Certificate for #3128 ⟨a, b, c | ab=aa, cbcc=1⟩

Back:⟨a, b, c | ab=aa, cbcc=1⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [6].

[2] cbcc=1

Axiom: cbcc=1.

Referenced by [3], [4].

[3] cbc=bcc

Overlap of [2] cbcc=1 with [2] cbcc=1:

cbc c cbcc

Critical pair: cbc=bcc.

Referenced by [4], [5].

[4] bccc=1

Overlap of [2] cbcc=1 with [3] cbc=bcc:

cbcc cbc

Critical pair: bccc=1.

Defines rule #3.

Referenced by [5], [6], [7].

[5] cbbcc=b

Overlap of [3] cbc=bcc with [3] cbc=bcc:

cb c cbc

Critical pair: cbbcc=bccbc.

Reduce RHS:

[3]bc(cbc)
[3]⇒ b(cbc)c
[4]⇒ b(bccc)
⇒ b

Referenced by [7].

[6] aaccc=a

Overlap of [1] ab=aa with [4] bccc=1:

a b bccc

Critical pair: a=aaccc.

Flip LHS and RHS.

Defines rule #4.

[7] cb=bc

Overlap of [5] cbbcc=b with [4] bccc=1:

cb bcc bccc

Critical pair: cb=bc.

Defines rule #2.