenced by [5], [6], [8].

[5] bc=cacaaac

Overlap of [2] ba=c with [4] aacaaac=c:

b a aacaaac

Critical pair: bc=cacaaac.

Referenced by [7].

[6] caaac=aacac

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

aaca aac aacaaac

Critical pair: aacac=caaac.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [8].

[7] bc=aacacac

Simplify [5] bc=cacaaac.

Reduce RHS:

[6]ca(caaac)
[6]⇒ (caaac)ac
⇒ aacacac

Defines rule #4.

[8] aaaacac=c

Overlap of [4] aacaaac=c with [6] caaac=aacac:

aa caaac caaac

Critical pair: aaaacac=c.

Defines rule #2.