Certificate for #4672 ⟨a, b | aababbba=aab⟩

Completion settings:

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

Axiom: aababbba=aab.

Referenced by [3].

Axiom: aaba=c.

Referenced by [3], [4].

Overlap of [1] aababbba=aab with [2] aaba=c:

Critical pair: cbbba=aab.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [2] aaba=c with [3] aab=cbbba:

Critical pair: cbbbaa=c.

Defines rule #6.

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

Overlap of [4] cbbbaa=c with [3] aab=cbbba:

Critical pair: cbbbcbbba=cb.

Defines rule #4.

Referenced by [7].

Overlap of [4] cbbbaa=c with [3] aab=cbbba:

Critical pair: cbbbacbbba=cab.

Defines rule #8.

Referenced by [9], [10].

Overlap of [5] cbbbcbbba=cb with [4] cbbbaa=c:

Critical pair: cbbbc=cba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [8].

Overlap of [7] cba=cbbbc with [3] aab=cbbba:

Critical pair: cbcbbba=cbbbcab.

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] cbbbacbbba=cab with [4] cbbbaa=c:

Critical pair: cbbbac=caba.

Flip LHS and RHS.

Defines rule #5.

Overlap of [6] cbbbacbbba=cab with [6] cbbbacbbba=cab:

Critical pair: cbbbacab=cabcbbba.

Defines rule #7.