Certificate for #19260 ⟨a, b | aaa=a, aabbb=ba⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #7.

Referenced by [3], [4], [9], [10].

Axiom: aabbb=ba.

Defines rule #4.

Referenced by [3], [5], [6], [7], [8], [9].

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

Critical pair: aba=abbb.

Defines rule #5.

Referenced by [4], [5], [8], [11], [12], [13], [15].

Overlap of [3] aba=abbb with [1] aaa=a:

Critical pair: aba=abbbaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [3] aba=abbb with [2] aabbb=ba:

Critical pair: abba=abbbabbb.

Flip LHS and RHS.

Referenced by [6], [13].

Overlap of [2] aabbb=ba with [5] abbbabbb=abba:

Critical pair: aabba=baabbb.

Reduce RHS:

Referenced by [7], [8].

Overlap of [6] aabba=bba with [2] aabbb=ba:

Critical pair: aabbba=bbaabbb.

Reduce LHS:

Reduce RHS:

Referenced by [9], [10], [11], [13], [14].

Overlap of [6] aabba=bba with [6] aabba=bba:

Critical pair: aabbbba=bbaabba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [2] aabbb=ba with [7] baa=bbba:

Critical pair: aabbbbba=baaa.

Reduce LHS:

Reduce RHS:

Referenced by [11], [15].

Overlap of [7] baa=bbba with [1] aaa=a:

Critical pair: ba=bbbaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [9] babba=ba with [7] baa=bbba:

Critical pair: babbbba=baa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [13], [14].

Overlap of [11] bbba=babbbbbb with [3] aba=abbb:

Critical pair: bbbabbb=babbbbbbba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [13], [15].

Overlap of [4] abbbaa=abbb with [7] baa=bbba:

Critical pair: abbbbba=abbb.

Reduce LHS:

Defines rule #1.

Simplify [7] baa=bbba.

Reduce RHS:

Defines rule #6.

Overlap of [9] babba=ba with [12] bba=babbbbbbbbb:

Critical pair: bababbbbbbbbb=ba.

Reduce LHS:

Defines rule #2.