Certificate for #12985 ⟨a, b | abb=aaa, baba=b⟩

Completion settings:

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

Axiom: abb=aaa.

Referenced by [5], [6], [7], [9].

Axiom: baba=b.

Referenced by [3], [4].

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

Critical pair: bab=bba.

Referenced by [4], [5].

Overlap of [2] baba=b with [3] bab=bba:

Critical pair: bbaa=b.

Referenced by [6], [7], [8], [10].

Overlap of [1] abb=aaa with [3] bab=bba:

Critical pair: abbba=aaaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [1] abb=aaa with [4] bbaa=b:

Critical pair: ab=aaaaa.

Defines rule #3.

Referenced by [9].

Overlap of [4] bbaa=b with [1] abb=aaa:

Critical pair: bbaaaa=bbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [7] bbb=baa with [4] bbaa=b:

Critical pair: bb=baaaa.

Defines rule #4.

Referenced by [10].

Overlap of [1] abb=aaa with [6] ab=aaaaa:

Critical pair: aaaaab=aaa.

Reduce LHS:

Defines rule #1.

Overlap of [4] bbaa=b with [8] bb=baaaa:

Critical pair: baaaaaa=b.

Defines rule #2.