Certificate for #4417 ⟨a, b, c | aba=1, acca=c⟩

Completion settings:

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

Axiom: aba=1.

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

Axiom: acca=c.

Defines rule #1.

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

Overlap of [1] aba=1 with [1] aba=1:

Critical pair: ab=ba.

Defines rule #6.

Referenced by [4], [5], [7].

Overlap of [1] aba=1 with [3] ab=ba:

Critical pair: baa=1.

Defines rule #4.

Referenced by [9].

Overlap of [1] aba=1 with [2] acca=c:

Critical pair: abc=cca.

Reduce LHS:

Defines rule #5.

Referenced by [8].

Overlap of [2] acca=c with [2] acca=c:

Critical pair: accc=ccca.

Flip LHS and RHS.

Defines rule #2.

Overlap of [2] acca=c with [3] ab=ba:

Critical pair: accba=cb.

Referenced by [9], [10].

Overlap of [5] bac=cca with [2] acca=c:

Critical pair: bc=ccaca.

Defines rule #3.

Overlap of [7] accba=cb with [4] baa=1:

Critical pair: acc=cba.

Flip LHS and RHS.

Referenced by [10].

Overlap of [7] accba=cb with [9] cba=acc:

Critical pair: acacc=cb.

Flip LHS and RHS.

Defines rule #7.