Certificate for #3563 ⟨a, b | aabaababaa=a⟩

Completion settings:

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

Axiom: aabaababaa=a.

Referenced by [3].

Axiom: aba=c.

Defines rule #3.

Referenced by [3], [4], [5], [6], [7], [11], [17], [18], [20], [22], [23].

Overlap of [1] aabaababaa=a with [2] aba=c:

Critical pair: acababaa=a.

Reduce LHS:

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

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

Critical pair: abc=cba.

Defines rule #4.

Referenced by [11], [17].

Overlap of [2] aba=c with [3] accbaa=a:

Critical pair: aba=cccbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [14].

Overlap of [3] accbaa=a with [2] aba=c:

Critical pair: accbac=aba.

Reduce RHS:

Referenced by [8], [9], [12], [15].

Overlap of [5] cccbaa=c with [2] aba=c:

Critical pair: cccbac=cba.

Referenced by [10].

Overlap of [6] accbac=c with [3] accbaa=a:

Critical pair: accba=ccbaa.

Flip LHS and RHS.

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

Overlap of [6] accbac=c with [6] accbac=c:

Critical pair: accbc=ccbac.

Flip LHS and RHS.

Referenced by [10], [15], [22].

Simplify [7] cccbac=cba.

Reduce LHS:

Referenced by [22].

Overlap of [4] abc=cba with [8] ccbaa=accba:

Critical pair: abaccba=cbacbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [6] accbac=c with [11] cbacbaa=cccba:

Critical pair: accccba=cbaa.

Flip LHS and RHS.

Defines rule #5.

Referenced by [16], [17], [18], [21], [23].

Overlap of [3] accbaa=a with [8] ccbaa=accba:

Critical pair: aaccba=a.

Referenced by [22].

Overlap of [5] cccbaa=c with [8] ccbaa=accba:

Critical pair: caccba=c.

Referenced by [21].

Overlap of [6] accbac=c with [9] ccbac=accbc:

Critical pair: aaccbc=c.

Referenced by [19].

Overlap of [8] ccbaa=accba with [12] cbaa=accccba:

Critical pair: caccccba=accba.

Referenced by [21].

Overlap of [4] abc=cba with [12] cbaa=accccba:

Critical pair: abaccccba=cbabaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [19], [20].

Overlap of [12] cbaa=accccba with [2] aba=c:

Critical pair: cbac=accccbaba.

Reduce RHS:

Defines rule #7.

Overlap of [15] aaccbc=c with [17] cbca=cccccba:

Critical pair: aaccccccba=ca.

Referenced by [21].

Overlap of [17] cbca=cccccba with [2] aba=c:

Critical pair: cbcc=cccccbaba.

Reduce RHS:

Defines rule #8.

Overlap of [19] aaccccccba=ca with [12] cbaa=accccba:

Critical pair: aacccccaccccba=caa.

Reduce LHS:

Referenced by [22], [23].

Overlap of [21] aacccc=caa with [9] ccbac=accbc:

Critical pair: aaccaccbc=caabac.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [23].

Overlap of [21] aacccc=caa with [12] cbaa=accccba:

Critical pair: aacccaccccba=caabaa.

Reduce LHS:

Reduce RHS:

Defines rule #1.