Certificate for #2450 ⟨a, b | aaa=1, babbb=a⟩

Completion settings:

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

Axiom: aaa=1.

Defines rule #3.

Referenced by [4], [5], [9], [11].

Axiom: babbb=a.

Referenced by [3], [6], [7], [8], [10].

Overlap of [2] babbb=a with [2] babbb=a:

Critical pair: babba=aabbb.

Flip LHS and RHS.

Referenced by [4].

Overlap of [1] aaa=1 with [3] aabbb=babba:

Critical pair: ababba=bbb.

Referenced by [5], [6].

Overlap of [4] ababba=bbb with [1] aaa=1:

Critical pair: ababb=bbbaa.

Referenced by [7].

Overlap of [4] ababba=bbb with [2] babbb=a:

Critical pair: ababa=bbbbbb.

Referenced by [9].

Overlap of [5] ababb=bbbaa with [2] babbb=a:

Critical pair: aa=bbbaab.

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [2] babbb=a with [7] bbbaab=aa:

Critical pair: babaa=abaab.

Flip LHS and RHS.

Referenced by [9].

Overlap of [7] bbbaab=aa with [8] abaab=babaa:

Critical pair: bbbababaa=aaaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10].

Overlap of [2] babbb=a with [9] ab=bbbbbbbbba:

Critical pair: bbbbbbbbbbabb=a.

Reduce LHS:

Referenced by [11].

Overlap of [10] bbbbbbbbbbbbbbbbbbbbbbbbbbbba=a with [1] aaa=1:

Critical pair: bbbbbbbbbbbbbbbbbbbbbbbbbbbb=aaa.

Reduce RHS:

Defines rule #1.