Certificate for #3929 ⟨a, b | aaaabbaaa=ba⟩

Completion settings:

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

Axiom: aaaabbaaa=ba.

Referenced by [3].

Axiom: aabb=c.

Defines rule #9.

Referenced by [3], [4], [5], [6], [7], [10].

Overlap of [1] aaaabbaaa=ba with [2] aabb=c:

Critical pair: aacaaa=ba.

Flip LHS and RHS.

Defines rule #7.

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

Overlap of [2] aabb=c with [3] ba=aacaaa:

Critical pair: aabaacaaa=ca.

Reduce LHS:

Defines rule #3.

Referenced by [7], [8], [9], [11].

Overlap of [3] ba=aacaaa with [2] aabb=c:

Critical pair: bc=aacaaaabb.

Reduce RHS:

Defines rule #8.

Referenced by [6].

Overlap of [2] aabb=c with [5] bc=aacaac:

Critical pair: aabaacaac=cc.

Reduce LHS:

Defines rule #5.

Referenced by [11].

Overlap of [4] aaaacaaaacaaa=ca with [2] aabb=c:

Critical pair: aaaacaaaacac=cabb.

Flip LHS and RHS.

Defines rule #10.

Overlap of [4] aaaacaaaacaaa=ca with [4] aaaacaaaacaaa=ca:

Critical pair: aaaacca=caacaaa.

Defines rule #1.

Referenced by [10].

Overlap of [4] aaaacaaaacaaa=ca with [4] aaaacaaaacaaa=ca:

Critical pair: aaaacaaaacaca=caaacaaaacaaa.

Defines rule #4.

Overlap of [8] aaaacca=caacaaa with [2] aabb=c:

Critical pair: aaaaccc=caacaaaabb.

Reduce RHS:

Defines rule #2.

Overlap of [4] aaaacaaaacaaa=ca with [6] aaaacaaaacaac=cc:

Critical pair: aaaacaaaacacc=caaacaaaacaac.

Defines rule #6.