Certificate for #13095 ⟨a, b | bab=aaa, baab=b⟩

Completion settings:

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

Axiom: bab=aaa.

Defines rule #4.

Referenced by [3], [4], [5], [6], [10].

Axiom: baab=b.

Defines rule #5.

Referenced by [4], [5].

Overlap of [1] bab=aaa with [1] bab=aaa:

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Referenced by [4], [9].

Overlap of [1] bab=aaa with [2] baab=b:

Critical pair: bab=aaaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] baab=b with [1] bab=aaa:

Critical pair: baaaaa=bab.

Reduce RHS:

Referenced by [6], [8].

Overlap of [1] bab=aaa with [5] baaaaa=aaa:

Critical pair: baaaa=aaaaaaaa.

Referenced by [7].

Simplify [4] abaaaa=aaa.

Reduce LHS:

Defines rule #1.

Referenced by [8], [10].

Overlap of [5] baaaaa=aaa with [7] aaaaaaaaa=aaa:

Critical pair: baaa=aaaaaaa.

Defines rule #2.

Referenced by [9].

Simplify [3] aaaab=baaaa.

Reduce RHS:

Referenced by [10].

Overlap of [9] aaaab=aaaaaaaa with [1] bab=aaa:

Critical pair: aaaaaaa=aaaaaaaaab.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.