Certificate for #13185 ⟨a, b | abb=aaa, bab=bb⟩

Completion settings:

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

Axiom: abb=aaa.

Defines rule #5.

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

Axiom: bab=bb.

Defines rule #6.

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

Overlap of [1] abb=aaa with [2] bab=bb:

Critical pair: abbb=aaaab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8], [9].

Overlap of [2] bab=bb with [1] abb=aaa:

Critical pair: baaa=bbb.

Flip LHS and RHS.

Defines rule #8.

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

Overlap of [1] abb=aaa with [4] bbb=baaa:

Critical pair: abaaa=aaab.

Defines rule #4.

Referenced by [8], [9].

Overlap of [1] abb=aaa with [4] bbb=baaa:

Critical pair: abbaaa=aaabb.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [2] bab=bb with [4] bbb=baaa:

Critical pair: babaaa=bbbb.

Reduce LHS:

Reduce RHS:

Defines rule #7.

Overlap of [5] abaaa=aaab with [1] abb=aaa:

Critical pair: abaaaaa=aaabbb.

Reduce LHS:

Reduce RHS:

Referenced by [9].

Overlap of [8] aaabaa=aaab with [5] abaaa=aaab:

Critical pair: aaaaab=aaaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.