Certificate for #12633 ⟨a, b | babb=aa, bbbb=b⟩

Completion settings:

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

Axiom: babb=aa.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [7], [9], [12], [13], [14].

Axiom: bbbb=b.

Defines rule #1.

Referenced by [4], [5], [6], [7], [8], [9], [12], [13], [14].

Overlap of [1] aa=babb with [1] aa=babb:

Critical pair: ababb=babba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5], [7], [12], [13].

Overlap of [2] bbbb=b with [3] babba=ababb:

Critical pair: bbbababb=babba.

Reduce RHS:

Referenced by [6], [7].

Overlap of [3] babba=ababb with [3] babba=ababb:

Critical pair: babababb=ababbbba.

Reduce RHS:

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

Overlap of [4] bbbababb=ababb with [2] bbbb=b:

Critical pair: bbbabab=ababbbb.

Reduce RHS:

Defines rule #4.

Referenced by [7], [9].

Overlap of [4] bbbababb=ababb with [6] bbbabab=abab:

Critical pair: bbbabaabab=ababbbabab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [14].

Overlap of [5] babababb=ababa with [2] bbbb=b:

Critical pair: bababab=abababb.

Referenced by [9], [10].

Overlap of [6] bbbabab=abab with [5] babababb=ababa:

Critical pair: bbbaababa=ababababb.

Reduce LHS:

Reduce RHS:

Defines rule #9.

Referenced by [12], [13].

Overlap of [5] babababb=ababa with [8] bababab=abababb:

Critical pair: abababbb=ababa.

Defines rule #5.

Referenced by [11].

Overlap of [5] babababb=ababa with [10] abababbb=ababa:

Critical pair: bababa=ababab.

Defines rule #7.

Overlap of [3] babba=ababb with [9] babbbaba=bbabbbabbb:

Critical pair: babbbabbbabbb=ababbbbbaba.

Reduce RHS:

Defines rule #10.

Overlap of [9] babbbaba=bbabbbabbb with [1] aa=babb:

Critical pair: babbbabbabb=bbabbbabbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Overlap of [1] aa=babb with [7] abbabbbab=bbbabbbabbb:

Critical pair: abbbabbbabbb=babbbbabbbab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.