Certificate for #4098 ⟨a, b | aabaabbaa=ba⟩

Completion settings:

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

Axiom: aabaabbaa=ba.

Referenced by [3].

Axiom: aabaabb=c.

Referenced by [3], [4].

Overlap of [1] aabaabbaa=ba with [2] aabaabb=c:

Critical pair: caa=ba.

Flip LHS and RHS.

Defines rule #1.

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

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

Critical pair: aacaaabb=c.

Defines rule #4.

Referenced by [5], [6], [7], [8].

Overlap of [3] ba=caa with [4] aacaaabb=c:

Critical pair: bc=caaacaaabb.

Reduce RHS:

Defines rule #2.

Referenced by [6], [7].

Overlap of [4] aacaaabb=c with [3] ba=caa:

Critical pair: aacaaabcaa=ca.

Reduce LHS:

Defines rule #3.

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

Overlap of [4] aacaaabb=c with [5] bc=cac:

Critical pair: aacaaabcac=cc.

Reduce LHS:

Defines rule #6.

Referenced by [10], [12].

Overlap of [6] aacaaacacaa=ca with [4] aacaaabb=c:

Critical pair: aacaaacacc=cacaaabb.

Flip LHS and RHS.

Defines rule #7.

Referenced by [11], [12].

Overlap of [6] aacaaacacaa=ca with [6] aacaaacacaa=ca:

Critical pair: aacaaacacca=cacaaacacaa.

Defines rule #5.

Overlap of [6] aacaaacacaa=ca with [7] aacaaacacac=cc:

Critical pair: aacaaacaccc=cacaaacacac.

Defines rule #8.

Overlap of [6] aacaaacacaa=ca with [8] cacaaabb=aacaaacacc:

Critical pair: aacaaaaacaaacacc=caabb.

Defines rule #9.

Overlap of [7] aacaaacacac=cc with [8] cacaaabb=aacaaacacc:

Critical pair: aacaaacaaacaaacacc=ccaaabb.

Defines rule #10.