Certificate for #27760 ⟨a, b | aa=1, bbabbb=bba⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #1.

Referenced by [8].

Axiom: bbabbb=bba.

Referenced by [4].

Axiom: bb=c.

Defines rule #7.

Referenced by [4], [5], [6], [9], [10].

Simplify [2] bbabbb=bba.

Reduce RHS:

Referenced by [5].

Overlap of [4] bbabbb=ca with [3] bb=c:

Critical pair: cabbb=ca.

Reduce LHS:

Referenced by [7].

Overlap of [3] bb=c with [3] bb=c:

Critical pair: bc=cb.

Flip LHS and RHS.

Referenced by [7], [8], [9], [13].

Simplify [5] cacb=ca.

Reduce LHS:

Referenced by [8], [9], [12].

Overlap of [7] cabc=ca with [7] cabc=ca:

Critical pair: cabca=caabc.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [7] cabc=ca with [6] cb=bc:

Critical pair: cabbc=cab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [12].

Overlap of [3] bb=c with [8] bcc=c:

Critical pair: bc=ccc.

Defines rule #4.

Referenced by [11], [13].

Overlap of [8] bcc=c with [10] bc=ccc:

Critical pair: cccc=c.

Defines rule #2.

Referenced by [12].

Overlap of [11] cccc=c with [7] cabc=ca:

Critical pair: cccca=cabc.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Simplify [6] cb=bc.

Reduce RHS:

Defines rule #5.