Certificate for #1748 ⟨a, b | abaaaaaab=b⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b

Axiom: abaaaaaab=b.

Referenced by [2], [3], [4], [5], [6], [7], [8].

Overlap of [1] abaaaaaab=b with [1] abaaaaaab=b:

Critical pair: abaaaaab=baaaaaab.

Flip LHS and RHS.

Referenced by [3], [8], [9].

Overlap of [2] baaaaaab=abaaaaab with [1] abaaaaaab=b:

Critical pair: baaaaab=abaaaaabaaaaaab.

Reduce RHS:

Referenced by [4], [8], [9], [10].

Overlap of [3] baaaaab=abaaaab with [1] abaaaaaab=b:

Critical pair: baaaab=abaaaabaaaaaab.

Reduce RHS:

Referenced by [5], [8], [9], [10], [11].

Overlap of [4] baaaab=abaaab with [1] abaaaaaab=b:

Critical pair: baaab=abaaabaaaaaab.

Reduce RHS:

Referenced by [6], [8], [9], [10], [11], [12].

Overlap of [5] baaab=abaab with [1] abaaaaaab=b:

Critical pair: baab=abaabaaaaaab.

Reduce RHS:

Referenced by [7], [8], [9], [10], [11], [12], [13].

Overlap of [6] baab=abab with [1] abaaaaaab=b:

Critical pair: bab=ababaaaaaab.

Reduce RHS:

Defines rule #1.

Referenced by [8], [9], [10], [11], [12], [13].

Overlap of [1] abaaaaaab=b with [2] baaaaaab=abaaaaab:

Critical pair: aabaaaaab=b.

Reduce LHS:

Defines rule #7.

Simplify [2] baaaaaab=abaaaaab.

Reduce RHS:

Defines rule #6.

Simplify [3] baaaaab=abaaaab.

Reduce RHS:

Defines rule #5.

Simplify [4] baaaab=abaaab.

Reduce RHS:

Defines rule #4.

Simplify [5] baaab=abaab.

Reduce RHS:

Defines rule #3.

Simplify [6] baab=abab.

Reduce RHS:

Defines rule #2.