Certificate for #4801 ⟨a, b | abaabbab=aba⟩

Completion settings:

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

Axiom: abaabbab=aba.

Referenced by [3].

Axiom: abaa=c.

Referenced by [3], [4].

Overlap of [1] abaabbab=aba with [2] abaa=c:

Critical pair: cbbab=aba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5], [6], [7], [9].

Overlap of [2] abaa=c with [3] aba=cbbab:

Critical pair: cbbaba=c.

Reduce LHS:

Defines rule #3.

Referenced by [6], [8], [9].

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

Critical pair: abcbbab=cbbabba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

Overlap of [4] cbbcbbab=c with [3] aba=cbbab:

Critical pair: cbbcbbcbbab=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

Overlap of [6] ca=cbbc with [3] aba=cbbab:

Critical pair: ccbbab=cbbcba.

Flip LHS and RHS.

Defines rule #2.

Overlap of [4] cbbcbbab=c with [5] cbbabba=abcbbab:

Critical pair: cbbabcbbab=cba.

Defines rule #8.

Referenced by [9], [10].

Overlap of [8] cbbabcbbab=cba with [3] aba=cbbab:

Critical pair: cbbabcbbcbbab=cbaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [8] cbbabcbbab=cba with [8] cbbabcbbab=cba:

Critical pair: cbbabcba=cbacbbab.

Defines rule #7.