Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < 100
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, 5, X₂, X₃) :|: 100 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < 21
t₆: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 21 ≤ X₁
t₇: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁+3, X₂, X₃)
t₈: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)

Preprocessing

Eliminate variables {X₂,X₃} that do not contribute to the problem

Found invariant 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ 100 ≤ X₀ for location l6

Found invariant 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ 100 ≤ X₀ for location l7

Found invariant X₁ ≤ 20 ∧ 80+X₁ ≤ X₀ ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀ for location l4

Found invariant X₀ ≤ 99 ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₈: l0(X₀, X₁) → l2(X₀, X₁)
t₁₉: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < 100 ∧ 0 ≤ X₀
t₂₀: l1(X₀, X₁) → l4(X₀, 5) :|: 100 ≤ X₀ ∧ 0 ≤ X₀
t₂₁: l2(X₀, X₁) → l1(0, X₁)
t₂₂: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 99 ∧ 0 ≤ X₀
t₂₃: l4(X₀, X₁) → l5(X₀, X₁) :|: X₁ < 21 ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀
t₂₄: l4(X₀, X₁) → l6(X₀, X₁) :|: 21 ≤ X₁ ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀
t₂₅: l5(X₀, X₁) → l4(X₀, X₁+3) :|: X₁ ≤ 20 ∧ 80+X₁ ≤ X₀ ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀
t₂₆: l6(X₀, X₁) → l7(X₀, X₁) :|: 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ 100 ≤ X₀

Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ X₀ ≤ 79+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l6

Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ X₀ ≤ 79+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l7

Found invariant X₁ ≤ 20 ∧ 80+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 120 ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ X₀ ≤ 95+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l5

Found invariant X₀ ≤ 100 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ X₀ ≤ 95+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l4

Found invariant X₀ ≤ 99 ∧ 0 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₉ 204 {O(1)}

TWN-Loops:

entry: t₂₁: l2(X₀, X₁) → l1(0, X₁)
results in twn-loop: twn:Inv: [0 ≤ X₀ ∧ X₀ ≤ 99 ∧ 0 ≤ X₀] , (X₀,X₁) -> (X₀+1,X₁) :|: X₀ < 100
order: [X₀]
closed-form:
X₀: X₀ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₀ < 100 ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₀ < 100
alphas_abs: 100
M: 0
N: 1
Bound: 202 {O(1)}

relevant size-bounds w.r.t. t₂₁:
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 204 {O(1)}

204 {O(1)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₂ 204 {O(1)}

relevant size-bounds w.r.t. t₂₁:
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 204 {O(1)}

204 {O(1)}

Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ X₀ ≤ 79+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l6

Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ X₀ ≤ 79+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l7

Found invariant X₁ ≤ 20 ∧ 80+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 120 ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ X₀ ≤ 95+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l5

Found invariant X₀ ≤ 100 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ X₀ ≤ 95+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l4

Found invariant X₀ ≤ 99 ∧ 0 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂₃ 56 {O(1)}

TWN-Loops:

entry: t₂₀: l1(X₀, X₁) → l4(X₀, 5) :|: 100 ≤ X₀ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀ ∧ X₁ ≤ 20 ∧ 80+X₁ ≤ X₀ ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀] , (X₀,X₁) -> (X₀,X₁+3) :|: X₁ < 21
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * 3 * n^1

Termination: true
Formula:

3 < 0
∨ 3 < 0 ∧ X₁ < 20 ∧ 3 ≤ 0 ∧ 0 ≤ 3
∨ 3 < 0 ∧ 3 ≤ 0 ∧ 0 ≤ 3 ∧ X₁ ≤ 20 ∧ 20 ≤ X₁
∨ 80+X₁ < X₀ ∧ 3 ≤ 0 ∧ 0 ≤ 3 ∧ 3 < 0
∨ 3 < 0 ∧ 80+X₁ < X₀ ∧ X₁ < 20 ∧ 3 ≤ 0 ∧ 0 ≤ 3
∨ 3 < 0 ∧ 80+X₁ < X₀ ∧ 3 ≤ 0 ∧ 0 ≤ 3 ∧ X₁ ≤ 20 ∧ 20 ≤ X₁
∨ 3 ≤ 0 ∧ 0 ≤ 3 ∧ 80+X₁ ≤ X₀ ∧ X₀ ≤ 80+X₁ ∧ 3 < 0
∨ 3 < 0 ∧ 80+X₁ ≤ X₀ ∧ X₀ ≤ 80+X₁ ∧ X₁ < 20 ∧ 3 ≤ 0 ∧ 0 ≤ 3
∨ 3 < 0 ∧ 80+X₁ ≤ X₀ ∧ X₀ ≤ 80+X₁ ∧ 3 ≤ 0 ∧ 0 ≤ 3 ∧ X₁ ≤ 20 ∧ 20 ≤ X₁
∨ X₁ < 21 ∧ 3 ≤ 0 ∧ 0 ≤ 3 ∧ 3 < 0
∨ X₁ < 21 ∧ 3 < 0 ∧ X₁ < 20 ∧ 3 ≤ 0 ∧ 0 ≤ 3
∨ X₁ < 21 ∧ 3 < 0 ∧ 3 ≤ 0 ∧ 0 ≤ 3 ∧ X₁ ≤ 20 ∧ 20 ≤ X₁
∨ X₁ < 21 ∧ 80+X₁ < X₀ ∧ 3 ≤ 0 ∧ 0 ≤ 3 ∧ 3 < 0
∨ X₁ < 21 ∧ 80+X₁ < X₀ ∧ X₁ < 20 ∧ 3 ≤ 0 ∧ 0 ≤ 3
∨ X₁ < 21 ∧ 80+X₁ < X₀ ∧ 3 ≤ 0 ∧ 0 ≤ 3 ∧ X₁ ≤ 20 ∧ 20 ≤ X₁
∨ X₁ < 21 ∧ 3 ≤ 0 ∧ 0 ≤ 3 ∧ 80+X₁ ≤ X₀ ∧ X₀ ≤ 80+X₁ ∧ 3 < 0
∨ X₁ < 21 ∧ 80+X₁ ≤ X₀ ∧ X₀ ≤ 80+X₁ ∧ X₁ < 20 ∧ 3 ≤ 0 ∧ 0 ≤ 3
∨ X₁ < 21 ∧ 80+X₁ ≤ X₀ ∧ X₀ ≤ 80+X₁ ∧ 3 ≤ 0 ∧ 0 ≤ 3 ∧ X₁ ≤ 20 ∧ 20 ≤ X₁

Stabilization-Threshold for: X₁ < 21
alphas_abs: X₁+21
M: 0
N: 1
Bound: 2⋅X₁+44 {O(n)}

relevant size-bounds w.r.t. t₂₀:
X₁: 5 {O(1)}
Runtime-bound of t₂₀: 1 {O(1)}
Results in: 56 {O(1)}

56 {O(1)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₅ 56 {O(1)}

relevant size-bounds w.r.t. t₂₀:
X₁: 5 {O(1)}
Runtime-bound of t₂₀: 1 {O(1)}
Results in: 56 {O(1)}

56 {O(1)}

All Bounds

Timebounds

Overall timebound:525 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 204 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 204 {O(1)}
t₂₃: 56 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 56 {O(1)}
t₂₆: 1 {O(1)}

Costbounds

Overall costbound: 525 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 204 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 204 {O(1)}
t₂₃: 56 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 56 {O(1)}
t₂₆: 1 {O(1)}

Sizebounds

t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₉, X₀: 99 {O(1)}
t₁₉, X₁: X₁ {O(n)}
t₂₀, X₀: 100 {O(1)}
t₂₀, X₁: 5 {O(1)}
t₂₁, X₀: 0 {O(1)}
t₂₁, X₁: X₁ {O(n)}
t₂₂, X₀: 100 {O(1)}
t₂₂, X₁: X₁ {O(n)}
t₂₃, X₀: 100 {O(1)}
t₂₃, X₁: 20 {O(1)}
t₂₄, X₀: 100 {O(1)}
t₂₄, X₁: 23 {O(1)}
t₂₅, X₀: 100 {O(1)}
t₂₅, X₁: 23 {O(1)}
t₂₆, X₀: 100 {O(1)}
t₂₆, X₁: 23 {O(1)}