Certificate for #1868 ⟨a, b | aaaabbaa=ba⟩

Completion settings:

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

Axiom: aaaabbaa=ba.

Referenced by [3].

Axiom: aaaabb=c.

Defines rule #4.

Referenced by [3], [4], [5], [6], [8].

Overlap of [1] aaaabbaa=ba with [2] aaaabb=c:

Critical pair: caa=ba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [5].

Overlap of [2] aaaabb=c with [3] ba=caa:

Critical pair: aaaabcaa=ca.

Referenced by [7].

Overlap of [3] ba=caa with [2] aaaabb=c:

Critical pair: bc=caaaaabb.

Reduce RHS:

Defines rule #3.

Referenced by [6], [7].

Overlap of [2] aaaabb=c with [5] bc=cac:

Critical pair: aaaabcac=cc.

Reduce LHS:

Defines rule #6.

Referenced by [10].

Simplify [4] aaaabcaa=ca.

Reduce LHS:

Defines rule #2.

Referenced by [8], [9], [10], [11].

Overlap of [7] aaaacacaa=ca with [2] aaaabb=c:

Critical pair: aaaacacc=caaabb.

Flip LHS and RHS.

Defines rule #7.

Referenced by [11].

Overlap of [7] aaaacacaa=ca with [7] aaaacacaa=ca:

Critical pair: aaaacacca=caaacacaa.

Defines rule #5.

Overlap of [7] aaaacacaa=ca with [6] aaaacacac=cc:

Critical pair: aaaacaccc=caaacacac.

Defines rule #8.

Overlap of [7] aaaacacaa=ca with [8] caaabb=aaaacacc:

Critical pair: aaaacaaaaacacc=caabb.

Defines rule #9.