Certificate for #5379 ⟨a, b, c | ab=a, bcaa=c⟩

Back:⟨a, b, c | ab=a, bcaa=c⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bcaa=c

Axiom: bcaa=c.

Defines rule #4.

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

[3] acaa=ac

Overlap of [1] ab=a with [2] bcaa=c:

a b bcaa

Critical pair: ac=acaa.

Flip LHS and RHS.

Defines rule #3.

[4] cb=c

Overlap of [2] bcaa=c with [1] ab=a:

bca a ab

Critical pair: bcaa=cb.

Reduce LHS:

[2](bcaa)
⇒ c

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] ccaa=cc

Overlap of [4] cb=c with [2] bcaa=c:

c b bcaa

Critical pair: cc=ccaa.

Flip LHS and RHS.

Defines rule #5.