Certificate for #915 ⟨a, b | aaabbaa=ba⟩

Back:⟨a, b | aaabbaa=ba⟩

Completion settings:

[1] aaabbaa=ba

Axiom: aaabbaa=ba.

Referenced by [3].

[2] bba=c

Axiom: bba=c.

Referenced by [3], [4].

[3] ba=aaaca

Overlap of [1] aaabbaa=ba with [2] bba=c:

aaa bbaa bba

Critical pair: aaaca=ba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

[4] aaacaaaca=c

Overlap of [2] bba=c with [3] ba=aaaca:

b ba ba

Critical pair: baaaca=c.

Reduce LHS:

[3](ba)aaca
⇒ aaacaaaca

Defines rule #2.

Referenced by [5], [6].

[5] bc=caaca

Overlap of [3] ba=aaaca with [4] aaacaaaca=c:

b a aaacaaaca

Critical pair: bc=aaacaaacaaaca.

Reduce RHS:

[4](aaacaaaca)aaca
⇒ caaca

Defines rule #4.

[6] aaacc=caaca

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

aaac aaaca aaacaaaca

Critical pair: aaacc=caaca.

Defines rule #1.