Certificate for #6746 ⟨a, b | aba=a, abba=ab⟩

Completion settings:

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

Axiom: aba=a.

Referenced by [7].

Axiom: abba=ab.

Referenced by [4].

Axiom: abb=c.

Referenced by [4], [5].

Overlap of [2] abba=ab with [3] abb=c:

Critical pair: ca=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6], [7], [8], [9].

Overlap of [3] abb=c with [4] ab=ca:

Critical pair: cab=c.

Reduce LHS:

Defines rule #3.

Referenced by [6], [9].

Overlap of [5] cca=c with [4] ab=ca:

Critical pair: ccca=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Simplify [1] aba=a.

Reduce LHS:

Defines rule #5.

Referenced by [8].

Overlap of [7] caa=a with [4] ab=ca:

Critical pair: caca=ab.

Reduce RHS:

Referenced by [9].

Overlap of [8] caca=ca with [4] ab=ca:

Critical pair: cacca=cab.

Reduce LHS:

Reduce RHS:

Defines rule #4.