Certificate for #5830 ⟨a, b | abaaab=babab⟩

Completion settings:

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

Axiom: abaaab=babab.

Referenced by [3].

Axiom: babab=c.

Defines rule #2.

Referenced by [3], [4], [6], [7], [9].

Simplify [1] abaaab=babab.

Reduce RHS:

Defines rule #8.

Referenced by [5], [6], [7], [8], [11].

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

Critical pair: bac=cab.

Defines rule #1.

Overlap of [3] abaaab=c with [3] abaaab=c:

Critical pair: abaac=caaab.

Referenced by [10].

Overlap of [3] abaaab=c with [2] babab=c:

Critical pair: abaaac=cabab.

Defines rule #9.

Overlap of [2] babab=c with [3] abaaab=c:

Critical pair: babc=caaab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [9], [10], [12].

Overlap of [7] caaab=babc with [3] abaaab=c:

Critical pair: caac=babcaaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [7] caaab=babc with [2] babab=c:

Critical pair: caaac=babcabab.

Defines rule #5.

Simplify [5] abaac=caaab.

Reduce RHS:

Defines rule #6.

Referenced by [11], [12].

Overlap of [3] abaaab=c with [10] abaac=babc:

Critical pair: abaababc=caac.

Defines rule #10.

Overlap of [7] caaab=babc with [10] abaac=babc:

Critical pair: caababc=babcaac.

Defines rule #7.