Certificate for #4795 ⟨a, b | abaababa=baa⟩

Completion settings:

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

Axiom: abaababa=baa.

Referenced by [4].

Axiom: aba=c.

Defines rule #8.

Referenced by [4], [5], [6], [7], [8].

Axiom: ccb=d.

Referenced by [4], [9], [13], [15].

Overlap of [1] abaababa=baa with [2] aba=c:

Critical pair: cababa=baa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [6], [7], [10], [12].

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

Critical pair: abc=cba.

Defines rule #12.

Overlap of [2] aba=c with [4] baa=da:

Critical pair: ada=ca.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8], [11].

Overlap of [4] baa=da with [2] aba=c:

Critical pair: bac=daba.

Reduce RHS:

Defines rule #13.

Referenced by [15].

Overlap of [6] ca=ada with [2] aba=c:

Critical pair: cc=adaba.

Reduce RHS:

Defines rule #6.

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

Overlap of [3] ccb=d with [8] cc=adc:

Critical pair: adcb=d.

Defines rule #7.

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

Overlap of [4] baa=da with [9] adcb=d:

Critical pair: bad=dadcb.

Reduce RHS:

Defines rule #11.

Referenced by [13], [14].

Overlap of [6] ca=ada with [9] adcb=d:

Critical pair: cd=adadcb.

Reduce RHS:

Defines rule #5.

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

Overlap of [9] adcb=d with [4] baa=da:

Critical pair: adcda=daa.

Reduce LHS:

Defines rule #1.

Overlap of [3] ccb=d with [10] bad=dd:

Critical pair: ccdd=dad.

Reduce LHS:

Defines rule #2.

Overlap of [10] bad=dd with [9] adcb=d:

Critical pair: bd=ddcb.

Defines rule #9.

Overlap of [3] ccb=d with [7] bac=dc:

Critical pair: ccdc=dac.

Reduce LHS:

Defines rule #3.