Certificate for #1523 ⟨a, b | aab=ba, bbbb=1⟩

Completion settings:

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

Axiom: aab=ba.

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

Axiom: bbbb=1.

Defines rule #3.

Referenced by [3], [4], [6], [9], [10].

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

Critical pair: aa=babbb.

Flip LHS and RHS.

Referenced by [4].

Overlap of [2] bbbb=1 with [3] babbb=aa:

Critical pair: bbbaa=abbb.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aab=ba with [4] abbb=bbbaa:

Critical pair: abbbaa=babb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] bbbb=1 with [5] babb=bbbaaaa:

Critical pair: bbbbbbaaaa=abb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aab=ba with [6] abb=bbaaaa:

Critical pair: abbaaaa=bab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [1] aab=ba with [7] bab=bbaaaaaaaa:

Critical pair: aabbaaaaaaaa=baab.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [2] bbbb=1 with [7] bab=bbaaaaaaaa:

Critical pair: bbbbbaaaaaaaa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [2] bbbb=1 with [8] bbaaaaaaaaaaaaaaaa=bba:

Critical pair: bbbba=aaaaaaaaaaaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.