Certificate for #2927 ⟨a, b | aaababaaaab=1⟩

Completion settings:

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

Axiom: aaababaaaab=1.

Referenced by [4], [5], [6], [9].

Axiom: aabaaab=c.

Referenced by [3], [5], [6], [7], [9], [10], [11].

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

Critical pair: aabac=caaab.

Referenced by [5].

Overlap of [1] aaababaaaab=1 with [1] aaababaaaab=1:

Critical pair: aaababa=abaaaab.

Referenced by [5], [9].

Overlap of [1] aaababaaaab=1 with [2] aabaaab=c:

Critical pair: aaababaac=aaab.

Reduce LHS:

Referenced by [7].

Overlap of [2] aabaaab=c with [1] aaababaaaab=1:

Critical pair: aab=cabaaaab.

Flip LHS and RHS.

Referenced by [8].

Overlap of [5] abaacaaab=aaab with [2] aabaaab=c:

Critical pair: abaacac=aaabaaab.

Reduce RHS:

Referenced by [8].

Overlap of [6] cabaaaab=aab with [7] abaacac=ac:

Critical pair: cabaaaac=aabaacac.

Reduce RHS:

Referenced by [15].

Overlap of [1] aaababaaaab=1 with [4] aaababa=abaaaab:

Critical pair: abaaaabaaab=1.

Reduce LHS:

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

Overlap of [2] aabaaab=c with [9] abaac=1:

Critical pair: aabaa=caac.

Referenced by [11], [12], [16].

Overlap of [2] aabaaab=c with [10] aabaa=caac:

Critical pair: caacab=c.

Referenced by [14].

Overlap of [10] aabaa=caac with [9] abaac=1:

Critical pair: a=caacc.

Flip LHS and RHS.

Defines rule #2.

Referenced by [13].

Overlap of [12] caacc=a with [12] caacc=a:

Critical pair: caaca=aaacc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [17], [18].

Overlap of [9] abaac=1 with [11] caacab=c:

Critical pair: abaac=aacab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [15], [19], [20].

Overlap of [8] cabaaaac=aac with [14] aacab=1:

Critical pair: cabaa=aacab.

Reduce RHS:

Referenced by [16], [17].

Overlap of [15] cabaa=1 with [10] aabaa=caac:

Critical pair: cabcaac=baa.

Referenced by [17].

Overlap of [15] cabaa=1 with [13] aaacc=caaca:

Critical pair: cabcaaca=acc.

Reduce LHS:

Referenced by [18], [19].

Overlap of [17] baaa=acc with [13] aaacc=caaca:

Critical pair: bcaaca=acccc.

Referenced by [20].

Overlap of [17] baaa=acc with [14] aacab=1:

Critical pair: ba=acccab.

Defines rule #4.

Overlap of [18] bcaaca=acccc with [14] aacab=1:

Critical pair: bc=accccb.

Defines rule #5.