Certificate for #1941 ⟨a, b | aabaaaba=ba⟩

Back:⟨a, b | aabaaaba=ba⟩

Completion settings:

[1] aabaaaba=ba

Axiom: aabaaaba=ba.

Referenced by [3].

[2] ba=c

Axiom: ba=c.

Defines rule #3.

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

[3] aabaaaba=c

Simplify [1] aabaaaba=ba.

Reduce RHS:

[2](ba)
⇒ c

Referenced by [4].

[4] aacaac=c

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

aa baaaba ba

Critical pair: aacaaba=c.

Reduce LHS:

[2]aacaa(ba)
⇒ aacaac

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

[5] bc=cacaac

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

b a aacaac

Critical pair: bc=cacaac.

Referenced by [7].

[6] caac=aacc

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

aac aac aacaac

Critical pair: aacc=caac.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [8].

[7] bc=caaacc

Simplify [5] bc=cacaac.

Reduce RHS:

[6]ca(caac)
⇒ caaacc

Defines rule #4.

[8] aaaacc=c

Overlap of [4] aacaac=c with [6] caac=aacc:

aa caac caac

Critical pair: aaaacc=c.

Defines rule #2.