Certificate for #336 ⟨a, b | abbaabba=1⟩

Completion settings:

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

Axiom: abbaabba=1.

Referenced by [4].

Axiom: aa=c.

Defines rule #6.

Referenced by [3], [4], [5], [6], [7].

Axiom: bbaabb=d.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [1] abbaabba=1 with [2] aa=c:

Critical pair: abbcbba=1.

Referenced by [6], [7], [8], [9], [11].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [10].

Overlap of [2] aa=c with [4] abbcbba=1:

Critical pair: a=cbbcbba.

Flip LHS and RHS.

Referenced by [10].

Overlap of [4] abbcbba=1 with [2] aa=c:

Critical pair: abbcbbc=a.

Referenced by [9].

Overlap of [4] abbcbba=1 with [4] abbcbba=1:

Critical pair: abbcbb=bbcbba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [10].

Overlap of [4] abbcbba=1 with [7] abbcbbc=a:

Critical pair: abbcbba=bbcbbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [12].

Simplify [6] cbbcbba=a.

Reduce LHS:

Referenced by [11].

Overlap of [4] abbcbba=1 with [10] acbbcbb=a:

Critical pair: abbcbba=cbbcbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [11] cbbcbb=1 with [9] bbcbbc=1:

Critical pair: cbbcb=bcbbc.

Defines rule #1.