Certificate for #2078 ⟨a, b | abbabaab=aa⟩

Completion settings:

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

Axiom: abbabaab=aa.

Referenced by [3].

Axiom: baba=c.

Defines rule #6.

Referenced by [3], [4], [5], [6], [8].

Overlap of [1] abbabaab=aa with [2] baba=c:

Critical pair: abcab=aa.

Defines rule #7.

Referenced by [5], [6], [7], [9].

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

Critical pair: bac=cba.

Flip LHS and RHS.

Defines rule #1.

Overlap of [2] baba=c with [3] abcab=aa:

Critical pair: babaa=cbcab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [8], [9].

Overlap of [3] abcab=aa with [2] baba=c:

Critical pair: abcac=aaaba.

Flip LHS and RHS.

Defines rule #2.

Overlap of [3] abcab=aa with [3] abcab=aa:

Critical pair: abcaa=aacab.

Flip LHS and RHS.

Defines rule #4.

Overlap of [5] cbcab=ca with [2] baba=c:

Critical pair: cbcac=caaba.

Flip LHS and RHS.

Defines rule #3.

Overlap of [5] cbcab=ca with [3] abcab=aa:

Critical pair: cbcaa=cacab.

Flip LHS and RHS.

Defines rule #5.