Certificate for #3607 ⟨a, b | aababbabaa=a⟩

Completion settings:

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

Axiom: aababbabaa=a.

Referenced by [3].

Axiom: ab=c.

Defines rule #1.

Referenced by [3], [4], [12].

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

Critical pair: acabbabaa=a.

Reduce LHS:

Referenced by [4], [5], [7], [11].

Overlap of [3] accbcaa=a with [2] ab=c:

Critical pair: accbcac=ab.

Reduce RHS:

Referenced by [5], [6], [8], [10], [13].

Overlap of [4] accbcac=c with [3] accbcaa=a:

Critical pair: accbca=ccbcaa.

Defines rule #4.

Referenced by [7], [8], [13].

Overlap of [4] accbcac=c with [4] accbcac=c:

Critical pair: accbcc=ccbcac.

Defines rule #7.

Referenced by [9].

Overlap of [3] accbcaa=a with [5] accbca=ccbcaa:

Critical pair: ccbcaaa=a.

Referenced by [9], [13].

Overlap of [4] accbcac=c with [5] accbca=ccbcaa:

Critical pair: ccbcaac=c.

Referenced by [14].

Overlap of [6] accbcc=ccbcac with [7] ccbcaaa=a:

Critical pair: accba=ccbcacbcaaa.

Flip LHS and RHS.

Referenced by [10].

Overlap of [4] accbcac=c with [9] ccbcacbcaaa=accba:

Critical pair: aaccba=cbcaaa.

Flip LHS and RHS.

Defines rule #2.

Referenced by [11], [12].

Overlap of [3] accbcaa=a with [10] cbcaaa=aaccba:

Critical pair: acaaccba=aa.

Referenced by [13].

Overlap of [10] cbcaaa=aaccba with [2] ab=c:

Critical pair: cbcaac=aaccbab.

Reduce RHS:

Defines rule #5.

Referenced by [14].

Overlap of [4] accbcac=c with [11] acaaccba=aa:

Critical pair: accbcaa=caaccba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [8] ccbcaac=c with [12] cbcaac=aaccbc:

Critical pair: caaccbc=c.

Defines rule #6.