Certificate for #4955 ⟨a, b, c | ab=a, cbccc=1⟩

Back:⟨a, b, c | ab=a, cbccc=1⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [6].

[2] cbccc=1

Axiom: cbccc=1.

Referenced by [3], [4].

[3] cbcc=bccc

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

cbcc c cbccc

Critical pair: cbcc=bccc.

Referenced by [4], [5].

[4] bcccc=1

Overlap of [2] cbccc=1 with [3] cbcc=bccc:

cbccc cbcc

Critical pair: bcccc=1.

Defines rule #4.

Referenced by [5], [6].

[5] cb=bc

Overlap of [3] cbcc=bccc with [3] cbcc=bccc:

cbc c cbcc

Critical pair: cbcbccc=bcccbcc.

Reduce LHS:

[3]cb(cbcc)c
[4]⇒ cb(bcccc)
⇒ cb

Reduce RHS:

[3]bcc(cbcc)
[3]⇒ bc(cbcc)c
[3]⇒ b(cbcc)cc
[4]⇒ b(bcccc)c
⇒ bc

Defines rule #2.

[6] acccc=a

Overlap of [1] ab=a with [4] bcccc=1:

a b bcccc

Critical pair: a=acccc.

Flip LHS and RHS.

Defines rule #3.