Certificate for #2608 ⟨a, b, c | aba=b, acca=1⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [7], [8], [9].

Axiom: acca=1.

Referenced by [4].

Axiom: cc=d.

Defines rule #7.

Referenced by [4], [6].

Overlap of [2] acca=1 with [3] cc=d:

Critical pair: ada=1.

Referenced by [5], [7], [8], [10].

Overlap of [4] ada=1 with [4] ada=1:

Critical pair: ad=da.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [9], [10], [12], [13].

Overlap of [3] cc=d with [3] cc=d:

Critical pair: cd=dc.

Flip LHS and RHS.

Defines rule #3.

Referenced by [11].

Overlap of [1] aba=b with [4] ada=1:

Critical pair: ab=bda.

Reduce RHS:

Defines rule #5.

Overlap of [4] ada=1 with [1] aba=b:

Critical pair: adb=ba.

Referenced by [9].

Overlap of [5] da=ad with [1] aba=b:

Critical pair: db=adba.

Reduce RHS:

Defines rule #6.

Overlap of [4] ada=1 with [5] da=ad:

Critical pair: aad=1.

Defines rule #2.

Referenced by [11], [13].

Overlap of [10] aad=1 with [6] dc=cd:

Critical pair: aacd=c.

Referenced by [12].

Overlap of [11] aacd=c with [5] da=ad:

Critical pair: aacad=ca.

Referenced by [13].

Overlap of [12] aacad=ca with [5] da=ad:

Critical pair: aacaad=caa.

Reduce LHS:

Defines rule #4.