Certificate for #365 ⟨a, b, c | aba=b, cac=1⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [4].

Axiom: cac=1.

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

Overlap of [2] cac=1 with [2] cac=1:

Critical pair: ca=ac.

Flip LHS and RHS.

Defines rule #1.

Referenced by [4], [6].

Overlap of [1] aba=b with [3] ac=ca:

Critical pair: abca=bc.

Referenced by [5].

Overlap of [4] abca=bc with [2] cac=1:

Critical pair: ab=bcc.

Defines rule #3.

Referenced by [7].

Overlap of [2] cac=1 with [3] ac=ca:

Critical pair: cca=1.

Defines rule #2.

Referenced by [7], [8].

Overlap of [6] cca=1 with [5] ab=bcc:

Critical pair: ccbcc=b.

Referenced by [8].

Overlap of [7] ccbcc=b with [6] cca=1:

Critical pair: ccb=ba.

Defines rule #4.