Certificate for #72 ⟨a, b | abbaab=1⟩

Completion settings:

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

Axiom: abbaab=1.

Referenced by [4].

Axiom: ab=c.

Defines rule #7.

Referenced by [4], [6], [8].

Axiom: bac=d.

Referenced by [4], [5], [7].

Overlap of [1] abbaab=1 with [2] ab=c:

Critical pair: cbaab=1.

Reduce LHS:

Defines rule #1.

Referenced by [5], [9], [13], [14], [15].

Overlap of [3] bac=d with [4] cd=1:

Critical pair: ba=dd.

Defines rule #8.

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

Overlap of [2] ab=c with [5] ba=dd:

Critical pair: add=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [10].

Overlap of [3] bac=d with [5] ba=dd:

Critical pair: ddc=d.

Referenced by [9], [11].

Overlap of [5] ba=dd with [2] ab=c:

Critical pair: bc=ddb.

Flip LHS and RHS.

Referenced by [13].

Overlap of [4] cd=1 with [7] ddc=d:

Critical pair: cd=dc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [12].

Overlap of [9] dc=1 with [6] ca=add:

Critical pair: dadd=a.

Referenced by [11].

Overlap of [10] dadd=a with [7] ddc=d:

Critical pair: dad=ac.

Referenced by [12].

Overlap of [11] dad=ac with [9] dc=1:

Critical pair: da=acc.

Defines rule #4.

Overlap of [4] cd=1 with [8] ddb=bc:

Critical pair: cbc=db.

Flip LHS and RHS.

Defines rule #5.

Referenced by [14].

Overlap of [4] cd=1 with [13] db=cbc:

Critical pair: ccbc=b.

Referenced by [15].

Overlap of [14] ccbc=b with [4] cd=1:

Critical pair: ccb=bd.

Defines rule #6.