Certificate for #25209 ⟨a, b | aa=a, abbba=abb⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #1.

Referenced by [6], [7].

Axiom: abbba=abb.

Referenced by [4].

Axiom: ab=c.

Defines rule #3.

Referenced by [4], [5], [6], [8], [11].

Simplify [2] abbba=abb.

Reduce RHS:

Referenced by [5].

Overlap of [4] abbba=cb with [3] ab=c:

Critical pair: cbba=cb.

Referenced by [7], [8], [9], [10].

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

Critical pair: ac=ab.

Reduce RHS:

Defines rule #2.

Referenced by [9], [10].

Overlap of [5] cbba=cb with [1] aa=a:

Critical pair: cbba=cba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [5] cbba=cb with [3] ab=c:

Critical pair: cbbc=cbb.

Referenced by [9].

Overlap of [5] cbba=cb with [6] ac=c:

Critical pair: cbbc=cbc.

Reduce LHS:

Defines rule #5.

Referenced by [10], [11].

Overlap of [6] ac=c with [5] cbba=cb:

Critical pair: acb=cbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [11].

Overlap of [10] cbca=cb with [3] ab=c:

Critical pair: cbcc=cbb.

Reduce RHS:

Defines rule #7.