Certificate for #2904 ⟨a, b, c | aab=a, cbc=a⟩

Completion settings:

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

Axiom: aab=a.

Referenced by [6].

Axiom: cbc=a.

Referenced by [4], [5], [7], [9], [12], [16].

Axiom: ac=d.

Referenced by [5], [7].

Overlap of [2] cbc=a with [2] cbc=a:

Critical pair: cba=abc.

Flip LHS and RHS.

Referenced by [11].

Overlap of [3] ac=d with [2] cbc=a:

Critical pair: aa=dbc.

Referenced by [6], [8].

Simplify [1] aab=a.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [8], [9], [11], [12], [16].

Overlap of [3] ac=d with [6] a=dbcb:

Critical pair: dbcbc=d.

Reduce LHS:

Referenced by [9], [12], [13], [14], [15].

Simplify [5] aa=dbc.

Reduce LHS:

Referenced by [9], [10], [14].

Overlap of [8] dbcbdbcb=dbc with [2] cbc=a:

Critical pair: dbcbdba=dbcc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [8] dbcbdbcb=dbc with [8] dbcbdbcb=dbc:

Critical pair: dbcbdbc=dbcdbcb.

Defines rule #9.

Referenced by [13].

Simplify [4] abc=cba.

Reduce LHS:

Reduce RHS:

Defines rule #7.

Referenced by [13].

Overlap of [7] dbdbcb=d with [2] cbc=a:

Critical pair: dbdba=dc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [7] dbdbcb=d with [11] dbcbbc=cbdbcb:

Critical pair: dbcbdbcb=dbc.

Reduce LHS:

Defines rule #8.

Overlap of [7] dbdbcb=d with [8] dbcbdbcb=dbc:

Critical pair: dbdbc=ddbcb.

Defines rule #3.

Referenced by [15].

Overlap of [7] dbdbcb=d with [14] dbdbc=ddbcb:

Critical pair: ddbcbb=d.

Defines rule #2.

Simplify [2] cbc=a.

Reduce RHS:

Defines rule #5.