Certificate for #6087 ⟨a, b, c | ab=c, bca=bc⟩

Back:⟨a, b, c | ab=c, bca=bc⟩

Completion settings:

[1] ab=c

Axiom: ab=c.

Defines rule #1.

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

[2] bca=bc

Axiom: bca=bc.

Defines rule #4.

Referenced by [3], [4].

[3] cca=cc

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

a b bca

Critical pair: abc=cca.

Reduce LHS:

[1](ab)c
⇒ cc

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[4] bcb=bcc

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

bc a ab

Critical pair: bcc=bcb.

Flip LHS and RHS.

Defines rule #5.

[5] ccb=ccc

Overlap of [3] cca=cc with [1] ab=c:

cc a ab

Critical pair: ccc=ccb.

Flip LHS and RHS.

Defines rule #3.