Certificate for #4584 ⟨a, b | aaabbbba=abb⟩

Completion settings:

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

Axiom: aaabbbba=abb.

Referenced by [3].

Axiom: abbb=c.

Referenced by [3], [4].

Overlap of [1] aaabbbba=abb with [2] abbb=c:

Critical pair: aacba=abb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [5].

Overlap of [2] abbb=c with [3] abb=aacba:

Critical pair: aacbab=c.

Defines rule #3.

Referenced by [5], [6].

Overlap of [4] aacbab=c with [3] abb=aacba:

Critical pair: aacbaacba=cb.

Defines rule #5.

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

Overlap of [5] aacbaacba=cb with [4] aacbab=c:

Critical pair: aacbc=cbb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

Overlap of [5] aacbaacba=cb with [5] aacbaacba=cb:

Critical pair: aacbcb=cbacba.

Defines rule #4.

Referenced by [8].

Overlap of [7] aacbcb=cbacba with [6] cbb=aacbc:

Critical pair: aacbaacbc=cbacbab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [9].

Overlap of [5] aacbaacba=cb with [8] cbacbab=aacbaacbc:

Critical pair: aacbaaaacbaacbc=cbcbab.

Defines rule #7.