Certificate for #5647 ⟨a, b | aabaab=aaaba⟩

Completion settings:

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

Axiom: aabaab=aaaba.

Referenced by [3].

Axiom: aaba=c.

Defines rule #8.

Referenced by [3], [4], [5], [6], [7], [8], [10].

Simplify [1] aabaab=aaaba.

Reduce RHS:

Referenced by [4].

Overlap of [3] aabaab=ac with [2] aaba=c:

Critical pair: cab=ac.

Defines rule #3.

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

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

Critical pair: aabc=caba.

Reduce RHS:

Defines rule #7.

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

Overlap of [2] aaba=c with [5] aabc=aca:

Critical pair: aabaca=cabc.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [8], [9].

Overlap of [5] aabc=aca with [4] cab=ac:

Critical pair: aabac=acaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [5] aabc=aca with [6] cca=acc:

Critical pair: aabacc=acaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [6] cca=acc with [4] cab=ac:

Critical pair: cac=accb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [10].

Overlap of [2] aaba=c with [9] accb=cac:

Critical pair: aabcac=cccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.