Certificate for #5316 ⟨a, b | abaabab=baab⟩

Completion settings:

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

Axiom: abaabab=baab.

Referenced by [3].

Axiom: baab=c.

Defines rule #12.

Referenced by [3], [4], [5], [6], [7], [9], [12].

Simplify [1] abaabab=baab.

Reduce RHS:

Referenced by [4].

Overlap of [3] abaabab=c with [2] baab=c:

Critical pair: acab=c.

Defines rule #6.

Referenced by [6], [10], [13], [15].

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

Critical pair: baac=caab.

Referenced by [8].

Overlap of [4] acab=c with [2] baab=c:

Critical pair: acac=caab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8], [11], [14].

Overlap of [6] caab=acac with [2] baab=c:

Critical pair: caac=acacaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Simplify [5] baac=caab.

Reduce RHS:

Defines rule #9.

Referenced by [9], [10], [11].

Overlap of [2] baab=c with [8] baac=acac:

Critical pair: baaacac=caac.

Defines rule #11.

Overlap of [8] baac=acac with [4] acab=c:

Critical pair: bac=acacab.

Reduce RHS:

Defines rule #8.

Referenced by [12], [13], [14], [15].

Overlap of [6] caab=acac with [8] baac=acac:

Critical pair: caaacac=acacaac.

Defines rule #3.

Overlap of [2] baab=c with [10] bac=acc:

Critical pair: baaacc=cac.

Defines rule #10.

Overlap of [4] acab=c with [10] bac=acc:

Critical pair: acaacc=cac.

Defines rule #2.

Overlap of [6] caab=acac with [10] bac=acc:

Critical pair: caaacc=acacac.

Defines rule #1.

Overlap of [10] bac=acc with [4] acab=c:

Critical pair: bc=accab.

Defines rule #7.