Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(F, 0, 0, X₃, X₄) :|: F+1 ≤ 0
t₁: l0(X₀, X₁, X₂, X₃, X₄) → l1(F, 0, 0, X₃, X₄) :|: 1 ≤ F
t₂: l0(X₀, X₁, X₂, X₃, X₄) → l1(0, 1023, 0, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂+1, X₃+2, X₄) :|: X₂ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₄ ∧ 1+X₁ ≤ X₂ ∧ X₄ ≤ 1022
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₂ ∧ 1023 ≤ X₄
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₂ ∧ X₄+1 ≤ 0

Preprocessing

Eliminate variables {X₀,X₃} that do not contribute to the problem

Found invariant X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ 1023 ∧ 0 ≤ X₁ for location l2

Found invariant X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1023+X₂ ∧ X₁ ≤ 1023 ∧ 0 ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₁, X₂, X₄
Temp_Vars: F
Locations: l0, l1, l2
Transitions:
t₁₃: l0(X₁, X₂, X₄) → l1(0, 0, X₄) :|: F+1 ≤ 0
t₁₄: l0(X₁, X₂, X₄) → l1(0, 0, X₄) :|: 1 ≤ F
t₁₅: l0(X₁, X₂, X₄) → l1(1023, 0, X₄)
t₁₆: l1(X₁, X₂, X₄) → l1(X₁, X₂+1, X₄) :|: X₂ ≤ X₁ ∧ X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1023+X₂ ∧ X₁ ≤ 1023 ∧ 0 ≤ X₁
t₁₇: l1(X₁, X₂, X₄) → l2(X₁, X₂, X₄) :|: 0 ≤ X₄ ∧ 1+X₁ ≤ X₂ ∧ X₄ ≤ 1022 ∧ X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1023+X₂ ∧ X₁ ≤ 1023 ∧ 0 ≤ X₁
t₁₈: l1(X₁, X₂, X₄) → l2(X₁, X₂, X₄) :|: 1+X₁ ≤ X₂ ∧ 1023 ≤ X₄ ∧ X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1023+X₂ ∧ X₁ ≤ 1023 ∧ 0 ≤ X₁
t₁₉: l1(X₁, X₂, X₄) → l2(X₁, X₂, X₄) :|: 1+X₁ ≤ X₂ ∧ X₄+1 ≤ 0 ∧ X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1023+X₂ ∧ X₁ ≤ 1023 ∧ 0 ≤ X₁

Found invariant X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 1024 ≤ X₂ ∧ 2047 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ 1023 ∧ 1023 ≤ X₁ for location l2

Found invariant X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 0 ≤ X₂ ∧ 1023 ≤ X₁+X₂ ∧ X₁ ≤ 1023+X₂ ∧ X₁ ≤ 1023 ∧ 1023 ≤ X₁ for location l1

Found invariant X₂ ≤ 1 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l2

Found invariant X₂ ≤ 1 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l1

Found invariant X₂ ≤ 1 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l2

Found invariant X₂ ≤ 1 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₁₆ 2058 {O(1)}

TWN-Loops:

entry: t₁₅: l0(X₁, X₂, X₄) → l1(1023, 0, X₄)
results in twn-loop: twn:Inv: [X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1023+X₂ ∧ X₁ ≤ 1023 ∧ 0 ≤ X₁] , (X₁,X₂,X₄) -> (X₁,X₂+1,X₄) :|: X₂ ≤ X₁
entry: t₁₄: l0(X₁, X₂, X₄) → l1(0, 0, X₄) :|: 1 ≤ F
results in twn-loop: twn:Inv: [X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1023+X₂ ∧ X₁ ≤ 1023 ∧ 0 ≤ X₁] , (X₁,X₂,X₄) -> (X₁,X₂+1,X₄) :|: X₂ ≤ X₁
entry: t₁₃: l0(X₁, X₂, X₄) → l1(0, 0, X₄) :|: F+1 ≤ 0
results in twn-loop: twn:Inv: [X₂ ≤ 1024 ∧ X₂ ≤ 1+X₁ ∧ X₁+X₂ ≤ 2047 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 1023+X₂ ∧ X₁ ≤ 1023 ∧ 0 ≤ X₁] , (X₁,X₂,X₄) -> (X₁,X₂+1,X₄) :|: X₂ ≤ X₁
order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂

Stabilization-Threshold for: X₂ ≤ X₁
alphas_abs: X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}

relevant size-bounds w.r.t. t₁₅:
X₁: 1023 {O(1)}
X₂: 0 {O(1)}
Runtime-bound of t₁₅: 1 {O(1)}
Results in: 2050 {O(1)}

order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂

Stabilization-Threshold for: X₂ ≤ X₁
alphas_abs: X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}

relevant size-bounds w.r.t. t₁₄:
X₁: 0 {O(1)}
X₂: 0 {O(1)}
Runtime-bound of t₁₄: 1 {O(1)}
Results in: 4 {O(1)}

order: [X₁; X₂]
closed-form:
X₁: X₁
X₂: X₂ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₂ < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂

Stabilization-Threshold for: X₂ ≤ X₁
alphas_abs: X₂+X₁
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+2 {O(n)}

relevant size-bounds w.r.t. t₁₃:
X₁: 0 {O(1)}
X₂: 0 {O(1)}
Runtime-bound of t₁₃: 1 {O(1)}
Results in: 4 {O(1)}

2058 {O(1)}

All Bounds

Timebounds

Overall timebound:2064 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 2058 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}

Costbounds

Overall costbound: 2064 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 2058 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}

Sizebounds

t₁₃, X₁: 0 {O(1)}
t₁₃, X₂: 0 {O(1)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₁: 0 {O(1)}
t₁₄, X₂: 0 {O(1)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₁: 1023 {O(1)}
t₁₅, X₂: 0 {O(1)}
t₁₅, X₄: X₄ {O(n)}
t₁₆, X₁: 1023 {O(1)}
t₁₆, X₂: 1024 {O(1)}
t₁₆, X₄: 3⋅X₄ {O(n)}
t₁₇, X₁: 1023 {O(1)}
t₁₇, X₂: 1024 {O(1)}
t₁₇, X₄: 1022 {O(1)}
t₁₈, X₁: 1023 {O(1)}
t₁₈, X₂: 1024 {O(1)}
t₁₈, X₄: 3⋅X₄ {O(n)}
t₁₉, X₁: 1023 {O(1)}
t₁₉, X₂: 1024 {O(1)}
t₁₉, X₄: 3⋅X₄ {O(n)}