Certificate for #5887 ⟨a, b, c | ab=a, bca=cc⟩

Back:⟨a, b, c | ab=a, bca=cc⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bca=cc

Axiom: bca=cc.

Defines rule #4.

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

[3] aca=acc

Overlap of [1] ab=a with [2] bca=cc:

a b bca

Critical pair: acc=aca.

Flip LHS and RHS.

Defines rule #3.

[4] ccb=cc

Overlap of [2] bca=cc with [1] ab=a:

bc a ab

Critical pair: bca=ccb.

Reduce LHS:

[2](bca)
⇒ cc

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] ccca=cccc

Overlap of [4] ccb=cc with [2] bca=cc:

cc b bca

Critical pair: cccc=ccca.

Flip LHS and RHS.

Defines rule #5.