Certificate for #1112 ⟨a, b | abaaba=aab⟩

Completion settings:

• Auxiliary generators:
  1. c = aba
• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1

Axiom: abaaba=aab.

Referenced by [3].

Axiom: aba=c.

Defines rule #2.

Referenced by [3], [4], [5], [6], [8].

Overlap of [1] abaaba=aab with [2] aba=c:

Critical pair: caba=aab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [5], [6].

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

Critical pair: abc=cba.

Flip LHS and RHS.

Defines rule #3.

Overlap of [2] aba=c with [3] aab=cc:

Critical pair: abcc=cab.

Flip LHS and RHS.

Defines rule #6.

Referenced by [7].

Overlap of [3] aab=cc with [2] aba=c:

Critical pair: ac=cca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

Overlap of [6] cca=ac with [5] cab=abcc:

Critical pair: cabcc=acb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [8].

Overlap of [2] aba=c with [7] acb=abcccc:

Critical pair: ababcccc=ccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.