Certificate for #14833 ⟨a, b | abba=b, aaaaa=a⟩

Completion settings:

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

Axiom: abba=b.

Defines rule #4.

Referenced by [3], [4], [5], [6], [7], [9], [10], [13], [15].

Axiom: aaaaa=a.

Defines rule #9.

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

Overlap of [1] abba=b with [1] abba=b:

Critical pair: abbb=bbba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [11], [13], [15].

Overlap of [1] abba=b with [2] aaaaa=a:

Critical pair: abba=baaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] aaaaa=a with [1] abba=b:

Critical pair: aaaab=abba.

Reduce RHS:

Referenced by [6].

Overlap of [5] aaaab=b with [1] abba=b:

Critical pair: aaab=bba.

Defines rule #7.

Referenced by [8], [11].

Overlap of [1] abba=b with [4] baaaa=b:

Critical pair: abb=baaa.

Flip LHS and RHS.

Referenced by [9].

Overlap of [2] aaaaa=a with [6] aaab=bba:

Critical pair: aaabba=aab.

Reduce LHS:

Defines rule #6.

Referenced by [13].

Overlap of [1] abba=b with [7] baaa=abb:

Critical pair: ababb=baa.

Flip LHS and RHS.

Defines rule #5.

Referenced by [10], [11].

Overlap of [1] abba=b with [9] baa=ababb:

Critical pair: abababb=ba.

Referenced by [11], [12], [14].

Overlap of [9] baa=ababb with [10] abababb=ba:

Critical pair: baba=ababbbababb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [10] abababb=ba with [11] bababbbbbbbbbbbb=baba:

Critical pair: ababa=babbbbbbbbbb.

Defines rule #8.

Referenced by [13], [14].

Overlap of [8] bbaba=aab with [12] ababa=babbbbbbbbbb:

Critical pair: bbbabbbbbbbbbb=aabba.

Reduce LHS:

Reduce RHS:

Referenced by [15].

Overlap of [10] abababb=ba with [12] ababa=babbbbbbbbbb:

Critical pair: babbbbbbbbbbbb=ba.

Defines rule #2.

Overlap of [13] abbbbbbbbbbbbb=ab with [3] bbba=abbb:

Critical pair: abbbbbbbbbbbabbb=abba.

Reduce LHS:

Reduce RHS:

Defines rule #1.