Certificate for #6501 ⟨a, b | aba=b, aabbb=b⟩

Completion settings:

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

Axiom: aba=b.

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

Axiom: aabbb=b.

Referenced by [4].

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

Critical pair: abb=bba.

Referenced by [4], [6], [7], [9], [10], [11].

Simplify [2] aabbb=b.

Reduce LHS:

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

Overlap of [4] bbaab=b with [1] aba=b:

Critical pair: bbab=ba.

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

Overlap of [3] abb=bba with [4] bbaab=b:

Critical pair: ab=bbaaab.

Flip LHS and RHS.

Referenced by [11].

Overlap of [3] abb=bba with [5] bbab=ba:

Critical pair: abba=bbabab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [5] bbab=ba with [1] aba=b:

Critical pair: bbb=baa.

Defines rule #3.

Referenced by [9], [11].

Overlap of [5] bbab=ba with [3] abb=bba:

Critical pair: bbbba=bab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [3] abb=bba with [9] bab=bbaaa:

Critical pair: abbbaaa=bbaab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [9] bab=bbaaa with [3] abb=bba:

Critical pair: bbba=bbaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.