Certificate for #1997 ⟨a, b, c | abc=bb, cba=1⟩

Completion settings:

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

Axiom: abc=bb.

Referenced by [6], [7], [8], [9].

Axiom: cba=1.

Defines rule #8.

Referenced by [4], [5], [6], [8], [20], [24], [27].

Axiom: ac=d.

Defines rule #7.

Referenced by [4], [5], [26].

Overlap of [2] cba=1 with [3] ac=d:

Critical pair: cbd=c.

Referenced by [7].

Overlap of [3] ac=d with [2] cba=1:

Critical pair: a=dba.

Flip LHS and RHS.

Referenced by [9].

Overlap of [1] abc=bb with [2] cba=1:

Critical pair: ab=bbba.

Flip LHS and RHS.

Referenced by [12], [17], [19].

Overlap of [1] abc=bb with [4] cbd=c:

Critical pair: abc=bbbd.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10], [11], [14], [17], [18].

Overlap of [2] cba=1 with [1] abc=bb:

Critical pair: cbbb=bc.

Flip LHS and RHS.

Defines rule #5.

Overlap of [5] dba=a with [1] abc=bb:

Critical pair: dbbb=abc.

Reduce RHS:

Referenced by [10], [11].

Overlap of [9] dbbb=bb with [7] bbbd=bb:

Critical pair: dbb=bbd.

Referenced by [11], [12], [13], [15], [21].

Overlap of [9] dbbb=bb with [7] bbbd=bb:

Critical pair: dbbb=bbbd.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [10] dbb=bbd with [6] bbba=ab:

Critical pair: dab=bbdba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [13], [14], [19].

Overlap of [10] dbb=bbd with [12] bba=dab:

Critical pair: ddab=bbda.

Flip LHS and RHS.

Referenced by [14], [15], [22].

Overlap of [7] bbbd=bb with [13] bbda=ddab:

Critical pair: bddab=bba.

Reduce RHS:

Referenced by [16].

Overlap of [10] dbb=bbd with [13] bbda=ddab:

Critical pair: dddab=bbdda.

Flip LHS and RHS.

Referenced by [16], [17].

Overlap of [15] bbdda=dddab with [14] bddab=dab:

Critical pair: bdab=dddabb.

Flip LHS and RHS.

Referenced by [17], [18].

Overlap of [7] bbbd=bb with [16] dddabb=bdab:

Critical pair: bbbbdab=bbddabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [18].

Overlap of [16] dddabb=bdab with [7] bbbd=bb:

Critical pair: dddabb=bdabbd.

Reduce LHS:

Reduce RHS:

Referenced by [19].

Overlap of [6] bbba=ab with [12] bba=dab:

Critical pair: bdab=ab.

Reduce LHS:

Referenced by [20], [23].

Overlap of [2] cba=1 with [19] abbd=ab:

Critical pair: cbab=bbd.

Reduce LHS:

Flip LHS and RHS.

Referenced by [21], [22].

Overlap of [10] dbb=bbd with [20] bbd=b:

Critical pair: db=bbdd.

Reduce RHS:

Referenced by [28].

Overlap of [13] bbda=ddab with [20] bbd=b:

Critical pair: ba=ddab.

Flip LHS and RHS.

Referenced by [23], [25].

Overlap of [22] ddab=ba with [19] abbd=ab:

Critical pair: ddab=babd.

Reduce LHS:

Flip LHS and RHS.

Referenced by [24].

Overlap of [2] cba=1 with [23] babd=ba:

Critical pair: cba=bd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [25], [28].

Overlap of [22] ddab=ba with [24] bd=1:

Critical pair: dda=bad.

Defines rule #4.

Referenced by [26].

Overlap of [25] dda=bad with [3] ac=d:

Critical pair: ddd=badc.

Flip LHS and RHS.

Referenced by [27].

Overlap of [2] cba=1 with [26] badc=ddd:

Critical pair: cddd=dc.

Flip LHS and RHS.

Defines rule #6.

Simplify [21] db=bd.

Reduce RHS:

Defines rule #2.