Certificate for #4305 ⟨a, b, c | aab=1, caca=c⟩

Back:⟨a, b, c | aab=1, caca=c⟩

Completion settings:

[1] aab=1

Axiom: aab=1.

Defines rule #2.

Referenced by [3].

[2] caca=c

Axiom: caca=c.

Defines rule #5.

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

[3] cab=cac

Overlap of [2] caca=c with [1] aab=1:

cac a aab

Critical pair: cac=cab.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[4] cca=cac

Overlap of [2] caca=c with [2] caca=c:

ca ca caca

Critical pair: cac=cca.

Flip LHS and RHS.

Defines rule #4.

[5] cb=cc

Overlap of [2] caca=c with [3] cab=cac:

ca ca cab

Critical pair: cacac=cb.

Reduce LHS:

[2](caca)c
⇒ cc

Flip LHS and RHS.

Defines rule #1.