Certificate for #9737 ⟨a, b | aa=1, ababbba=b⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #4.

Referenced by [3], [4], [5], [6], [9], [13].

Axiom: ababbba=b.

Referenced by [3], [4], [9].

Overlap of [1] aa=1 with [2] ababbba=b:

Critical pair: ab=babbba.

Flip LHS and RHS.

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

Overlap of [2] ababbba=b with [1] aa=1:

Critical pair: ababbb=ba.

Referenced by [5].

Overlap of [1] aa=1 with [4] ababbb=ba:

Critical pair: aba=babbb.

Defines rule #5.

Referenced by [6], [7].

Overlap of [1] aa=1 with [5] aba=babbb:

Critical pair: ababbb=ba.

Reduce LHS:

Defines rule #2.

Referenced by [9], [12], [14], [15].

Overlap of [5] aba=babbb with [5] aba=babbb:

Critical pair: abbabbb=babbbba.

Flip LHS and RHS.

Defines rule #9.

Overlap of [3] babbba=ab with [3] babbba=ab:

Critical pair: babbab=abbbba.

Referenced by [15].

Overlap of [2] ababbba=b with [6] babbbbbb=ba:

Critical pair: ababbba=bbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [10].

Overlap of [9] bbbbbbb=b with [3] babbba=ab:

Critical pair: bbbbbbab=babbba.

Reduce RHS:

Referenced by [11], [12].

Overlap of [10] bbbbbbab=ab with [3] babbba=ab:

Critical pair: bbbbbab=abbba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [13].

Overlap of [10] bbbbbbab=ab with [6] babbbbbb=ba:

Critical pair: bbbbbba=abbbbbb.

Defines rule #3.

Overlap of [1] aa=1 with [11] abbba=bbbbbab:

Critical pair: abbbbbab=bbba.

Referenced by [14].

Overlap of [13] abbbbbab=bbba with [6] babbbbbb=ba:

Critical pair: abbbbba=bbbabbbbb.

Defines rule #7.

Overlap of [8] babbab=abbbba with [6] babbbbbb=ba:

Critical pair: babba=abbbbabbbbb.

Defines rule #8.