Certificate for #12545 ⟨a, b | abab=ba, bbbb=b⟩

Completion settings:

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

Axiom: abab=ba.

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

Axiom: bbbb=b.

Defines rule #1.

Referenced by [4].

Overlap of [1] abab=ba with [1] abab=ba:

Critical pair: abba=baab.

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] abab=ba with [2] bbbb=b:

Critical pair: abab=babbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6], [8], [9], [10], [11].

Overlap of [1] abab=ba with [4] babbb=ba:

Critical pair: aba=babb.

Defines rule #3.

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

Overlap of [4] babbb=ba with [4] babbb=ba:

Critical pair: babbba=baabbb.

Reduce LHS:

Reduce RHS:

Defines rule #4.

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

Overlap of [5] aba=babb with [6] baa=abbabb:

Critical pair: aabbabb=babba.

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

Overlap of [6] baa=abbabb with [7] aabbabb=babba:

Critical pair: bbabba=abbabbbbabb.

Reduce RHS:

Defines rule #5.

Referenced by [10].

Overlap of [7] aabbabb=babba with [4] babbb=ba:

Critical pair: aabba=babbab.

Defines rule #6.

Overlap of [7] aabbabb=babba with [4] babbb=ba:

Critical pair: aabbabba=babbaabbb.

Reduce LHS:

Reduce RHS:

Referenced by [11].

Overlap of [10] aaabbbab=bbbab with [4] babbb=ba:

Critical pair: aaabbba=bbbabbb.

Reduce RHS:

Defines rule #7.