Certificate for #12209 ⟨a, b | aaaa=bb, baab=b⟩

Completion settings:

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

Axiom: aaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4], [5], [6], [7].

Axiom: baab=b.

Defines rule #5.

Referenced by [4], [5].

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

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Referenced by [4], [7], [8].

Overlap of [1] bb=aaaa with [2] baab=b:

Critical pair: bb=aaaaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] baab=b with [1] bb=aaaa:

Critical pair: baaaaaa=bb.

Reduce RHS:

Referenced by [6], [7].

Overlap of [1] bb=aaaa with [5] baaaaaa=aaaa:

Critical pair: baaaa=aaaaaaaaaa.

Defines rule #2.

Referenced by [8].

Overlap of [5] baaaaaa=aaaa with [3] aaaab=baaaa:

Critical pair: baaaabaaaa=aaaaaab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Simplify [3] aaaab=baaaa.

Reduce RHS:

Defines rule #3.