Certificate for #6267 ⟨a, b, c | aa=1, bcbbbc=1⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #1.

Axiom: bcbbbc=1.

Referenced by [4].

Axiom: bc=d.

Defines rule #7.

Referenced by [4], [7], [10], [11], [16], [19].

Overlap of [2] bcbbbc=1 with [3] bc=d:

Critical pair: dbbbc=1.

Reduce LHS:

Referenced by [5], [6].

Overlap of [4] dbbd=1 with [4] dbbd=1:

Critical pair: dbb=bbd.

Flip LHS and RHS.

Defines rule #12.

Referenced by [6], [8], [12].

Overlap of [4] dbbd=1 with [5] bbd=dbb:

Critical pair: ddbb=1.

Defines rule #11.

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

Overlap of [6] ddbb=1 with [3] bc=d:

Critical pair: ddbd=c.

Defines rule #4.

Referenced by [8], [9], [10], [13], [14], [15], [18], [19], [20], [21].

Overlap of [6] ddbb=1 with [5] bbd=dbb:

Critical pair: ddbdbb=bd.

Reduce LHS:

Defines rule #14.

Referenced by [11], [12], [14].

Overlap of [7] ddbd=c with [6] ddbb=1:

Critical pair: ddb=cdbb.

Flip LHS and RHS.

Referenced by [12].

Overlap of [7] ddbd=c with [7] ddbd=c:

Critical pair: ddbc=cdbd.

Reduce LHS:

Flip LHS and RHS.

Referenced by [18].

Overlap of [8] cbb=bd with [3] bc=d:

Critical pair: cbd=bdc.

Defines rule #10.

Referenced by [14].

Overlap of [8] cbb=bd with [5] bbd=dbb:

Critical pair: cdbb=bdd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [13], [14], [17], [19], [20], [21].

Overlap of [7] ddbd=c with [12] bdd=ddb:

Critical pair: ddddb=cd.

Defines rule #3.

Referenced by [19], [20].

Overlap of [8] cbb=bd with [12] bdd=ddb:

Critical pair: cbddb=bddd.

Reduce LHS:

Reduce RHS:

Referenced by [15], [16], [17].

Overlap of [7] ddbd=c with [14] bdcdb=c:

Critical pair: ddc=ccdb.

Flip LHS and RHS.

Referenced by [17].

Overlap of [14] bdcdb=c with [3] bc=d:

Critical pair: bdcdd=cc.

Referenced by [17].

Overlap of [14] bdcdb=c with [12] bdd=ddb:

Critical pair: bdcdddb=cdd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [18], [20].

Overlap of [17] cdd=ddc with [7] ddbd=c:

Critical pair: cdc=ddcdbd.

Reduce RHS:

Defines rule #6.

Overlap of [12] bdd=ddb with [13] ddddb=cd:

Critical pair: bcd=ddbddb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #9.

Overlap of [12] bdd=ddb with [13] ddddb=cd:

Critical pair: bdcd=ddbdddb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [21].

Overlap of [12] bdd=ddb with [20] ddcb=bdcd:

Critical pair: bdbdcd=ddbdcb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #13.