Certificate for #4440 ⟨a, b | aaaababa=aab⟩

Completion settings:

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

Axiom: aaaababa=aab.

Referenced by [3].

Axiom: ababa=c.

Defines rule #10.

Referenced by [3], [4], [5], [6], [7].

Overlap of [1] aaaababa=aab with [2] ababa=c:

Critical pair: aaac=aab.

Flip LHS and RHS.

Defines rule #9.

Referenced by [5], [6].

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

Critical pair: abc=cba.

Defines rule #5.

Overlap of [2] ababa=c with [3] aab=aaac:

Critical pair: ababaaac=cab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [6], [7], [8], [10].

Overlap of [3] aab=aaac with [2] ababa=c:

Critical pair: ac=aaacaba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [10], [11].

Overlap of [5] cab=caac with [2] ababa=c:

Critical pair: cc=caacaba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [8], [9], [11].

Overlap of [7] caacaaca=cc with [5] cab=caac:

Critical pair: caacaacaac=ccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] caacaaca=cc with [7] caacaaca=cc:

Critical pair: caacc=ccaca.

Defines rule #1.

Overlap of [6] aaacaaca=ac with [5] cab=caac:

Critical pair: aaacaacaac=acb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] aaacaaca=ac with [7] caacaaca=cc:

Critical pair: aaacc=acaca.

Defines rule #2.