Certificate for #13164 ⟨a, b | aba=aab, baa=ba⟩

Completion settings:

[1] aba=aab

Axiom: aba=aab.

Referenced by [4].

[2] baa=ba

Axiom: baa=ba.

Referenced by [5].

[3] ba=c

Axiom: ba=c.

Defines rule #3.

Referenced by [4], [5], [6], [7], [8].

[4] aab=ac

Overlap of [1] aba=aab with [3] ba=c:

a ba ba

Critical pair: ac=aab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8].

[5] baa=c

Simplify [2] baa=ba.

Reduce RHS:

[3](ba)
⇒ c

Referenced by [6].

[6] ca=c

Overlap of [5] baa=c with [3] ba=c:

baa ba

Critical pair: ca=c.

Defines rule #1.

Referenced by [7], [8].

[7] cb=cc

Overlap of [3] ba=c with [4] aab=ac:

b a aab

Critical pair: bac=cab.

Reduce LHS:

[3](ba)c
⇒ cc

Reduce RHS:

[6](ca)b
⇒ cb

Flip LHS and RHS.

Defines rule #2.

[8] aac=ac

Overlap of [4] aab=ac with [3] ba=c:

aa b ba

Critical pair: aac=aca.

Reduce RHS:

[6]a(ca)
⇒ ac

Defines rule #4.