Certificate for #14502 ⟨a, b | aaab=b, abbba=b⟩

Completion settings:

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

Axiom: aaab=b.

Referenced by [3], [4].

Axiom: abbba=b.

Defines rule #6.

Referenced by [3], [4], [5], [6], [11], [12].

Overlap of [1] aaab=b with [2] abbba=b:

Critical pair: aab=bbba.

Defines rule #4.

Referenced by [4], [5], [6], [7], [8], [9], [14].

Overlap of [2] abbba=b with [1] aaab=b:

Critical pair: abbbb=baab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [7], [8], [9], [11], [12], [13], [14].

Overlap of [2] abbba=b with [3] aab=bbba:

Critical pair: abbbbbba=bab.

Reduce LHS:

Referenced by [8].

Overlap of [3] aab=bbba with [2] abbba=b:

Critical pair: ab=bbbabba.

Flip LHS and RHS.

Referenced by [7], [9].

Overlap of [6] bbbabba=ab with [3] aab=bbba:

Critical pair: bbbabbbbba=abab.

Reduce LHS:

Referenced by [10].

Overlap of [5] abbabbbb=bab with [4] bbbba=abbbb:

Critical pair: abbaabbbb=baba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [9], [10].

Overlap of [6] bbbabba=ab with [8] baba=ababbbbbbb:

Critical pair: bbbabababbbbbbb=abba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Simplify [7] bbbababbbb=abab.

Reduce LHS:

Referenced by [11].

Overlap of [10] ababbbbbbbbbbbbbbbbbbbbbbbbb=abab with [4] bbbba=abbbb:

Critical pair: ababbbbbbbbbbbbbbbbbbbbbbbabbbb=ababbba.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [11] abbbbbbbbbbbbbbbbbbbbbbbbbb=abb with [4] bbbba=abbbb:

Critical pair: abbbbbbbbbbbbbbbbbbbbbbbabbbb=abbba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [13], [14].

Overlap of [12] bbbbbbbbbbbbbbbbbbbbbbbbb=b with [4] bbbba=abbbb:

Critical pair: bbbbbbbbbbbbbbbbbbbbbabbbb=ba.

Reduce LHS:

Defines rule #2.

Referenced by [14].

Overlap of [13] babbbbbbbbbbbbbbbbbbbbbbbb=ba with [4] bbbba=abbbb:

Critical pair: babbbbbbbbbbbbbbbbbbbbabbbb=baa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.