Certificate for #1712 ⟨a, b | aabbaaaba=b⟩

Completion settings:

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

Axiom: aabbaaaba=b.

Referenced by [3].

Axiom: aa=c.

Defines rule #3.

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

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

Critical pair: cbbaaaba=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] cbbcaba=b.

Reduce LHS:

Defines rule #5.

Referenced by [6], [7], [9], [10], [12].

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

Critical pair: cbbacbc=ba.

Defines rule #2.

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

Overlap of [6] cbbacbc=ba with [5] cbbacba=b:

Critical pair: cbbacbb=babbacba.

Flip LHS and RHS.

Defines rule #9.

Referenced by [9].

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

Critical pair: cbbacbba=babbacbc.

Defines rule #6.

Referenced by [10], [11].

Overlap of [5] cbbacba=b with [7] babbacba=cbbacbb:

Critical pair: cbbaccbbacbb=bbbacba.

Flip LHS and RHS.

Defines rule #7.

Overlap of [8] cbbacbba=babbacbc with [5] cbbacba=b:

Critical pair: cbbab=babbacbccba.

Flip LHS and RHS.

Defines rule #10.

Referenced by [12].

Overlap of [8] cbbacbba=babbacbc with [6] cbbacbc=ba:

Critical pair: cbbaba=babbacbccbc.

Defines rule #4.

Overlap of [5] cbbacba=b with [10] babbacbccba=cbbab:

Critical pair: cbbaccbbab=bbbacbccba.

Flip LHS and RHS.

Defines rule #8.