Certificate for #2179 ⟨a, b, c | aabb=1, bacc=1⟩

Completion settings:

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

Axiom: aabb=1.

Referenced by [4].

Axiom: bacc=1.

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

Axiom: aa=d.

Defines rule #5.

Referenced by [4], [5], [8], [18].

Overlap of [1] aabb=1 with [3] aa=d:

Critical pair: dbb=1.

Defines rule #2.

Referenced by [6], [7], [14], [18].

Overlap of [3] aa=d with [3] aa=d:

Critical pair: ad=da.

Defines rule #3.

Referenced by [6].

Overlap of [5] ad=da with [4] dbb=1:

Critical pair: a=dabb.

Flip LHS and RHS.

Referenced by [8], [11].

Overlap of [4] dbb=1 with [2] bacc=1:

Critical pair: db=acc.

Flip LHS and RHS.

Referenced by [9], [15].

Overlap of [6] dabb=a with [2] bacc=1:

Critical pair: dab=aacc.

Reduce RHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [2] bacc=1 with [7] acc=db:

Critical pair: bdb=1.

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

Overlap of [9] bdb=1 with [9] bdb=1:

Critical pair: bd=db.

Defines rule #1.

Referenced by [11], [12], [14], [18].

Overlap of [10] bd=db with [6] dabb=a:

Critical pair: ba=dbabb.

Flip LHS and RHS.

Referenced by [13].

Overlap of [10] bd=db with [8] dcc=dab:

Critical pair: bdab=dbcc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [9] bdb=1 with [11] dbabb=ba:

Critical pair: bba=abb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [17].

Overlap of [9] bdb=1 with [12] dbcc=dbab:

Critical pair: bdbab=cc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [15], [16].

Overlap of [7] acc=db with [14] cc=ab:

Critical pair: acab=dbc.

Referenced by [17].

Overlap of [14] cc=ab with [14] cc=ab:

Critical pair: cab=abc.

Flip LHS and RHS.

Defines rule #7.

Overlap of [15] acab=dbc with [13] abb=bba:

Critical pair: acbba=dbcb.

Referenced by [18].

Overlap of [17] acbba=dbcb with [3] aa=d:

Critical pair: acbbd=dbcba.

Reduce LHS:

Defines rule #6.