Certificate for #5378 ⟨a, b, c | ab=a, bcaa=b⟩

Back:⟨a, b, c | ab=a, bcaa=b⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bcaa=b

Axiom: bcaa=b.

Defines rule #4.

Referenced by [3], [4].

[3] acaa=a

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

a b bcaa

Critical pair: ab=acaa.

Reduce LHS:

[1](ab)
⇒ a

Flip LHS and RHS.

Defines rule #3.

[4] bb=b

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

bca a ab

Critical pair: bcaa=bb.

Reduce LHS:

[2](bcaa)
⇒ b

Flip LHS and RHS.

Defines rule #2.