Certificate for #5277 ⟨a, b | aabbbba=bbaa⟩

Completion settings:

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

Axiom: aabbbba=bbaa.

Referenced by [5].

Axiom: bbbb=c.

Defines rule #20.

Referenced by [5], [9], [10].

Axiom: caa=d.

Defines rule #8.

Referenced by [7], [8], [10], [14], [15].

Axiom: aca=e.

Defines rule #3.

Referenced by [5], [6], [7], [8], [11], [17], [18], [19], [20], [21].

Overlap of [1] aabbbba=bbaa with [2] bbbb=c:

Critical pair: aaca=bbaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #15.

Referenced by [10], [11], [12], [13], [14], [16].

Overlap of [4] aca=e with [4] aca=e:

Critical pair: ace=eca.

Defines rule #5.

Referenced by [12].

Overlap of [3] caa=d with [4] aca=e:

Critical pair: cae=dca.

Defines rule #10.

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

Overlap of [4] aca=e with [3] caa=d:

Critical pair: ad=ea.

Defines rule #1.

Referenced by [13], [15], [16].

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

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #13.

Referenced by [14].

Overlap of [2] bbbb=c with [5] bbaa=ae:

Critical pair: bbae=caa.

Reduce RHS:

Defines rule #17.

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

Overlap of [5] bbaa=ae with [4] aca=e:

Critical pair: bbae=aeca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [15], [16], [17], [19], [21].

Overlap of [5] bbaa=ae with [6] ace=eca:

Critical pair: bbaeca=aece.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [5] bbaa=ae with [8] ad=ea:

Critical pair: bbaea=aed.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [9] cb=bc with [5] bbaa=ae:

Critical pair: cae=bcbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [3] caa=d with [11] aeca=d:

Critical pair: cad=deca.

Reduce LHS:

Defines rule #9.

Referenced by [18], [19].

Overlap of [5] bbaa=ae with [11] aeca=d:

Critical pair: bbad=aeeca.

Reduce LHS:

Defines rule #16.

Referenced by [20], [21].

Overlap of [7] cae=dca with [11] aeca=d:

Critical pair: cd=dcaca.

Reduce RHS:

Defines rule #7.

Overlap of [15] cea=deca with [4] aca=e:

Critical pair: cee=decaca.

Reduce RHS:

Defines rule #11.

Overlap of [15] cea=deca with [11] aeca=d:

Critical pair: ced=decaeca.

Reduce RHS:

Defines rule #12.

Overlap of [16] bbea=aeeca with [4] aca=e:

Critical pair: bbee=aeecaca.

Reduce RHS:

Defines rule #18.

Overlap of [16] bbea=aeeca with [11] aeca=d:

Critical pair: bbed=aeecaeca.

Reduce RHS:

Defines rule #19.