Certificate for #12477 ⟨a, b | aabb=ba, baaa=b⟩

Completion settings:

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

Axiom: aabb=ba.

Referenced by [3], [4], [5], [8], [10], [11], [13].

Axiom: baaa=b.

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

Overlap of [2] baaa=b with [1] aabb=ba:

Critical pair: baba=bbb.

Defines rule #4.

Referenced by [5], [6], [7], [12].

Overlap of [2] baaa=b with [1] aabb=ba:

Critical pair: baaba=babb.

Referenced by [9].

Overlap of [3] baba=bbb with [1] aabb=ba:

Critical pair: babba=bbbabb.

Defines rule #5.

Referenced by [8], [9].

Overlap of [3] baba=bbb with [2] baaa=b:

Critical pair: bab=bbbaa.

Flip LHS and RHS.

Referenced by [8], [10], [11].

Overlap of [3] baba=bbb with [3] baba=bbb:

Critical pair: babbb=bbbba.

Defines rule #2.

Referenced by [10], [11], [13].

Overlap of [1] aabb=ba with [6] bbbaa=bab:

Critical pair: aabbab=babbaa.

Reduce LHS:

Reduce RHS:

Referenced by [9].

Simplify [4] baaba=babb.

Reduce LHS:

Referenced by [10].

Overlap of [1] aabb=ba with [9] bbbbbbbabb=babb:

Critical pair: aabbabb=babbbbbbabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [1] aabb=ba with [10] bbbbbbbba=bba:

Critical pair: aabba=babbbbbba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [12].

Overlap of [2] baaa=b with [11] baa=bbbbbab:

Critical pair: bbbbbaba=b.

Reduce LHS:

Defines rule #1.

Referenced by [13].

Overlap of [1] aabb=ba with [12] bbbbbbb=b:

Critical pair: aab=babbbbb.

Reduce RHS:

Defines rule #6.