Certificate for #3069 ⟨a, b, c | abc=a, cba=c⟩

Back:⟨a, b, c | abc=a, cba=c⟩

Completion settings:

[1] abc=a

Axiom: abc=a.

Defines rule #2.

Referenced by [3], [4].

[2] cba=c

Axiom: cba=c.

Defines rule #3.

Referenced by [3], [4].

[3] aba=a

Overlap of [1] abc=a with [2] cba=c:

ab c cba

Critical pair: abc=aba.

Reduce LHS:

[1](abc)
⇒ a

Flip LHS and RHS.

Defines rule #1.

[4] cbc=c

Overlap of [2] cba=c with [1] abc=a:

cb a abc

Critical pair: cba=cbc.

Reduce LHS:

[2](cba)
⇒ c

Flip LHS and RHS.

Defines rule #4.