Certificate for #20251 ⟨a, b | aba=b, aaaa=abb⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [3], [4], [5], [6], [7], [8], [9].

Axiom: aaaa=abb.

Flip LHS and RHS.

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

Overlap of [1] aba=b with [1] aba=b:

Critical pair: abb=bba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4], [9].

Overlap of [3] bba=aaaa with [1] aba=b:

Critical pair: bbb=aaaaba.

Reduce RHS:

Referenced by [5].

Overlap of [1] aba=b with [2] abb=aaaa:

Critical pair: abaaaa=bbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [6], [10].

Overlap of [5] aaab=baaa with [1] aba=b:

Critical pair: aab=baaaa.

Referenced by [7], [10].

Overlap of [6] aab=baaaa with [1] aba=b:

Critical pair: ab=baaaaa.

Defines rule #3.

Referenced by [8], [9], [10].

Overlap of [1] aba=b with [7] ab=baaaaa:

Critical pair: baaaaaa=b.

Defines rule #2.

Referenced by [10].

Overlap of [1] aba=b with [7] ab=baaaaa:

Critical pair: abbaaaaa=bb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [10].

Overlap of [2] abb=aaaa with [7] ab=baaaaa:

Critical pair: baaaaab=aaaa.

Reduce LHS:

Defines rule #1.