Certificate for #4306 ⟨a, b | ababbaaab=aa⟩

Completion settings:

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

Axiom: ababbaaab=aa.

Referenced by [3].

Axiom: babba=c.

Defines rule #14.

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

Overlap of [1] ababbaaab=aa with [2] babba=c:

Critical pair: acaab=aa.

Defines rule #8.

Referenced by [5], [6], [8], [10], [12], [13].

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

Critical pair: babc=cbba.

Flip LHS and RHS.

Defines rule #11.

Overlap of [2] babba=c with [3] acaab=aa:

Critical pair: babbaa=ccaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [7], [9], [11].

Overlap of [3] acaab=aa with [2] babba=c:

Critical pair: acaac=aaabba.

Flip LHS and RHS.

Defines rule #13.

Overlap of [5] ccaab=ca with [2] babba=c:

Critical pair: ccaac=caabba.

Flip LHS and RHS.

Defines rule #12.

Referenced by [8], [9].

Overlap of [3] acaab=aa with [7] caabba=ccaac:

Critical pair: accaac=aaba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [10], [11].

Overlap of [5] ccaab=ca with [7] caabba=ccaac:

Critical pair: cccaac=caba.

Flip LHS and RHS.

Defines rule #5.

Overlap of [3] acaab=aa with [8] aaba=accaac:

Critical pair: acaccaac=aaa.

Defines rule #2.

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

Overlap of [5] ccaab=ca with [8] aaba=accaac:

Critical pair: ccaccaac=caa.

Defines rule #1.

Referenced by [12], [15].

Overlap of [11] ccaccaac=caa with [3] acaab=aa:

Critical pair: ccaccaaa=caaaab.

Flip LHS and RHS.

Defines rule #9.

Overlap of [10] acaccaac=aaa with [3] acaab=aa:

Critical pair: acaccaaa=aaaaab.

Flip LHS and RHS.

Defines rule #10.

Overlap of [10] acaccaac=aaa with [10] acaccaac=aaa:

Critical pair: acaccaaaa=aaaaccaac.

Flip LHS and RHS.

Defines rule #4.

Overlap of [11] ccaccaac=caa with [10] acaccaac=aaa:

Critical pair: ccaccaaaa=caaaccaac.

Flip LHS and RHS.

Defines rule #3.