Certificate for #12534 ⟨a, b | abab=ba, abbb=a⟩

Completion settings:

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

Axiom: abab=ba.

Referenced by [3], [4].

Axiom: abbb=a.

Defines rule #1.

Referenced by [3], [6], [7], [8], [9], [10].

Overlap of [1] abab=ba with [2] abbb=a:

Critical pair: aba=babb.

Defines rule #3.

Referenced by [4], [5], [6], [8], [10].

Overlap of [1] abab=ba with [3] aba=babb:

Critical pair: abbabb=baa.

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [3] aba=babb with [4] baa=abbabb:

Critical pair: aabbabb=babba.

Referenced by [6], [7], [8].

Overlap of [4] baa=abbabb with [5] aabbabb=babba:

Critical pair: bbabba=abbabbbbabb.

Reduce RHS:

Defines rule #5.

Referenced by [8], [10].

Overlap of [5] aabbabb=babba with [2] abbb=a:

Critical pair: aabba=babbab.

Defines rule #6.

Overlap of [5] aabbabb=babba with [6] bbabba=aab:

Critical pair: aaaab=babbaa.

Reduce RHS:

Referenced by [9].

Overlap of [8] aaaab=bbbab with [2] abbb=a:

Critical pair: aaaa=bbbabbb.

Reduce RHS:

Defines rule #7.

Referenced by [10].

Overlap of [4] baa=abbabb with [9] aaaa=bbba:

Critical pair: bbbba=abbabbaa.

Reduce RHS:

Defines rule #2.