Certificate for #14836 ⟨a, b | abba=b, aaaab=b⟩

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], [12], [13], [14].

Axiom: aaaab=b.

Referenced by [4].

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

Critical pair: abbb=bbba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [8], [9], [11], [12], [15].

Overlap of [2] aaaab=b with [1] abba=b:

Critical pair: aaab=bba.

Defines rule #7.

Referenced by [5], [6], [9], [12].

Overlap of [1] abba=b with [4] aaab=bba:

Critical pair: abbbba=baab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [8], [9], [11], [12], [15].

Overlap of [4] aaab=bba with [1] abba=b:

Critical pair: aab=bbaba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

Overlap of [1] abba=b with [5] baab=ababbb:

Critical pair: abababbb=bab.

Referenced by [9], [10].

Overlap of [6] bbaba=aab with [5] baab=ababbb:

Critical pair: bbaababbb=aabab.

Reduce LHS:

Referenced by [11].

Overlap of [7] abababbb=bab with [3] bbba=abbb:

Critical pair: ababaabbb=baba.

Reduce LHS:

Referenced by [10], [11], [12].

Overlap of [7] abababbb=bab with [9] bababbbbbbbbbbbb=baba:

Critical pair: ababa=babbbbbbbbbb.

Defines rule #8.

Referenced by [13].

Overlap of [9] bababbbbbbbbbbbb=baba with [3] bbba=abbb:

Critical pair: bababbbbbbbbbabbb=babaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [1] abba=b with [11] babaa=aababbbbbbb:

Critical pair: abaababbbbbbb=bbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [1] abba=b with [12] bbaa=bababb:

Critical pair: abababb=ba.

Reduce LHS:

Defines rule #2.

Referenced by [14], [15].

Overlap of [1] abba=b with [13] babbbbbbbbbbbb=ba:

Critical pair: abba=bbbbbbbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [13] babbbbbbbbbbbb=ba with [3] bbba=abbb:

Critical pair: babbbbbbbbbabbb=baa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.