Certificate for #14591 ⟨a, b | aaba=a, bbabb=a⟩

Completion settings:

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

Axiom: aaba=a.

Referenced by [9], [15].

Axiom: bbabb=a.

Referenced by [5].

Axiom: bb=c.

Defines rule #8.

Referenced by [5], [6], [10], [13].

Axiom: abab=d.

Referenced by [9], [10], [11], [12].

Overlap of [2] bbabb=a with [3] bb=c:

Critical pair: cabb=a.

Reduce LHS:

Defines rule #15.

Referenced by [7], [8], [18], [20].

Overlap of [3] bb=c with [3] bb=c:

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #7.

Referenced by [8], [14].

Overlap of [5] cac=a with [5] cac=a:

Critical pair: caa=aac.

Flip LHS and RHS.

Defines rule #12.

Referenced by [14].

Overlap of [5] cac=a with [6] cb=bc:

Critical pair: cabc=ab.

Referenced by [16].

Overlap of [1] aaba=a with [4] abab=d:

Critical pair: ad=ab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [10], [11], [12], [13], [14], [15], [16], [17].

Overlap of [4] abab=d with [3] bb=c:

Critical pair: abac=db.

Reduce LHS:

Defines rule #13.

Referenced by [18], [19], [20], [22].

Overlap of [4] abab=d with [4] abab=d:

Critical pair: abd=dab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [4] abab=d with [9] ab=ad:

Critical pair: adab=d.

Reduce LHS:

Defines rule #4.

Referenced by [21], [22], [23].

Overlap of [9] ab=ad with [3] bb=c:

Critical pair: ac=adb.

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] aac=caa with [6] cb=bc:

Critical pair: aabc=caab.

Reduce LHS:

Reduce RHS:

Defines rule #14.

Overlap of [1] aaba=a with [9] ab=ad:

Critical pair: aada=a.

Defines rule #9.

Simplify [8] cabc=ab.

Reduce RHS:

Referenced by [17].

Overlap of [16] cabc=ad with [9] ab=ad:

Critical pair: cadc=ad.

Defines rule #16.

Referenced by [19], [20], [21].

Overlap of [10] adac=db with [5] cac=a:

Critical pair: adaa=dbac.

Flip LHS and RHS.

Defines rule #17.

Overlap of [10] adac=db with [17] cadc=ad:

Critical pair: adaad=dbadc.

Flip LHS and RHS.

Defines rule #18.

Overlap of [17] cadc=ad with [5] cac=a:

Critical pair: cada=adac.

Reduce RHS:

Defines rule #10.

Referenced by [21], [22], [23].

Overlap of [17] cadc=ad with [17] cadc=ad:

Critical pair: cadad=adadc.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [23].

Overlap of [10] adac=db with [20] cada=db:

Critical pair: adadb=dbada.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Overlap of [20] cada=db with [12] adad=d:

Critical pair: cd=dbd.

Reduce RHS:

Defines rule #2.