Certificate for #3406 ⟨a, b, c | ac=ab, bca=c⟩

Back:⟨a, b, c | ac=ab, bca=c⟩

Completion settings:

[1] ab=ac

Axiom: ac=ab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3], [4].

[2] bca=c

Axiom: bca=c.

Defines rule #3.

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

[3] acca=ac

Overlap of [1] ab=ac with [2] bca=c:

a b bca

Critical pair: ac=acca.

Flip LHS and RHS.

Defines rule #4.

[4] cb=cc

Overlap of [2] bca=c with [1] ab=ac:

bc a ab

Critical pair: bcac=cb.

Reduce LHS:

[2](bca)c
⇒ cc

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] ccca=cc

Overlap of [4] cb=cc with [2] bca=c:

c b bca

Critical pair: cc=ccca.

Flip LHS and RHS.

Defines rule #5.