Certificate for #1899 ⟨a, b, c | aba=cc, bcc=1⟩

Back:⟨a, b, c | aba=cc, bcc=1⟩

Completion settings:

[1] aba=cc

Axiom: aba=cc.

Defines rule #1.

Referenced by [3].

[2] bcc=1

Axiom: bcc=1.

Defines rule #2.

Referenced by [3], [4].

[3] ccba=a

Overlap of [1] aba=cc with [1] aba=cc:

ab a aba

Critical pair: abcc=ccba.

Reduce LHS:

[2]a(bcc)
⇒ a

Flip LHS and RHS.

Referenced by [4], [5].

[4] cba=bca

Overlap of [2] bcc=1 with [3] ccba=a:

bc c ccba

Critical pair: bca=cba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] cbca=a

Overlap of [3] ccba=a with [4] cba=bca:

c cba cba

Critical pair: cbca=a.

Defines rule #4.