Certificate for #2480 ⟨a, b | aabaab=aaab⟩

Completion settings:

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

Axiom: aabaab=aaab.

Referenced by [3].

Axiom: aaab=c.

Defines rule #3.

Referenced by [3], [5], [7].

Simplify [1] aabaab=aaab.

Reduce RHS:

Defines rule #7.

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

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

Critical pair: aabc=caab.

Flip LHS and RHS.

Referenced by [5], [9].

Overlap of [2] aaab=c with [3] aabaab=c:

Critical pair: ac=caab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [3] aabaab=c with [5] aabc=ac:

Critical pair: aabac=cc.

Defines rule #6.

Referenced by [8].

Overlap of [2] aaab=c with [5] aabc=ac:

Critical pair: aac=cc.

Defines rule #1.

Overlap of [3] aabaab=c with [6] aabac=cc:

Critical pair: aabcc=cac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Simplify [4] caab=aabc.

Reduce RHS:

Defines rule #5.