Certificate for #6177 ⟨a, b, c | aa=1, abcacb=1⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #1.

Referenced by [5], [9], [11], [13], [16], [17], [19].

Axiom: abcacb=1.

Referenced by [4].

Axiom: cb=d.

Defines rule #3.

Referenced by [4], [6], [10], [18], [20].

Overlap of [2] abcacb=1 with [3] cb=d:

Critical pair: abcad=1.

Referenced by [5].

Overlap of [1] aa=1 with [4] abcad=1:

Critical pair: a=bcad.

Flip LHS and RHS.

Defines rule #8.

Referenced by [6], [7], [10], [14], [16].

Overlap of [3] cb=d with [5] bcad=a:

Critical pair: ca=dcad.

Flip LHS and RHS.

Defines rule #10.

Referenced by [7], [8], [15].

Overlap of [5] bcad=a with [6] dcad=ca:

Critical pair: bcaca=acad.

Referenced by [9], [12].

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

Critical pair: dcaca=cacad.

Flip LHS and RHS.

Defines rule #12.

Referenced by [16].

Overlap of [7] bcaca=acad with [1] aa=1:

Critical pair: bcac=acada.

Defines rule #9.

Referenced by [10].

Overlap of [9] bcac=acada with [3] cb=d:

Critical pair: bcad=acadab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11], [12].

Overlap of [1] aa=1 with [10] acadab=a:

Critical pair: aa=cadab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [15].

Overlap of [7] bcaca=acad with [10] acadab=a:

Critical pair: bca=acaddab.

Flip LHS and RHS.

Referenced by [13].

Overlap of [1] aa=1 with [12] acaddab=bca:

Critical pair: abca=caddab.

Flip LHS and RHS.

Referenced by [14], [15], [16].

Overlap of [5] bcad=a with [13] caddab=abca:

Critical pair: babca=adab.

Referenced by [19].

Overlap of [6] dcad=ca with [13] caddab=abca:

Critical pair: dabca=cadab.

Reduce RHS:

Referenced by [17].

Overlap of [13] caddab=abca with [5] bcad=a:

Critical pair: caddaa=abcacad.

Reduce LHS:

Reduce RHS:

Defines rule #11.

Overlap of [15] dabca=1 with [1] aa=1:

Critical pair: dabc=a.

Defines rule #6.

Referenced by [18].

Overlap of [17] dabc=a with [3] cb=d:

Critical pair: dabd=ab.

Defines rule #5.

Overlap of [14] babca=adab with [1] aa=1:

Critical pair: babc=adaba.

Defines rule #4.

Referenced by [20].

Overlap of [19] babc=adaba with [3] cb=d:

Critical pair: babd=adabab.

Defines rule #2.