Certificate for #1602 ⟨a, b | aaa=bb, aba=a⟩

Completion settings:

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

Axiom: aaa=bb.

Defines rule #5.

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

Axiom: aba=a.

Defines rule #4.

Referenced by [4], [5].

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

Critical pair: abb=bba.

Flip LHS and RHS.

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

Overlap of [1] aaa=bb with [2] aba=a:

Critical pair: aaa=bbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [2] aba=a with [1] aaa=bb:

Critical pair: abbb=aaa.

Reduce RHS:

Referenced by [6], [8].

Overlap of [1] aaa=bb with [5] abbb=bb:

Critical pair: aabb=bbbbb.

Referenced by [7], [8].

Overlap of [4] babb=bb with [3] bba=abb:

Critical pair: baabb=bba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [5] abbb=bb with [3] bba=abb:

Critical pair: abbabb=bbba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Simplify [3] bba=abb.

Reduce RHS:

Defines rule #3.