Certificate for #9154 ⟨a, b | aa=a, abba=bab⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #1.

Referenced by [6], [7].

Axiom: abba=bab.

Referenced by [4].

Axiom: ba=c.

Defines rule #4.

Referenced by [4], [5], [6], [8], [10].

Simplify [2] abba=bab.

Reduce RHS:

Referenced by [5].

Overlap of [4] abba=cb with [3] ba=c:

Critical pair: abc=cb.

Referenced by [7], [8], [11].

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

Critical pair: ba=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

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

Critical pair: acb=abc.

Reduce RHS:

Referenced by [9].

Overlap of [5] abc=cb with [6] ca=c:

Critical pair: abc=cba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [9], [11].

Simplify [7] acb=cb.

Reduce LHS:

Reduce RHS:

Defines rule #5.

Referenced by [10].

Overlap of [3] ba=c with [9] acc=cc:

Critical pair: bcc=ccc.

Defines rule #7.

Simplify [5] abc=cb.

Reduce RHS:

Defines rule #6.