Certificate for #1073 ⟨a, b | aababa=baa⟩

Completion settings:

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

Axiom: aababa=baa.

Referenced by [4].

Axiom: baa=c.

Defines rule #8.

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

Axiom: aba=d.

Defines rule #3.

Referenced by [5], [6], [7], [8], [11], [12], [13], [14].

Simplify [1] aababa=baa.

Reduce RHS:

Referenced by [5].

Overlap of [4] aababa=c with [3] aba=d:

Critical pair: adba=c.

Defines rule #4.

Referenced by [9], [10], [11], [12], [14].

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

Critical pair: abd=dba.

Defines rule #5.

Overlap of [2] baa=c with [3] aba=d:

Critical pair: bad=cba.

Defines rule #10.

Referenced by [12], [14].

Overlap of [3] aba=d with [2] baa=c:

Critical pair: ac=da.

Defines rule #1.

Referenced by [9].

Overlap of [2] baa=c with [5] adba=c:

Critical pair: bac=cdba.

Reduce LHS:

Defines rule #9.

Referenced by [13], [14].

Overlap of [5] adba=c with [2] baa=c:

Critical pair: adc=ca.

Defines rule #2.

Overlap of [5] adba=c with [3] aba=d:

Critical pair: adbd=cba.

Defines rule #6.

Overlap of [7] bad=cba with [5] adba=c:

Critical pair: bc=cbaba.

Reduce RHS:

Defines rule #7.

Overlap of [9] bda=cdba with [3] aba=d:

Critical pair: bdd=cdbaba.

Reduce RHS:

Defines rule #11.

Overlap of [9] bda=cdba with [5] adba=c:

Critical pair: bdc=cdbadba.

Reduce RHS:

Defines rule #12.