Certificate for #19275 ⟨a, b | aaa=a, abbab=ba⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #8.

Referenced by [3], [13].

Axiom: abbab=ba.

Referenced by [3], [4], [5], [7], [8], [9], [11].

Overlap of [1] aaa=a with [2] abbab=ba:

Critical pair: aaba=abbab.

Reduce RHS:

Referenced by [5], [6], [13].

Overlap of [2] abbab=ba with [2] abbab=ba:

Critical pair: abbba=babab.

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] aaba=ba with [2] abbab=ba:

Critical pair: aabba=babbab.

Reduce RHS:

Referenced by [6], [7].

Overlap of [3] aaba=ba with [5] aabba=bba:

Critical pair: aabbba=baabba.

Reduce RHS:

Referenced by [15].

Overlap of [5] aabba=bba with [2] abbab=ba:

Critical pair: aba=bbab.

Defines rule #3.

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

Overlap of [2] abbab=ba with [7] aba=bbab:

Critical pair: abbbbab=baa.

Referenced by [11], [12].

Overlap of [7] aba=bbab with [2] abbab=ba:

Critical pair: abba=bbabbbab.

Flip LHS and RHS.

Referenced by [17].

Simplify [4] babab=abbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [11], [15], [17].

Overlap of [10] abbba=bbbabb with [2] abbab=ba:

Critical pair: abbbba=bbbabbbbab.

Reduce RHS:

Defines rule #6.

Referenced by [12].

Simplify [8] abbbbab=baa.

Reduce LHS:

Referenced by [13], [14].

Overlap of [12] bbbbaab=baa with [3] aaba=ba:

Critical pair: bbbbba=baaa.

Reduce RHS:

Defines rule #1.

Referenced by [14], [16], [17].

Overlap of [13] bbbbba=ba with [12] bbbbaab=baa:

Critical pair: bbaa=baab.

Flip LHS and RHS.

Defines rule #7.

Simplify [6] aabbba=bbba.

Reduce LHS:

Referenced by [16].

Overlap of [13] bbbbba=ba with [15] bbbabbbb=bbba:

Critical pair: bbbbba=babbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [9] bbabbbab=abba with [10] abbba=bbbabb:

Critical pair: bbbbbabbb=abba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.