Certificate for #13247 ⟨a, b | bab=aaa, bba=bb⟩

Completion settings:

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

Axiom: bab=aaa.

Defines rule #6.

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

Axiom: bba=bb.

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

Overlap of [1] bab=aaa with [1] bab=aaa:

Critical pair: baaaa=aaaab.

Flip LHS and RHS.

Referenced by [7], [10].

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

Critical pair: baaa=bbb.

Flip LHS and RHS.

Referenced by [5], [6].

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

Critical pair: bbb=baaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [7], [8], [9], [10], [12].

Overlap of [4] bbb=baaa with [4] bbb=baaa:

Critical pair: bbaaa=baaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [9], [11].

Overlap of [1] bab=aaa with [6] baaab=bb:

Critical pair: babb=aaaaaab.

Reduce LHS:

Reduce RHS:

Referenced by [9], [10], [12], [13].

Overlap of [1] bab=aaa with [5] baaaa=baaa:

Critical pair: babaaa=aaaaaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [7] aaab=aabaaa with [1] bab=aaa:

Critical pair: aaaaaa=aabaaaab.

Reduce RHS:

Flip LHS and RHS.

Referenced by [11].

Simplify [3] aaaab=baaaa.

Reduce LHS:

Reduce RHS:

Referenced by [11], [12].

Overlap of [10] aabaaa=baaa with [6] baaab=bb:

Critical pair: aabb=baaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [7] aaab=aabaaa with [10] aabaaa=baaa:

Critical pair: abaaa=aabaaaaaa.

Reduce RHS:

Defines rule #3.

Referenced by [13].

Simplify [7] aaab=aabaaa.

Reduce RHS:

Defines rule #4.