Certificate for #1569 ⟨a, b, c | aaa=bb, abc=1⟩

Completion settings:

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

Axiom: aaa=bb.

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

Axiom: abc=1.

Referenced by [4], [7], [9].

Overlap of [1] aaa=bb with [1] aaa=bb:

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] aaa=bb with [2] abc=1:

Critical pair: aa=bbbc.

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

Overlap of [1] aaa=bb with [4] aa=bbbc:

Critical pair: bbbca=bb.

Referenced by [8], [10].

Overlap of [3] bba=abb with [4] aa=bbbc:

Critical pair: bbbbbc=abba.

Reduce RHS:

Defines rule #1.

Referenced by [11].

Overlap of [4] aa=bbbc with [2] abc=1:

Critical pair: a=bbbcbc.

Defines rule #5.

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

Overlap of [4] aa=bbbc with [4] aa=bbbc:

Critical pair: abbbc=bbbca.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Referenced by [11].

Overlap of [2] abc=1 with [7] a=bbbcbc:

Critical pair: bbbcbcbc=1.

Defines rule #2.

Simplify [5] bbbca=bb.

Reduce LHS:

Referenced by [11].

Overlap of [8] bbbcbcbbbc=bb with [10] bbbcbbbcbc=bb:

Critical pair: bbbcbcbb=bbbbbcbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.