Certificate for #3375 ⟨a, b | aa=1, ababba=b⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #1.

Referenced by [3], [4], [5], [7], [8], [9], [10].

Axiom: ababba=b.

Referenced by [3], [6].

Overlap of [2] ababba=b with [1] aa=1:

Critical pair: ababb=ba.

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

Overlap of [1] aa=1 with [3] ababb=ba:

Critical pair: aba=babb.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [8].

Overlap of [4] babb=aba with [4] babb=aba:

Critical pair: bababa=abaabb.

Reduce RHS:

Defines rule #5.

Referenced by [6], [7], [8].

Overlap of [2] ababba=b with [5] bababa=abbb:

Critical pair: abababbb=bbaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [5] bababa=abbb with [1] aa=1:

Critical pair: babab=abbba.

Flip LHS and RHS.

Referenced by [10].

Overlap of [5] bababa=abbb with [3] ababb=ba:

Critical pair: babba=abbbbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [1] aa=1 with [8] abbbbb=ab:

Critical pair: aab=bbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [1] aa=1 with [7] abbba=babab:

Critical pair: ababab=bbba.

Flip LHS and RHS.

Defines rule #3.