Certificate for #3055 ⟨a, b | aababaaabab=1⟩

Completion settings:

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

Axiom: aababaaabab=1.

Referenced by [3].

Axiom: abab=c.

Referenced by [3], [5], [9].

Overlap of [1] aababaaabab=1 with [2] abab=c:

Critical pair: acaaabab=1.

Reduce LHS:

Referenced by [4], [6], [8], [11].

Overlap of [3] acaac=1 with [3] acaac=1:

Critical pair: aca=aac.

Referenced by [6], [7], [11], [12].

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

Critical pair: abc=cab.

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] acaac=1 with [4] aca=aac:

Critical pair: aacac=1.

Reduce LHS:

Defines rule #2.

Referenced by [7], [15].

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

Critical pair: acaac=aacca.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [3] acaac=1 with [7] aacca=1:

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [10], [12], [13], [14], [15].

Overlap of [7] aacca=1 with [2] abab=c:

Critical pair: aaccc=bab.

Flip LHS and RHS.

Defines rule #5.

Simplify [5] cab=abc.

Reduce LHS:

Referenced by [11], [12].

Overlap of [3] acaac=1 with [10] acb=abc:

Critical pair: acaabc=b.

Reduce LHS:

Referenced by [12], [13].

Overlap of [8] ca=ac with [11] aaabcc=b:

Critical pair: cb=acaabcc.

Reduce RHS:

Defines rule #3.

Overlap of [11] aaabcc=b with [8] ca=ac:

Critical pair: aaabcac=ba.

Reduce LHS:

Referenced by [14].

Overlap of [13] aaabacc=ba with [8] ca=ac:

Critical pair: aaabacac=baa.

Reduce LHS:

Referenced by [15].

Overlap of [14] aaabaacc=baa with [8] ca=ac:

Critical pair: aaabaacac=baaa.

Reduce LHS:

Defines rule #4.