Certificate for #1572 ⟨a, b, c | aaa=bb, acc=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: acc=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] acc=1:

Critical pair: aa=bbcc.

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

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

Critical pair: bbcca=bb.

Referenced by [8], [10].

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

Critical pair: bbbbcc=abba.

Reduce RHS:

Defines rule #1.

Referenced by [11].

Overlap of [4] aa=bbcc with [2] acc=1:

Critical pair: a=bbcccc.

Defines rule #5.

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

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

Critical pair: abbcc=bbcca.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Referenced by [11].

Overlap of [2] acc=1 with [7] a=bbcccc:

Critical pair: bbcccccc=1.

Defines rule #2.

Simplify [5] bbcca=bb.

Reduce LHS:

Referenced by [11].

Overlap of [8] bbccccbbcc=bb with [10] bbccbbcccc=bb:

Critical pair: bbccccbb=bbbbcccc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.