Certificate for #455 ⟨a, b | aabbaa=ab⟩

Completion settings:

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

Axiom: aabbaa=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #1.

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

Simplify [1] aabbaa=ab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aabbaa=c with [2] ab=c:

Critical pair: acbaa=c.

Defines rule #7.

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

Overlap of [4] acbaa=c with [2] ab=c:

Critical pair: acbac=cb.

Defines rule #3.

Referenced by [6], [7], [8], [9], [10], [11].

Overlap of [4] acbaa=c with [4] acbaa=c:

Critical pair: acbac=ccbaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [10], [11].

Overlap of [4] acbaa=c with [5] acbac=cb:

Critical pair: acbacb=ccbac.

Reduce LHS:

Defines rule #2.

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

Overlap of [5] acbac=cb with [4] acbaa=c:

Critical pair: acbc=cbbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [5] acbac=cb with [5] acbac=cb:

Critical pair: acbcb=cbbac.

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [5] acbac=cb with [6] ccbaa=cb:

Critical pair: acbacb=cbcbaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [6] ccbaa=cb with [5] acbac=cb:

Critical pair: ccbacb=cbcbac.

Flip LHS and RHS.

Defines rule #6.