Certificate for #4832 ⟨a, b | ababbaab=aab⟩

Completion settings:

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

Axiom: ababbaab=aab.

Referenced by [3].

Axiom: ababba=c.

Defines rule #4.

Referenced by [3], [4], [5], [6], [7].

Overlap of [1] ababbaab=aab with [2] ababba=c:

Critical pair: cab=aab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6].

Overlap of [2] ababba=c with [2] ababba=c:

Critical pair: ababbc=cbabba.

Defines rule #3.

Referenced by [5], [7].

Overlap of [2] ababba=c with [3] aab=cab:

Critical pair: ababbcab=cab.

Reduce LHS:

Defines rule #6.

Overlap of [3] aab=cab with [2] ababba=c:

Critical pair: ac=cababba.

Reduce RHS:

Defines rule #1.

Referenced by [7].

Overlap of [2] ababba=c with [6] ac=cc:

Critical pair: ababbcc=cc.

Reduce LHS:

Defines rule #5.