Certificate for #6764 ⟨a, b | aba=b, aaaa=bb⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [4], [5], [6], [7], [8].

Axiom: aaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [8].

Overlap of [2] bb=aaaa with [2] bb=aaaa:

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Referenced by [4].

Overlap of [3] aaaab=baaaa with [1] aba=b:

Critical pair: aaab=baaaaa.

Referenced by [5].

Overlap of [4] aaab=baaaaa with [1] aba=b:

Critical pair: aab=baaaaaa.

Referenced by [6].

Overlap of [5] aab=baaaaaa with [1] aba=b:

Critical pair: ab=baaaaaaa.

Defines rule #3.

Referenced by [7], [8].

Overlap of [1] aba=b with [6] ab=baaaaaaa:

Critical pair: baaaaaaaa=b.

Defines rule #2.

Overlap of [1] aba=b with [6] ab=baaaaaaa:

Critical pair: abbaaaaaaa=bb.

Reduce LHS:

Reduce RHS:

Defines rule #1.