Certificate for #5819 ⟨a, b | abaaab=ababa⟩

Back:⟨a, b | abaaab=ababa⟩

Completion settings:

[1] abaaab=ababa

Axiom: abaaab=ababa.

Referenced by [3].

[2] ababa=c

Axiom: ababa=c.

Defines rule #5.

Referenced by [3], [4], [6], [7].

[3] abaaab=c

Simplify [1] abaaab=ababa.

Reduce RHS:

[2](ababa)
⇒ c

Defines rule #6.

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

[4] cba=abc

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

ab aba ababa

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #1.

[5] caaab=abaac

Overlap of [3] abaaab=c with [3] abaaab=c:

abaa ab abaaab

Critical pair: abaac=caaab.

Flip LHS and RHS.

Defines rule #4.

[6] caba=abaac

Overlap of [3] abaaab=c with [2] ababa=c:

abaa ab ababa

Critical pair: abaac=caba.

Flip LHS and RHS.

Defines rule #2.

[7] caab=abc

Overlap of [2] ababa=c with [3] abaaab=c:

ab aba abaaab

Critical pair: abc=caab.

Flip LHS and RHS.

Defines rule #3.