Certificate for #1115 ⟨a, b | abaaba=bab⟩

Completion settings:

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

Axiom: abaaba=bab.

Referenced by [4].

Axiom: aba=c.

Defines rule #13.

Referenced by [4], [5], [6], [12].

Axiom: acc=d.

Defines rule #2.

Referenced by [5], [7], [11], [13], [15].

Overlap of [1] abaaba=bab with [2] aba=c:

Critical pair: caba=bab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

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

Overlap of [2] aba=c with [4] bab=cc:

Critical pair: acc=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8], [9], [10], [12], [14].

Overlap of [4] bab=cc with [2] aba=c:

Critical pair: bc=cca.

Defines rule #4.

Referenced by [9], [10].

Overlap of [3] acc=d with [5] cb=d:

Critical pair: acd=db.

Defines rule #7.

Overlap of [5] cb=d with [4] bab=cc:

Critical pair: ccc=dab.

Flip LHS and RHS.

Defines rule #11.

Overlap of [5] cb=d with [6] bc=cca:

Critical pair: ccca=dc.

Defines rule #3.

Referenced by [11], [12], [13].

Overlap of [6] bc=cca with [5] cb=d:

Critical pair: bd=ccab.

Defines rule #8.

Overlap of [3] acc=d with [9] ccca=dc:

Critical pair: adc=dca.

Defines rule #6.

Referenced by [14].

Overlap of [9] ccca=dc with [2] aba=c:

Critical pair: cccc=dcba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [15].

Overlap of [9] ccca=dc with [3] acc=d:

Critical pair: cccd=dccc.

Defines rule #1.

Overlap of [11] adc=dca with [5] cb=d:

Critical pair: add=dcab.

Defines rule #12.

Overlap of [12] dda=cccc with [3] acc=d:

Critical pair: ddd=cccccc.

Defines rule #9.