Certificate for #4550 ⟨a, b | aaabbaba=aab⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(c) = deg(a) = 0, c < a; deg(b) = 1
• Auxiliary generators:
  1. aab=c

Axiom: aaabbaba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #1.

Referenced by [3], [4], [5], [7].

Simplify [1] aaabbaba=aab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaabbaba=c with [2] aab=c:

Critical pair: acbaba=c.

Defines rule #5.

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

Overlap of [4] acbaba=c with [2] aab=c:

Critical pair: acbabc=cab.

Defines rule #4.

Referenced by [6], [9].

Overlap of [4] acbaba=c with [4] acbaba=c:

Critical pair: acbabc=ccbaba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [6] ccbaba=cab with [2] aab=c:

Critical pair: ccbabc=cabab.

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] ccbaba=cab with [4] acbaba=c:

Critical pair: ccbabc=cabcbaba.

Flip LHS and RHS.

Defines rule #7.

Overlap of [6] ccbaba=cab with [5] acbabc=cab:

Critical pair: ccbabcab=cabcbabc.

Flip LHS and RHS.

Defines rule #6.