Certificate for #12187 ⟨a, b | aaaa=ab, babb=b⟩

Completion settings:

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

Axiom: aaaa=ab.

Defines rule #4.

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

Axiom: babb=b.

Referenced by [5], [7], [8], [10].

Overlap of [1] aaaa=ab with [1] aaaa=ab:

Critical pair: aab=aba.

Flip LHS and RHS.

Referenced by [4], [5], [11].

Overlap of [1] aaaa=ab with [3] aba=aab:

Critical pair: aaaaab=abba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [3] aba=aab with [2] babb=b:

Critical pair: ab=aabbb.

Flip LHS and RHS.

Referenced by [6], [11].

Overlap of [1] aaaa=ab with [5] aabbb=ab:

Critical pair: aaab=abbbb.

Referenced by [8].

Overlap of [2] babb=b with [4] abba=aabb:

Critical pair: baabb=ba.

Referenced by [8], [9].

Overlap of [7] baabb=ba with [4] abba=aabb:

Critical pair: baaabb=baa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [7] baabb=ba with [8] baa=bbbb:

Critical pair: bbbbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [10], [11].

Overlap of [2] babb=b with [9] ba=bbbbbb:

Critical pair: bbbbbbbb=b.

Defines rule #1.

Overlap of [5] aabbb=ab with [9] ba=bbbbbb:

Critical pair: aabbbbbbbb=aba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.