Certificate for #3665 ⟨a, b | aabbbaaaba=b⟩

Completion settings:

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

Axiom: aabbbaaaba=b.

Referenced by [3].

Axiom: aa=c.

Defines rule #3.

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

Overlap of [1] aabbbaaaba=b with [2] aa=c:

Critical pair: cbbbaaaba=b.

Reduce LHS:

Referenced by [5].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [5].

Simplify [3] cbbbcaba=b.

Reduce LHS:

Defines rule #4.

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

Overlap of [5] cbbbacba=b with [2] aa=c:

Critical pair: cbbbacbc=ba.

Defines rule #2.

Referenced by [7], [8].

Overlap of [6] cbbbacbc=ba with [5] cbbbacba=b:

Critical pair: cbbbacbb=babbbacba.

Flip LHS and RHS.

Defines rule #7.

Referenced by [9].

Overlap of [6] cbbbacbc=ba with [6] cbbbacbc=ba:

Critical pair: cbbbacbba=babbbacbc.

Defines rule #5.

Overlap of [5] cbbbacba=b with [7] babbbacba=cbbbacbb:

Critical pair: cbbbaccbbbacbb=bbbbacba.

Flip LHS and RHS.

Defines rule #6.