Certificate for #20300 ⟨a, b | aba=b, baab=aaa⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [3], [4], [5], [7], [8], [9], [10].

Axiom: baab=aaa.

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

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

Critical pair: abb=bba.

Referenced by [7].

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

Critical pair: aaaa=bab.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aba=b with [4] bab=aaaa:

Critical pair: aaaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [7].

Overlap of [2] baab=aaa with [5] bb=aaaaa:

Critical pair: baaaaaaa=aaab.

Flip LHS and RHS.

Referenced by [7], [8].

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

Critical pair: abbaaaaaaa=baab.

Reduce LHS:

Reduce RHS:

Defines rule #1.

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

Critical pair: aab=baaaaaaaa.

Referenced by [9].

Overlap of [8] aab=baaaaaaaa with [1] aba=b:

Critical pair: ab=baaaaaaaaa.

Defines rule #3.

Referenced by [10].

Overlap of [1] aba=b with [9] ab=baaaaaaaaa:

Critical pair: baaaaaaaaaa=b.

Defines rule #2.