Certificate for #3193 ⟨a, b | abaaabbaaab=1⟩

Completion settings:

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

Axiom: abaaabbaaab=1.

Referenced by [3].

Axiom: baaab=c.

Referenced by [3], [4], [6], [9].

Overlap of [1] abaaabbaaab=1 with [2] baaab=c:

Critical pair: acbaaab=1.

Reduce LHS:

Defines rule #2.

Referenced by [5], [7], [8], [10], [11], [13], [14], [16], [17], [18], [19], [20].

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

Critical pair: baaac=caaab.

Referenced by [5], [12].

Overlap of [4] baaac=caaab with [3] acc=1:

Critical pair: baa=caaabc.

Referenced by [6], [7], [12], [15], [17], [21].

Overlap of [2] baaab=c with [5] baa=caaabc:

Critical pair: caaabcab=c.

Referenced by [8], [12].

Overlap of [5] baa=caaabc with [3] acc=1:

Critical pair: ba=caaabccc.

Flip LHS and RHS.

Referenced by [14].

Overlap of [3] acc=1 with [6] caaabcab=c:

Critical pair: acc=aaabcab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [2] baaab=c with [8] aaabcab=1:

Critical pair: b=ccab.

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] acc=1 with [9] ccab=b:

Critical pair: acb=cab.

Flip LHS and RHS.

Referenced by [11], [15], [17].

Overlap of [3] acc=1 with [10] cab=acb:

Critical pair: acacb=ab.

Referenced by [12].

Overlap of [4] baaac=caaab with [11] acacb=ab:

Critical pair: baaab=caaabacb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [3] acc=1 with [12] caaabacb=c:

Critical pair: acc=aaabacb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15], [17].

Overlap of [3] acc=1 with [7] caaabccc=ba:

Critical pair: acba=aaabccc.

Flip LHS and RHS.

Referenced by [15].

Overlap of [5] baa=caaabc with [14] aaabccc=acba:

Critical pair: bacba=caaabcabccc.

Reduce RHS:

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

Overlap of [15] bacba=cccc with [3] acc=1:

Critical pair: bacb=cccccc.

Defines rule #5.

Overlap of [15] bacba=cccc with [5] baa=caaabc:

Critical pair: baccaaabc=cccca.

Reduce LHS:

Flip LHS and RHS.

Referenced by [19].

Overlap of [15] bacba=cccc with [15] bacba=cccc:

Critical pair: baccccc=cccccba.

Reduce LHS:

Defines rule #4.

Overlap of [3] acc=1 with [17] cccca=cc:

Critical pair: acc=cca.

Reduce LHS:

Flip LHS and RHS.

Referenced by [20].

Overlap of [3] acc=1 with [19] cca=1:

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [21].

Simplify [5] baa=caaabc.

Reduce RHS:

Defines rule #3.