Certificate for #1793 ⟨a, b | ababbbaab=a⟩

Completion settings:

• Auxiliary generators:
  1. c = babbba
• Reduction order:
  • Right-to-left recursive path with deg(c) = 0; deg(a) = 1; deg(b) = 2

Axiom: ababbbaab=a.

Referenced by [3].

Axiom: babbba=c.

Defines rule #18.

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

Overlap of [1] ababbbaab=a with [2] babbba=c:

Critical pair: acab=a.

Defines rule #9.

Referenced by [5], [6], [8], [10], [12], [14], [16].

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

Critical pair: babbc=cbbba.

Flip LHS and RHS.

Defines rule #15.

Overlap of [2] babbba=c with [3] acab=a:

Critical pair: babbba=ccab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [7], [9], [11], [13].

Overlap of [3] acab=a with [2] babbba=c:

Critical pair: acac=aabbba.

Flip LHS and RHS.

Defines rule #17.

Overlap of [5] ccab=c with [2] babbba=c:

Critical pair: ccac=cabbba.

Flip LHS and RHS.

Defines rule #16.

Referenced by [8], [9].

Overlap of [3] acab=a with [7] cabbba=ccac:

Critical pair: accac=abba.

Flip LHS and RHS.

Defines rule #14.

Referenced by [10], [11].

Overlap of [5] ccab=c with [7] cabbba=ccac:

Critical pair: cccac=cbba.

Flip LHS and RHS.

Defines rule #13.

Overlap of [3] acab=a with [8] abba=accac:

Critical pair: acaccac=aba.

Flip LHS and RHS.

Defines rule #12.

Referenced by [12], [13].

Overlap of [5] ccab=c with [8] abba=accac:

Critical pair: ccaccac=cba.

Flip LHS and RHS.

Defines rule #11.

Overlap of [3] acab=a with [10] aba=acaccac:

Critical pair: acacaccac=aa.

Defines rule #5.

Referenced by [16], [17], [18], [19].

Overlap of [5] ccab=c with [10] aba=acaccac:

Critical pair: ccacaccac=ca.

Defines rule #2.

Referenced by [14], [15], [18], [19].

Overlap of [13] ccacaccac=ca with [3] acab=a:

Critical pair: ccacacca=caab.

Flip LHS and RHS.

Defines rule #8.

Overlap of [13] ccacaccac=ca with [13] ccacaccac=ca:

Critical pair: ccacaca=caaccac.

Flip LHS and RHS.

Defines rule #1.

Overlap of [12] acacaccac=aa with [3] acab=a:

Critical pair: acacacca=aaab.

Flip LHS and RHS.

Defines rule #10.

Overlap of [12] acacaccac=aa with [12] acacaccac=aa:

Critical pair: acacaccaa=aaacaccac.

Flip LHS and RHS.

Defines rule #6.

Overlap of [12] acacaccac=aa with [13] ccacaccac=ca:

Critical pair: acacaca=aaaccac.

Flip LHS and RHS.

Defines rule #3.

Overlap of [13] ccacaccac=ca with [12] acacaccac=aa:

Critical pair: ccacaccaa=caacaccac.

Flip LHS and RHS.

Defines rule #4.