Certificate for #21731 ⟨a, b | aaa=1, ababbbb=b⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(b) = 0; deg(a) = 1

Axiom: aaa=1.

Defines rule #5.

Referenced by [3].

Axiom: ababbbb=b.

Referenced by [3], [4], [5], [6], [9], [10], [12].

Overlap of [1] aaa=1 with [2] ababbbb=b:

Critical pair: aab=babbbb.

Defines rule #3.

Referenced by [4], [11].

Overlap of [3] aab=babbbb with [2] ababbbb=b:

Critical pair: ab=babbbbabbbb.

Flip LHS and RHS.

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

Overlap of [2] ababbbb=b with [4] babbbbabbbb=ab:

Critical pair: ababbbab=babbbbabbbb.

Reduce RHS:

Referenced by [10].

Overlap of [4] babbbbabbbb=ab with [4] babbbbabbbb=ab:

Critical pair: babbbab=ababbbb.

Reduce RHS:

Referenced by [7], [8], [13].

Overlap of [6] babbbab=b with [4] babbbbabbbb=ab:

Critical pair: babbab=bbbbabbbb.

Referenced by [9].

Overlap of [6] babbbab=b with [6] babbbab=b:

Critical pair: babbb=bbbab.

Flip LHS and RHS.

Referenced by [9], [10], [13].

Overlap of [2] ababbbb=b with [8] bbbab=babbb:

Critical pair: ababbabbb=bab.

Reduce LHS:

Referenced by [11].

Overlap of [2] ababbbb=b with [8] bbbab=babbb:

Critical pair: ababbbabbb=bbab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11].

Simplify [9] abbabbbbbbbb=bab.

Reduce LHS:

Referenced by [12], [13].

Overlap of [2] ababbbb=b with [11] babbbbbbbbbbbbb=bab:

Critical pair: abab=bbbbbbbbbb.

Defines rule #4.

Referenced by [13].

Overlap of [11] babbbbbbbbbbbbb=bab with [8] bbbab=babbb:

Critical pair: babbbbbbbbbbbbbabbb=babbbab.

Reduce LHS:

Reduce RHS:

Defines rule #1.