Certificate for #3800 ⟨a, b | abbaaaabba=b⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(c) = 0; deg(d) = deg(a) = 1, d < a; deg(b) = 2
• Auxiliary generators:
  1. aaabba=c
  2. cb=d

Axiom: abbaaaabba=b.

Referenced by [4].

Axiom: aaabba=c.

Referenced by [4], [5], [6], [11].

Axiom: cb=d.

Referenced by [7], [8], [9], [10], [11], [12].

Overlap of [1] abbaaaabba=b with [2] aaabba=c:

Critical pair: abbac=b.

Referenced by [6], [7], [8].

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

Critical pair: aaabbc=caabba.

Referenced by [9].

Overlap of [2] aaabba=c with [4] abbac=b:

Critical pair: aab=cc.

Referenced by [7], [9], [11].

Overlap of [6] aab=cc with [4] abbac=b:

Critical pair: ab=ccbac.

Reduce RHS:

Referenced by [8], [10].

Overlap of [4] abbac=b with [7] ab=cdac:

Critical pair: cdacbac=b.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [12].

Simplify [5] aaabbc=caabba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [10].

Overlap of [9] acdc=ccda with [3] cb=d:

Critical pair: acdd=ccdab.

Reduce RHS:

Defines rule #3.

Overlap of [2] aaabba=c with [6] aab=cc:

Critical pair: accba=c.

Reduce LHS:

Defines rule #4.

Referenced by [13], [15].

Overlap of [3] cb=d with [8] b=cdadac:

Critical pair: ccdadac=d.

Defines rule #6.

Referenced by [13], [14], [15].

Overlap of [12] ccdadac=d with [11] acda=c:

Critical pair: ccdadc=dda.

Defines rule #2.

Referenced by [15].

Overlap of [12] ccdadac=d with [12] ccdadac=d:

Critical pair: ccdadad=dcdadac.

Defines rule #7.

Overlap of [13] ccdadc=dda with [12] ccdadac=d:

Critical pair: ccdadd=ddacdadac.

Reduce RHS:

Defines rule #5.