Certificate for #2318 ⟨a, b | abaabba=bab⟩

Completion settings:

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

Axiom: abaabba=bab.

Referenced by [3].

Axiom: ab=c.

Defines rule #1.

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

Simplify [1] abaabba=bab.

Reduce RHS:

Referenced by [4].

Overlap of [3] abaabba=bc with [2] ab=c:

Critical pair: caabba=bc.

Reduce LHS:

Defines rule #3.

Referenced by [5], [8].

Overlap of [4] cacba=bc with [2] ab=c:

Critical pair: cacbc=bcb.

Flip LHS and RHS.

Defines rule #5.

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

Overlap of [2] ab=c with [5] bcb=cacbc:

Critical pair: acacbc=ccb.

Defines rule #2.

Referenced by [8], [9].

Overlap of [5] bcb=cacbc with [5] bcb=cacbc:

Critical pair: bccacbc=cacbccb.

Defines rule #7.

Overlap of [6] acacbc=ccb with [4] cacba=bc:

Critical pair: acacbbc=ccbacba.

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] acacbc=ccb with [5] bcb=cacbc:

Critical pair: acaccacbc=ccbb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [10].

Overlap of [9] ccbb=acaccacbc with [5] bcb=cacbc:

Critical pair: ccbcacbc=acaccacbccb.

Defines rule #6.