Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
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) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₉: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₁+X₄+50, X₁, X₂, X₃, X₄)
t₁₀: l11(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₈: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁-1, X₂, X₃, X₄)
t₁₅: l13(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂-1, X₃, X₄)
t₁₆: l14(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₄)
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₁₃: l5(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₂
t₁₄: l5(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄) :|: X₂ < 0
t₁₁: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₁₂: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₀, X₃, X₄)
t₅: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₃, X₂, X₃, X₄)
t₇: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 100
t₆: l9(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄) :|: 100 < X₁

Preprocessing

Found invariant X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l11

Found invariant X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l6

Found invariant X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₁+X₂ ≤ 99 ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100 for location l15

Found invariant 101 ≤ X₃ ∧ 202 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 101 ≤ X₁ for location l12

Found invariant X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l7

Found invariant X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100 for location l5

Found invariant 0 ≤ 150+X₄ ∧ 0 ≤ 150+X₂+X₄ ∧ X₂ ≤ 150+X₄ ∧ X₁ ≤ 250+X₄ ∧ 0 ≤ 150+X₀+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ 100+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ 0 ≤ X₀ for location l13

Found invariant X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l10

Found invariant X₁ ≤ X₃ for location l9

Found invariant X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₁+X₂ ≤ 99 ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100 for location l14

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
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) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₉: l10(X₀, X₁, X₂, X₃, X₄) → l11(X₁+X₄+50, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃ ∧ X₁ ≤ 100
t₁₀: l11(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100
t₈: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁-1, X₂, X₃, X₄) :|: 101 ≤ X₃ ∧ 202 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 101 ≤ X₁
t₁₅: l13(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂-1, X₃, X₄) :|: 0 ≤ 150+X₄ ∧ 0 ≤ 150+X₂+X₄ ∧ X₂ ≤ 150+X₄ ∧ X₁ ≤ 250+X₄ ∧ 0 ≤ 150+X₀+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ 100+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ 0 ≤ X₀
t₁₆: l14(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₁+X₂ ≤ 99 ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₁₃: l5(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₂ ∧ X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100
t₁₄: l5(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄) :|: X₂ < 0 ∧ X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100
t₁₁: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100
t₁₂: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₀, X₃, X₄) :|: X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100
t₅: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₃, X₂, X₃, X₄)
t₇: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 100 ∧ X₁ ≤ X₃
t₆: l9(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄) :|: 100 < X₁ ∧ X₁ ≤ X₃

Found invariant X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l11

Found invariant X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l6

Found invariant X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₁+X₂ ≤ 99 ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100 for location l15

Found invariant 101 ≤ X₃ ∧ 202 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 101 ≤ X₁ for location l12

Found invariant X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l7

Found invariant X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100 for location l5

Found invariant 0 ≤ 150+X₄ ∧ 0 ≤ 150+X₂+X₄ ∧ X₂ ≤ 150+X₄ ∧ X₁ ≤ 250+X₄ ∧ 0 ≤ 150+X₀+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ 100+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ 0 ≤ X₀ for location l13

Found invariant X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l10

Found invariant X₁ ≤ X₃ for location l9

Found invariant X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₁+X₂ ≤ 99 ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100 for location l14

Time-Bound by TWN-Loops:

TWN-Loops: t₈ 2⋅X₃+4 {O(n)}

TWN-Loops:

entry: t₅: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₃, X₂, X₃, X₄)
results in twn-loop: twn:Inv: [X₁ ≤ X₃ ∧ 101 ≤ X₃ ∧ 202 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 101 ≤ X₁] , (X₀,X₁,X₂,X₃,X₄) -> (X₀,X₁-1,X₂,X₃,X₄) :|: 100 < X₁
order: [X₁; X₃]
closed-form:
X₁: X₁ + [[n != 0]] * -1 * n^1
X₃: X₃

Termination: true
Formula:

1 < 0
∨ 100 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: 100 < X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₅:
X₁: X₃ {O(n)}
Runtime-bound of t₅: 1 {O(1)}
Results in: 2⋅X₃+4 {O(n)}

2⋅X₃+4 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₆ 2⋅X₃+4 {O(n)}

relevant size-bounds w.r.t. t₅:
X₁: X₃ {O(n)}
Runtime-bound of t₅: 1 {O(1)}
Results in: 2⋅X₃+4 {O(n)}

2⋅X₃+4 {O(n)}

Found invariant X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l11

Found invariant X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l6

Found invariant X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₁+X₂ ≤ 99 ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100 for location l15

Found invariant 101 ≤ X₃ ∧ 202 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 101 ≤ X₁ for location l12

Found invariant X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l7

Found invariant X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100 for location l5

Found invariant 0 ≤ 150+X₄ ∧ 0 ≤ 150+X₂+X₄ ∧ X₂ ≤ 150+X₄ ∧ X₁ ≤ 250+X₄ ∧ 0 ≤ 150+X₀+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ 100+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ 0 ≤ X₀ for location l13

Found invariant X₁ ≤ X₃ ∧ X₁ ≤ 100 for location l10

Found invariant X₁ ≤ X₃ for location l9

Found invariant X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₁+X₂ ≤ 99 ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100 for location l14

Time-Bound by TWN-Loops:

TWN-Loops: t₁₅ 4⋅X₃+4⋅X₄+104 {O(n)}

TWN-Loops:

entry: t₁₂: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₀, X₃, X₄) :|: X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100
results in twn-loop: twn:Inv: [X₂ ≤ 150+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 100 ∧ 0 ≤ 150+X₄ ∧ 0 ≤ 150+X₂+X₄ ∧ X₂ ≤ 150+X₄ ∧ X₁ ≤ 250+X₄ ∧ 0 ≤ 150+X₀+X₄ ∧ X₀ ≤ 150+X₄ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ 100+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100+X₀ ∧ 0 ≤ X₀] , (X₀,X₁,X₂,X₃,X₄) -> (X₀,X₁,X₂-1,X₃,X₄) :|: 0 ≤ X₂
order: [X₀; X₁; X₂; X₃; X₄]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ + [[n != 0]] * -1 * n^1
X₃: X₃
X₄: X₄

Termination: true
Formula:

1 < 0
∨ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0

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

relevant size-bounds w.r.t. t₁₂:
X₂: 2⋅X₃+2⋅X₄+50 {O(n)}
Runtime-bound of t₁₂: 1 {O(1)}
Results in: 4⋅X₃+4⋅X₄+104 {O(n)}

4⋅X₃+4⋅X₄+104 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₃ 4⋅X₃+4⋅X₄+104 {O(n)}

relevant size-bounds w.r.t. t₁₂:
X₂: 2⋅X₃+2⋅X₄+50 {O(n)}
Runtime-bound of t₁₂: 1 {O(1)}
Results in: 4⋅X₃+4⋅X₄+104 {O(n)}

4⋅X₃+4⋅X₄+104 {O(n)}

All Bounds

Timebounds

Overall timebound:12⋅X₃+8⋅X₄+229 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₈: 2⋅X₃+4 {O(n)}
t₁₅: 4⋅X₃+4⋅X₄+104 {O(n)}
t₁₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₃: 4⋅X₃+4⋅X₄+104 {O(n)}
t₁₄: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 2⋅X₃+4 {O(n)}
t₇: 1 {O(1)}

Costbounds

Overall costbound: 12⋅X₃+8⋅X₄+229 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₈: 2⋅X₃+4 {O(n)}
t₁₅: 4⋅X₃+4⋅X₄+104 {O(n)}
t₁₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₁₃: 4⋅X₃+4⋅X₄+104 {O(n)}
t₁₄: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 2⋅X₃+4 {O(n)}
t₇: 1 {O(1)}

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)}
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)}
t₉, X₀: 2⋅X₃+2⋅X₄+50 {O(n)}
t₉, X₁: 2⋅X₃ {O(n)}
t₉, X₂: 2⋅X₂ {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}
t₉, X₄: 2⋅X₄ {O(n)}
t₁₀, X₀: 2⋅X₃+2⋅X₄+50 {O(n)}
t₁₀, X₁: 2⋅X₃ {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: 2⋅X₃ {O(n)}
t₁₀, X₄: 2⋅X₄ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₃ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₁₅, X₀: 2⋅X₃+2⋅X₄+50 {O(n)}
t₁₅, X₁: 2⋅X₃ {O(n)}
t₁₅, X₂: 2⋅X₃+2⋅X₄+51 {O(n)}
t₁₅, X₃: 2⋅X₃ {O(n)}
t₁₅, X₄: 2⋅X₄ {O(n)}
t₁₆, X₀: 4⋅X₃+4⋅X₄+100 {O(n)}
t₁₆, X₁: 4⋅X₃ {O(n)}
t₁₆, X₂: 4⋅X₃+4⋅X₄+101 {O(n)}
t₁₆, X₃: 4⋅X₃ {O(n)}
t₁₆, X₄: 4⋅X₄ {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)}
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)}
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)}
t₁₃, X₀: 2⋅X₃+2⋅X₄+50 {O(n)}
t₁₃, X₁: 2⋅X₃ {O(n)}
t₁₃, X₂: 2⋅X₃+2⋅X₄+51 {O(n)}
t₁₃, X₃: 2⋅X₃ {O(n)}
t₁₃, X₄: 2⋅X₄ {O(n)}
t₁₄, X₀: 4⋅X₃+4⋅X₄+100 {O(n)}
t₁₄, X₁: 4⋅X₃ {O(n)}
t₁₄, X₂: 4⋅X₃+4⋅X₄+101 {O(n)}
t₁₄, X₃: 4⋅X₃ {O(n)}
t₁₄, X₄: 4⋅X₄ {O(n)}
t₁₁, X₀: 2⋅X₃+2⋅X₄+50 {O(n)}
t₁₁, X₁: 2⋅X₃ {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 2⋅X₃ {O(n)}
t₁₁, X₄: 2⋅X₄ {O(n)}
t₁₂, X₀: 2⋅X₃+2⋅X₄+50 {O(n)}
t₁₂, X₁: 2⋅X₃ {O(n)}
t₁₂, X₂: 2⋅X₃+2⋅X₄+50 {O(n)}
t₁₂, X₃: 2⋅X₃ {O(n)}
t₁₂, X₄: 2⋅X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₃ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₃ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: 2⋅X₀ {O(n)}
t₇, X₁: 2⋅X₃ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₇, X₄: 2⋅X₄ {O(n)}