Certificate for #3646 ⟨a, b | aabbabaaba=b⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
• Auxiliary generators:
  1. ba=c

Axiom: aabbabaaba=b.

Referenced by [3].

Axiom: ba=c.

Defines rule #1.

Referenced by [3], [4], [5], [7].

Overlap of [1] aabbabaaba=b with [2] ba=c:

Critical pair: aabcbaaba=b.

Reduce LHS:

Defines rule #2.

Referenced by [4], [7].

Overlap of [2] ba=c with [3] aabccac=b:

Critical pair: bb=cabccac.

Defines rule #4.

Referenced by [5], [6].

Overlap of [4] bb=cabccac with [2] ba=c:

Critical pair: bc=cabccaca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [8], [9], [10].

Overlap of [4] bb=cabccac with [4] bb=cabccac:

Critical pair: bcabccac=cabccacb.

Flip LHS and RHS.

Defines rule #9.

Overlap of [3] aabccac=b with [5] cabccaca=bc:

Critical pair: aabccabc=babccaca.

Reduce RHS:

Defines rule #6.

Referenced by [9].

Overlap of [5] cabccaca=bc with [5] cabccaca=bc:

Critical pair: cabccabc=bcbccaca.

Defines rule #8.

Referenced by [10].

Overlap of [7] aabccabc=cbccaca with [5] cabccaca=bc:

Critical pair: aabcbc=cbccacacaca.

Defines rule #5.

Overlap of [8] cabccabc=bcbccaca with [5] cabccaca=bc:

Critical pair: cabcbc=bcbccacacaca.

Defines rule #7.