Certificate for #1427 ⟨a, b | abba=b, baba=1⟩

Completion settings:

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

Axiom: abba=b.

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

Axiom: baba=1.

Referenced by [4], [5], [10].

Overlap of [1] abba=b with [1] abba=b:

Critical pair: abbb=bbba.

Flip LHS and RHS.

Referenced by [6], [10].

Overlap of [1] abba=b with [2] baba=1:

Critical pair: ab=bba.

Flip LHS and RHS.

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

Overlap of [2] baba=1 with [1] abba=b:

Critical pair: babb=bba.

Reduce RHS:

Referenced by [7], [8].

Overlap of [4] bba=ab with [1] abba=b:

Critical pair: bbb=abbba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [5] babb=ab with [1] abba=b:

Critical pair: bb=aba.

Flip LHS and RHS.

Referenced by [8], [11].

Overlap of [5] babb=ab with [4] bba=ab:

Critical pair: babab=abba.

Reduce LHS:

Reduce RHS:

Referenced by [9].

Overlap of [8] bbbb=b with [4] bba=ab:

Critical pair: bbab=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [11].

Overlap of [2] baba=1 with [9] ba=abb:

Critical pair: abbba=1.

Reduce LHS:

Defines rule #1.

Referenced by [12].

Simplify [7] aba=bb.

Reduce LHS:

Referenced by [12].

Overlap of [11] aabb=bb with [10] bbb=1:

Critical pair: aa=bbb.

Reduce RHS:

Defines rule #3.