Certificate for #2625 ⟨a, b, c | aba=b, cacc=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 [5], [10].

Axiom: cacc=1.

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

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

Critical pair: cac=acc.

Flip LHS and RHS.

Referenced by [4].

Overlap of [3] acc=cac with [2] cacc=1:

Critical pair: ac=cacacc.

Reduce RHS:

Defines rule #1.

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

Overlap of [1] aba=b with [4] ac=ca:

Critical pair: abca=bc.

Referenced by [6].

Overlap of [5] abca=bc with [4] ac=ca:

Critical pair: abcca=bcc.

Referenced by [7].

Overlap of [6] abcca=bcc with [4] ac=ca:

Critical pair: abccca=bccc.

Referenced by [9].

Overlap of [2] cacc=1 with [4] ac=ca:

Critical pair: ccac=1.

Reduce LHS:

Defines rule #2.

Referenced by [9], [10].

Overlap of [7] abccca=bccc with [8] ccca=1:

Critical pair: ab=bccc.

Defines rule #3.

Overlap of [8] ccca=1 with [1] aba=b:

Critical pair: cccb=ba.

Defines rule #4.