Certificate for #4472 ⟨a, b | aaaabbba=aab⟩

Completion settings:

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

Axiom: aaaabbba=aab.

Referenced by [3].

Axiom: aab=c.

Defines rule #1.

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

Simplify [1] aaaabbba=aab.

Reduce RHS:

Referenced by [4].

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

Critical pair: aacbba=c.

Defines rule #6.

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

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

Critical pair: aacbbc=cab.

Defines rule #4.

Referenced by [6], [9].

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

Critical pair: aacbbc=cacbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

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

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

Critical pair: cacbbc=cabab.

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] cacbba=cab with [4] aacbba=c:

Critical pair: cacbbc=cabacbba.

Flip LHS and RHS.

Defines rule #7.

Overlap of [6] cacbba=cab with [5] aacbbc=cab:

Critical pair: cacbbcab=cabacbbc.

Flip LHS and RHS.

Defines rule #5.