Certificate for #1783 ⟨a, b | abababaab=a⟩

Completion settings:

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

Axiom: abababaab=a.

Referenced by [3].

Axiom: ba=c.

Defines rule #3.

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

Overlap of [1] abababaab=a with [2] ba=c:

Critical pair: acbabaab=a.

Reduce LHS:

Defines rule #11.

Referenced by [4], [5], [7], [8].

Overlap of [2] ba=c with [3] acccab=a:

Critical pair: ba=ccccab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

Overlap of [3] acccab=a with [2] ba=c:

Critical pair: acccac=aa.

Defines rule #7.

Referenced by [8], [9], [10], [11], [13], [15], [17].

Overlap of [4] ccccab=c with [2] ba=c:

Critical pair: ccccac=ca.

Defines rule #1.

Referenced by [7], [10], [12], [14], [16], [18].

Overlap of [6] ccccac=ca with [3] acccab=a:

Critical pair: cccca=caccab.

Flip LHS and RHS.

Defines rule #10.

Referenced by [11], [12].

Overlap of [5] acccac=aa with [3] acccab=a:

Critical pair: accca=aaccab.

Flip LHS and RHS.

Defines rule #17.

Overlap of [5] acccac=aa with [5] acccac=aa:

Critical pair: acccaa=aaccac.

Flip LHS and RHS.

Defines rule #14.

Overlap of [6] ccccac=ca with [5] acccac=aa:

Critical pair: ccccaa=caccac.

Flip LHS and RHS.

Defines rule #6.

Referenced by [13], [14].

Overlap of [5] acccac=aa with [7] caccab=cccca:

Critical pair: acccccca=aacab.

Flip LHS and RHS.

Defines rule #16.

Overlap of [6] ccccac=ca with [7] caccab=cccca:

Critical pair: ccccccca=cacab.

Flip LHS and RHS.

Defines rule #9.

Referenced by [15], [16].

Overlap of [5] acccac=aa with [10] caccac=ccccaa:

Critical pair: accccccaa=aacac.

Flip LHS and RHS.

Defines rule #13.

Overlap of [6] ccccac=ca with [10] caccac=ccccaa:

Critical pair: cccccccaa=cacac.

Flip LHS and RHS.

Defines rule #5.

Referenced by [17], [18].

Overlap of [5] acccac=aa with [12] cacab=ccccccca:

Critical pair: accccccccca=aaab.

Flip LHS and RHS.

Defines rule #15.

Overlap of [6] ccccac=ca with [12] cacab=ccccccca:

Critical pair: cccccccccca=caab.

Flip LHS and RHS.

Defines rule #8.

Overlap of [5] acccac=aa with [14] cacac=cccccccaa:

Critical pair: acccccccccaa=aaac.

Flip LHS and RHS.

Defines rule #12.

Overlap of [6] ccccac=ca with [14] cacac=cccccccaa:

Critical pair: ccccccccccaa=caac.

Flip LHS and RHS.

Defines rule #4.