Certificate for #4180 ⟨a, b | aabbabbaa=ab⟩

Completion settings:

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

Axiom: aabbabbaa=ab.

Referenced by [3].

Axiom: abb=c.

Referenced by [3], [4].

Overlap of [1] aabbabbaa=ab with [2] abb=c:

Critical pair: acabbaa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

Overlap of [2] abb=c with [3] ab=accaa:

Critical pair: accaab=c.

Reduce LHS:

Defines rule #2.

Referenced by [5], [6].

Overlap of [4] accaaccaa=c with [3] ab=accaa:

Critical pair: accaaccaaccaa=cb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: accac=cccaa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

Simplify [5] cb=cccaa.

Reduce RHS:

Defines rule #4.