Certificate for #4161 ⟨a, b | aabbaaabb=ba⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(c) = deg(d) = 0, c < d; deg(a) = 1; deg(b) = 2
• Auxiliary generators:
  1. aab=c
  2. cba=d

Axiom: aabbaaabb=ba.

Referenced by [4].

Axiom: aab=c.

Defines rule #7.

Referenced by [4], [6], [8].

Axiom: cba=d.

Defines rule #4.

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

Overlap of [1] aabbaaabb=ba with [2] aab=c:

Critical pair: cbaaabb=ba.

Reduce LHS:

Defines rule #5.

Referenced by [5].

Overlap of [4] dcb=ba with [3] cba=d:

Critical pair: dd=baa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7], [8].

Overlap of [2] aab=c with [5] baa=dd:

Critical pair: aadd=caa.

Flip LHS and RHS.

Defines rule #2.

Overlap of [3] cba=d with [5] baa=dd:

Critical pair: cdd=da.

Flip LHS and RHS.

Defines rule #1.

Overlap of [5] baa=dd with [2] aab=c:

Critical pair: bc=ddb.

Flip LHS and RHS.

Defines rule #6.