Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₁: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₃
t₁₂: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₀, X₃, X₄, X₅) :|: X₃ ≤ 0
t₁₃: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₃-1, X₄, X₅)
t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l13(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < 0
t₁₅: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l14(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₂
t₁₆: l13(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₂+1, X₃, X₄, X₅)
t₁₇: l14(X₀, X₁, X₂, X₃, X₄, X₅) → l15(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₄, X₅, X₂, X₃, X₄, X₅)
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₁, X₄, X₅) :|: X₀ ≤ X₁
t₈: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₀
t₁₀: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀+999, X₁+1000, X₂, X₃, X₄, X₅)

Preprocessing

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l11

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l15

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l12

Found invariant X₅ ≤ X₁ ∧ 1+X₄ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l13

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location l8

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ for location l10

Found invariant X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l9

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l14

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₁: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l11(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₃ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁
t₁₂: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₀, X₃, X₄, X₅) :|: X₃ ≤ 0 ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁
t₁₃: l11(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₃-1, X₄, X₅) :|: X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₁₄: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l13(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ < 0 ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₁₅: l12(X₀, X₁, X₂, X₃, X₄, X₅) → l14(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₂ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₁₆: l13(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₂+1, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ 1+X₄ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₁₇: l14(X₀, X₁, X₂, X₃, X₄, X₅) → l15(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₄: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₄, X₅, X₂, X₃, X₄, X₅)
t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₁, X₄, X₅) :|: X₀ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀
t₈: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₀ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀
t₁₀: l9(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀+999, X₁+1000, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l11

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l15

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l12

Found invariant X₅ ≤ X₁ ∧ 1+X₄ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l13

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location l8

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ for location l10

Found invariant X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l9

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l14

Time-Bound by TWN-Loops:

TWN-Loops: t₈ 2⋅X₄+2⋅X₅+4 {O(n)}

TWN-Loops:

entry: t₇: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₄, X₅, X₂, X₃, X₄, X₅)
results in twn-loop: twn:Inv: [X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+999,X₁+1000,X₂,X₃,X₄,X₅) :|: X₁ < X₀
order: [X₀; X₁; X₄; X₅]
closed-form:
X₀: X₀ + [[n != 0]] * 999 * n^1
X₁: X₁ + [[n != 0]] * 1000 * n^1
X₄: X₄
X₅: X₅

Termination: true
Formula:

1 < 0
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₁ < X₀
alphas_abs: X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₇:
X₀: X₄ {O(n)}
X₁: X₅ {O(n)}
Runtime-bound of t₇: 1 {O(1)}
Results in: 2⋅X₄+2⋅X₅+4 {O(n)}

2⋅X₄+2⋅X₅+4 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₀ 2⋅X₄+2⋅X₅+4 {O(n)}

relevant size-bounds w.r.t. t₇:
X₀: X₄ {O(n)}
X₁: X₅ {O(n)}
Runtime-bound of t₇: 1 {O(1)}
Results in: 2⋅X₄+2⋅X₅+4 {O(n)}

2⋅X₄+2⋅X₅+4 {O(n)}

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l11

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l15

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l12

Found invariant X₅ ≤ X₁ ∧ 1+X₄ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l13

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location l8

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ for location l10

Found invariant X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l9

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l14

Time-Bound by TWN-Loops:

TWN-Loops: t₁₁ 4000⋅X₄+4004⋅X₅+8004 {O(n)}

TWN-Loops:

entry: t₉: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l10(X₀, X₁, X₂, X₁, X₄, X₅) :|: X₀ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀
results in twn-loop: twn:Inv: [X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀,X₁,X₂,X₃-1,X₄,X₅) :|: 0 < X₃
order: [X₀; X₁; X₃; X₄; X₅]
closed-form:
X₀: X₀
X₁: X₁
X₃: X₃ + [[n != 0]] * -1 * n^1
X₄: X₄
X₅: X₅

Termination: true
Formula:

1 < 0
∨ 0 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: 0 < X₃
alphas_abs: X₃
M: 0
N: 1
Bound: 2⋅X₃+2 {O(n)}

relevant size-bounds w.r.t. t₉:
X₃: 2000⋅X₄+2002⋅X₅+4000 {O(n)}
Runtime-bound of t₉: 1 {O(1)}
Results in: 4000⋅X₄+4004⋅X₅+8004 {O(n)}

4000⋅X₄+4004⋅X₅+8004 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₃ 4000⋅X₄+4004⋅X₅+8004 {O(n)}

relevant size-bounds w.r.t. t₉:
X₃: 2000⋅X₄+2002⋅X₅+4000 {O(n)}
Runtime-bound of t₉: 1 {O(1)}
Results in: 4000⋅X₄+4004⋅X₅+8004 {O(n)}

4000⋅X₄+4004⋅X₅+8004 {O(n)}

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location l11

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l15

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l12

Found invariant X₅ ≤ X₁ ∧ 1+X₄ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location l13

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location l8

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ for location l10

Found invariant X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l9

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l14

Time-Bound by TWN-Loops:

TWN-Loops: t₁₄ 7992⋅X₅+8000⋅X₄+15988 {O(n)}

TWN-Loops:

entry: t₁₂: l10(X₀, X₁, X₂, X₃, X₄, X₅) → l12(X₀, X₁, X₀, X₃, X₄, X₅) :|: X₃ ≤ 0 ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁
results in twn-loop: twn:Inv: [X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₅ ≤ X₁ ∧ 1+X₄ ≤ 0 ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 2+X₂+X₄ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₂+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀,X₁,X₂+1,X₃,X₄,X₅) :|: X₂ < 0
order: [X₀; X₁; X₂; X₃; X₄; X₅]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1
X₃: X₃
X₄: X₄
X₅: X₅

Termination: true
Formula:

1 < 0
∨ X₂ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₂ < 0
alphas_abs: X₂
M: 0
N: 1
Bound: 2⋅X₂+2 {O(n)}

relevant size-bounds w.r.t. t₁₂:
X₂: 3996⋅X₅+4000⋅X₄+7992 {O(n)}
Runtime-bound of t₁₂: 1 {O(1)}
Results in: 7992⋅X₅+8000⋅X₄+15988 {O(n)}

7992⋅X₅+8000⋅X₄+15988 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₆ 7992⋅X₅+8000⋅X₄+15988 {O(n)}

relevant size-bounds w.r.t. t₁₂:
X₂: 3996⋅X₅+4000⋅X₄+7992 {O(n)}
Runtime-bound of t₁₂: 1 {O(1)}
Results in: 7992⋅X₅+8000⋅X₄+15988 {O(n)}

7992⋅X₅+8000⋅X₄+15988 {O(n)}

All Bounds

Timebounds

Overall timebound:23996⋅X₅+24004⋅X₄+48004 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: 4000⋅X₄+4004⋅X₅+8004 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 4000⋅X₄+4004⋅X₅+8004 {O(n)}
t₁₄: 7992⋅X₅+8000⋅X₄+15988 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 7992⋅X₅+8000⋅X₄+15988 {O(n)}
t₁₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 2⋅X₄+2⋅X₅+4 {O(n)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₄+2⋅X₅+4 {O(n)}

Costbounds

Overall costbound: 23996⋅X₅+24004⋅X₄+48004 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: 4000⋅X₄+4004⋅X₅+8004 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 4000⋅X₄+4004⋅X₅+8004 {O(n)}
t₁₄: 7992⋅X₅+8000⋅X₄+15988 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 7992⋅X₅+8000⋅X₄+15988 {O(n)}
t₁₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 2⋅X₄+2⋅X₅+4 {O(n)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₄+2⋅X₅+4 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₁₁, X₀: 1998⋅X₅+2000⋅X₄+3996 {O(n)}
t₁₁, X₁: 2000⋅X₄+2002⋅X₅+4000 {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 2000⋅X₄+2002⋅X₅+4000 {O(n)}
t₁₁, X₄: 2⋅X₄ {O(n)}
t₁₁, X₅: 2⋅X₅ {O(n)}
t₁₂, X₀: 3996⋅X₅+4000⋅X₄+7992 {O(n)}
t₁₂, X₁: 4000⋅X₄+4004⋅X₅+8000 {O(n)}
t₁₂, X₂: 3996⋅X₅+4000⋅X₄+7992 {O(n)}
t₁₂, X₃: 4000⋅X₄+4004⋅X₅+8000 {O(n)}
t₁₂, X₄: 4⋅X₄ {O(n)}
t₁₂, X₅: 4⋅X₅ {O(n)}
t₁₃, X₀: 1998⋅X₅+2000⋅X₄+3996 {O(n)}
t₁₃, X₁: 2000⋅X₄+2002⋅X₅+4000 {O(n)}
t₁₃, X₂: 2⋅X₂ {O(n)}
t₁₃, X₃: 2000⋅X₄+2002⋅X₅+4000 {O(n)}
t₁₃, X₄: 2⋅X₄ {O(n)}
t₁₃, X₅: 2⋅X₅ {O(n)}
t₁₄, X₀: 3996⋅X₅+4000⋅X₄+7992 {O(n)}
t₁₄, X₁: 4000⋅X₄+4004⋅X₅+8000 {O(n)}
t₁₄, X₂: 3996⋅X₅+4000⋅X₄+7992 {O(n)}
t₁₄, X₃: 4000⋅X₄+4004⋅X₅+8000 {O(n)}
t₁₄, X₄: 4⋅X₄ {O(n)}
t₁₄, X₅: 4⋅X₅ {O(n)}
t₁₅, X₀: 7992⋅X₅+8000⋅X₄+15984 {O(n)}
t₁₅, X₁: 8000⋅X₄+8008⋅X₅+16000 {O(n)}
t₁₅, X₂: 7992⋅X₅+8000⋅X₄+15984 {O(n)}
t₁₅, X₃: 8000⋅X₄+8008⋅X₅+16000 {O(n)}
t₁₅, X₄: 8⋅X₄ {O(n)}
t₁₅, X₅: 8⋅X₅ {O(n)}
t₁₆, X₀: 3996⋅X₅+4000⋅X₄+7992 {O(n)}
t₁₆, X₁: 4000⋅X₄+4004⋅X₅+8000 {O(n)}
t₁₆, X₂: 3996⋅X₅+4000⋅X₄+7992 {O(n)}
t₁₆, X₃: 4000⋅X₄+4004⋅X₅+8000 {O(n)}
t₁₆, X₄: 4⋅X₄ {O(n)}
t₁₆, X₅: 4⋅X₅ {O(n)}
t₁₇, X₀: 7992⋅X₅+8000⋅X₄+15984 {O(n)}
t₁₇, X₁: 8000⋅X₄+8008⋅X₅+16000 {O(n)}
t₁₇, X₂: 7992⋅X₅+8000⋅X₄+15984 {O(n)}
t₁₇, X₃: 8000⋅X₄+8008⋅X₅+16000 {O(n)}
t₁₇, X₄: 8⋅X₄ {O(n)}
t₁₇, X₅: 8⋅X₅ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₇, X₀: X₄ {O(n)}
t₇, X₁: X₅ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₈, X₀: 1998⋅X₅+1999⋅X₄+3996 {O(n)}
t₈, X₁: 2000⋅X₄+2001⋅X₅+4000 {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: X₅ {O(n)}
t₉, X₀: 1998⋅X₅+2000⋅X₄+3996 {O(n)}
t₉, X₁: 2000⋅X₄+2002⋅X₅+4000 {O(n)}
t₉, X₂: 2⋅X₂ {O(n)}
t₉, X₃: 2000⋅X₄+2002⋅X₅+4000 {O(n)}
t₉, X₄: 2⋅X₄ {O(n)}
t₉, X₅: 2⋅X₅ {O(n)}
t₁₀, X₀: 1998⋅X₅+1999⋅X₄+3996 {O(n)}
t₁₀, X₁: 2000⋅X₄+2001⋅X₅+4000 {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: X₅ {O(n)}