Certificate for #25251 ⟨a, b | aa=a, bbabb=abb⟩

Completion settings:

• Auxiliary generators:
  1. c = abb
• Reduction order:
  • Left-to-right shortlex with c < a < b

Axiom: aa=a.

Defines rule #3.

Referenced by [6].

Axiom: bbabb=abb.

Referenced by [4].

Axiom: abb=c.

Defines rule #5.

Referenced by [4], [5], [6], [7], [8].

Simplify [2] bbabb=abb.

Reduce RHS:

Referenced by [5].

Overlap of [4] bbabb=c with [3] abb=c:

Critical pair: bbc=c.

Defines rule #6.

Referenced by [7], [8].

Overlap of [1] aa=a with [3] abb=c:

Critical pair: ac=abb.

Reduce RHS:

Defines rule #2.

Referenced by [7].

Overlap of [3] abb=c with [5] bbc=c:

Critical pair: ac=cc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [3] abb=c with [5] bbc=c:

Critical pair: abc=cbc.

Defines rule #4.