Certificate for #7281 ⟨a, b, c | ab=1, aaaa=cc⟩

Completion settings:

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

Axiom: ab=1.

Referenced by [3], [5], [7], [9], [11].

Axiom: aaaa=cc.

Referenced by [3], [4], [6].

Overlap of [2] aaaa=cc with [1] ab=1:

Critical pair: aaa=ccb.

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

Overlap of [2] aaaa=cc with [2] aaaa=cc:

Critical pair: acc=cca.

Flip LHS and RHS.

Referenced by [5].

Overlap of [4] cca=acc with [1] ab=1:

Critical pair: cc=accb.

Flip LHS and RHS.

Referenced by [6], [8], [10], [12].

Overlap of [2] aaaa=cc with [5] accb=cc:

Critical pair: aaacc=ccccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Overlap of [3] aaa=ccb with [1] ab=1:

Critical pair: aa=ccbb.

Referenced by [8], [9], [10].

Overlap of [3] aaa=ccb with [5] accb=cc:

Critical pair: aacc=ccbccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [7] aa=ccbb with [1] ab=1:

Critical pair: a=ccbbb.

Defines rule #6.

Referenced by [10], [11], [12].

Overlap of [7] aa=ccbb with [5] accb=cc:

Critical pair: acc=ccbbccb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [1] ab=1 with [9] a=ccbbb:

Critical pair: ccbbbb=1.

Defines rule #2.

Overlap of [5] accb=cc with [9] a=ccbbb:

Critical pair: ccbbbccb=cc.

Defines rule #5.