Certificate for #5707 ⟨a, b, c | aa=b, acb=ca⟩

Completion settings:

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

Axiom: aa=b.

Defines rule #7.

Referenced by [5], [6], [7], [8], [9].

Axiom: acb=ca.

Referenced by [4].

Axiom: cb=d.

Defines rule #5.

Referenced by [4], [6].

Overlap of [2] acb=ca with [3] cb=d:

Critical pair: ad=ca.

Flip LHS and RHS.

Referenced by [6], [8], [12].

Overlap of [1] aa=b with [1] aa=b:

Critical pair: ab=ba.

Defines rule #3.

Overlap of [4] ca=ad with [1] aa=b:

Critical pair: cb=ada.

Reduce LHS:

Flip LHS and RHS.

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

Overlap of [1] aa=b with [6] ada=d:

Critical pair: ad=bda.

Defines rule #4.

Referenced by [8], [9], [12].

Overlap of [4] ca=ad with [6] ada=d:

Critical pair: cd=adda.

Reduce RHS:

Referenced by [11].

Overlap of [6] ada=d with [7] ad=bda:

Critical pair: bdaa=d.

Reduce LHS:

Defines rule #1.

Referenced by [10], [11].

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

Critical pair: bdd=ddb.

Defines rule #2.

Simplify [8] cd=bdbdb.

Reduce RHS:

Defines rule #6.

Simplify [4] ca=ad.

Reduce RHS:

Defines rule #8.