Certificate for #13293 ⟨a, b | aaaaa=1, ababbb=1⟩

Completion settings:

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

Axiom: aaaaa=1.

Referenced by [3], [4].

Axiom: ababbb=1.

Referenced by [3], [5], [7], [8], [11], [12], [13].

Overlap of [1] aaaaa=1 with [2] ababbb=1:

Critical pair: aaaa=babbb.

Referenced by [4], [5].

Overlap of [1] aaaaa=1 with [3] aaaa=babbb:

Critical pair: babbba=1.

Referenced by [6].

Overlap of [3] aaaa=babbb with [2] ababbb=1:

Critical pair: aaa=babbbbabbb.

Referenced by [10].

Overlap of [4] babbba=1 with [4] babbba=1:

Critical pair: babb=bbba.

Flip LHS and RHS.

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

Overlap of [2] ababbb=1 with [6] bbba=babb:

Critical pair: ababbabb=ba.

Referenced by [9].

Overlap of [2] ababbb=1 with [6] bbba=babb:

Critical pair: ababbbabb=bba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

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

Simplify [7] ababbabb=ba.

Reduce LHS:

Referenced by [11], [12].

Simplify [5] aaa=babbbbabbb.

Reduce RHS:

Defines rule #4.

Referenced by [11].

Overlap of [10] aaa=baabbbbbbb with [9] abaabbbb=ba:

Critical pair: aaba=baabbbbbbbbaabbbb.

Reduce RHS:

Referenced by [12].

Overlap of [11] aaba=abbbbbbbbbbbbbbbbb with [9] abaabbbb=ba:

Critical pair: aba=abbbbbbbbbbbbbbbbbabbbb.

Reduce RHS:

Defines rule #3.

Referenced by [13].

Overlap of [2] ababbb=1 with [12] aba=bbbbbbbbbbbbbbbbb:

Critical pair: bbbbbbbbbbbbbbbbbbbb=1.

Defines rule #1.