Certificate for #6660 ⟨a, b | aab=a, bbbb=ba⟩

Completion settings:

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

Axiom: aab=a.

Referenced by [3], [5], [6], [11], [12].

Axiom: bbbb=ba.

Defines rule #4.

Referenced by [3], [4], [6], [8], [12].

Overlap of [1] aab=a with [2] bbbb=ba:

Critical pair: aaba=abbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

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

Critical pair: bba=bab.

Flip LHS and RHS.

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

Overlap of [1] aab=a with [4] bab=bba:

Critical pair: aabba=aab.

Reduce LHS:

Reduce RHS:

Referenced by [7].

Overlap of [2] bbbb=ba with [4] bab=bba:

Critical pair: bbbbba=baab.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [5] aba=a with [4] bab=bba:

Critical pair: abba=ab.

Referenced by [9], [10].

Overlap of [2] bbbb=ba with [6] bbaa=ba:

Critical pair: bbba=baaa.

Referenced by [9].

Overlap of [4] bab=bba with [7] abba=ab:

Critical pair: bab=bbaba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Overlap of [7] abba=ab with [4] bab=bba:

Critical pair: abbba=abb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11], [12].

Overlap of [1] aab=a with [10] abb=aaa:

Critical pair: aaaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [12].

Overlap of [10] abb=aaa with [2] bbbb=ba:

Critical pair: aba=aaabb.

Reduce LHS:

Reduce RHS:

Defines rule #1.