Certificate for #26599 ⟨a, b | aa=1, ababbbba=b⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #4.

Referenced by [3], [4], [6], [7], [13].

Axiom: ababbbba=b.

Referenced by [3], [7].

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

Critical pair: ab=babbbba.

Flip LHS and RHS.

Referenced by [4], [5], [7], [8], [9], [11], [15].

Overlap of [3] babbbba=ab with [1] aa=1:

Critical pair: babbbb=aba.

Flip LHS and RHS.

Defines rule #5.

Referenced by [6], [14].

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

Critical pair: babbbab=abbbbba.

Referenced by [11], [12].

Overlap of [1] aa=1 with [4] aba=babbbb:

Critical pair: ababbbb=ba.

Reduce LHS:

Referenced by [7], [10], [16].

Overlap of [2] ababbbba=b with [6] babbbbbbbb=ba:

Critical pair: ababbbba=bbbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [8], [17], [19].

Overlap of [7] bbbbbbbbb=b with [3] babbbba=ab:

Critical pair: bbbbbbbbab=babbbba.

Reduce RHS:

Defines rule #2.

Referenced by [9], [10], [12], [17], [18], [19].

Overlap of [8] bbbbbbbbab=ab with [3] babbbba=ab:

Critical pair: bbbbbbbab=abbbba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [13], [14], [19].

Overlap of [8] bbbbbbbbab=ab with [6] babbbbbbbb=ba:

Critical pair: bbbbbbbba=abbbbbbbb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [17], [19].

Overlap of [5] babbbab=abbbbba with [3] babbbba=ab:

Critical pair: babbab=abbbbbabbba.

Flip LHS and RHS.

Defines rule #13.

Overlap of [8] bbbbbbbbab=ab with [5] babbbab=abbbbba:

Critical pair: bbbbbbbabbbbba=abbbab.

Flip LHS and RHS.

Defines rule #8.

Referenced by [17], [19].

Overlap of [1] aa=1 with [9] abbbba=bbbbbbbab:

Critical pair: abbbbbbbab=bbbba.

Referenced by [15], [16].

Overlap of [9] abbbba=bbbbbbbab with [4] aba=babbbb:

Critical pair: abbbbbabbbb=bbbbbbbabba.

Defines rule #11.

Referenced by [17], [19].

Overlap of [13] abbbbbbbab=bbbba with [3] babbbba=ab:

Critical pair: abbbbbbab=bbbbabbba.

Defines rule #9.

Referenced by [17], [19].

Overlap of [13] abbbbbbbab=bbbba with [6] babbbbbbbb=ba:

Critical pair: abbbbbbba=bbbbabbbbbbb.

Defines rule #7.

Overlap of [15] abbbbbbab=bbbbabbba with [10] abbbbbbbb=bbbbbbbba:

Critical pair: abbbbbbbbbbbbbba=bbbbabbbabbbbbbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [18].

Overlap of [8] bbbbbbbbab=ab with [17] bbabbabb=abbbbbba:

Critical pair: bbbbbbabbbbbba=abbabb.

Flip LHS and RHS.

Defines rule #10.

Referenced by [19].

Overlap of [15] abbbbbbab=bbbbabbba with [14] abbbbbabbbb=bbbbbbbabba:

Critical pair: abbbbbbbbbbbbbabba=bbbbabbbabbbbabbbb.

Reduce LHS:

Reduce RHS:

Defines rule #12.