Certificate for #16291 ⟨a, b | aab=bb, abaa=ba⟩

Completion settings:

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

Axiom: aab=bb.

Defines rule #4.

Referenced by [3], [4], [5], [6], [7], [8], [9], [11].

Axiom: abaa=ba.

Referenced by [3], [4], [5], [11].

Overlap of [1] aab=bb with [2] abaa=ba:

Critical pair: aba=bbaa.

Flip LHS and RHS.

Referenced by [8], [9], [10], [11], [12].

Overlap of [2] abaa=ba with [1] aab=bb:

Critical pair: abbb=bab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6], [7], [8], [9], [10].

Overlap of [2] abaa=ba with [1] aab=bb:

Critical pair: ababb=baab.

Reduce LHS:

Reduce RHS:

Referenced by [6], [7].

Overlap of [1] aab=bb with [4] bab=abbb:

Critical pair: aaabbb=bbab.

Reduce LHS:

Reduce RHS:

Referenced by [7], [9], [10].

Overlap of [4] bab=abbb with [4] bab=abbb:

Critical pair: baabbb=abbbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [10].

Overlap of [1] aab=bb with [3] bbaa=aba:

Critical pair: aaaba=bbbaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [4] bab=abbb with [3] bbaa=aba:

Critical pair: baaba=abbbbaa.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [7] bbbb=bbb with [3] bbaa=aba:

Critical pair: bbaba=bbbaa.

Reduce LHS:

Reduce RHS:

Referenced by [11].

Overlap of [10] abba=aba with [3] bbaa=aba:

Critical pair: aaba=abaa.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [12].

Overlap of [3] bbaa=aba with [11] bba=ba:

Critical pair: baa=aba.

Defines rule #5.