Certificate for #3783 ⟨a, b | ababbabaab=a⟩

Completion settings:

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

Axiom: ababbabaab=a.

Referenced by [4].

Axiom: ab=c.

Referenced by [4], [5].

Axiom: cbcaa=d.

Referenced by [4], [6].

Overlap of [1] ababbabaab=a with [2] ab=c:

Critical pair: cabbabaab=a.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [5], [6].

Overlap of [2] ab=c with [4] a=cdb:

Critical pair: cdbb=c.

Defines rule #2.

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

Overlap of [3] cbcaa=d with [4] a=cdb:

Critical pair: cbccdba=d.

Reduce LHS:

Referenced by [7], [8], [10], [14].

Overlap of [6] cbccdbcdb=d with [5] cdbb=c:

Critical pair: cbccdbc=db.

Defines rule #4.

Referenced by [8], [9], [10], [13].

Overlap of [6] cbccdbcdb=d with [7] cbccdbc=db:

Critical pair: dbdb=d.

Defines rule #7.

Referenced by [9], [10], [12], [13].

Overlap of [7] cbccdbc=db with [7] cbccdbc=db:

Critical pair: cbccdbdb=dbbccdbc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [11], [12], [13].

Overlap of [6] cbccdbcdb=d with [8] dbdb=d:

Critical pair: cbccdbcd=ddb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [5] cdbb=c with [9] dbbccdbc=cbccd:

Critical pair: ccbccd=cccdbc.

Flip LHS and RHS.

Defines rule #3.

Overlap of [8] dbdb=d with [9] dbbccdbc=cbccd:

Critical pair: dbcbccd=dbccdbc.

Flip LHS and RHS.

Defines rule #9.

Overlap of [9] dbbccdbc=cbccd with [7] cbccdbc=db:

Critical pair: dbbccdbdb=cbccdbccdbc.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [14].

Overlap of [6] cbccdbcdb=d with [13] dbcdbc=dbbccd:

Critical pair: cbccdbbccd=dc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.