Certificate for #1249 ⟨a, b | abaab=baba⟩

Completion settings:

• Auxiliary generators:
  1. c = abaab
  2. d = bba
• Reduction order:
  • Right-to-left recursive path with deg(a) = 0; deg(d) = deg(c) = 1, d < c; deg(b) = 2

Axiom: abaab=baba.

Flip LHS and RHS.

Referenced by [4].

Axiom: abaab=c.

Defines rule #9.

Referenced by [4], [7], [8], [9], [10].

Axiom: bba=d.

Defines rule #10.

Referenced by [6], [10], [11], [12].

Simplify [1] baba=abaab.

Reduce RHS:

Defines rule #11.

Referenced by [5], [6], [7], [8], [11], [12].

Overlap of [4] baba=c with [4] baba=c:

Critical pair: bac=cba.

Defines rule #7.

Referenced by [9].

Overlap of [3] bba=d with [4] baba=c:

Critical pair: bc=dba.

Referenced by [7], [13].

Overlap of [4] baba=c with [2] abaab=c:

Critical pair: bc=cab.

Reduce LHS:

Defines rule #3.

Referenced by [11], [13].

Overlap of [2] abaab=c with [4] baba=c:

Critical pair: abaac=caba.

Defines rule #8.

Overlap of [2] abaab=c with [2] abaab=c:

Critical pair: abac=caab.

Reduce LHS:

Defines rule #4.

Referenced by [12].

Overlap of [2] abaab=c with [3] bba=d:

Critical pair: abaad=cba.

Defines rule #5.

Overlap of [7] dba=cab with [4] baba=c:

Critical pair: dc=cabba.

Reduce RHS:

Defines rule #1.

Overlap of [9] acba=caab with [4] baba=c:

Critical pair: acc=caabba.

Reduce RHS:

Defines rule #2.

Simplify [6] bc=dba.

Reduce RHS:

Defines rule #6.