Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(10-2⋅X₀, X₁)
t₅: l4(X₀, X₁) → l5(X₀, X₁)
Preprocessing
Found invariant X₀ ≤ 0 for location l5
Found invariant X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(10-2⋅X₀, X₁) :|: 1 ≤ X₀
t₅: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0
Found invariant X₀ ≤ 0 for location l5
Found invariant X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₀ for location l3
Time-Bound by TWN-Loops:
TWN-Loops: t₂ 93 {O(1)}
TWN-Loops:
entry: t₁: l2(X₀, X₁) → l1(X₁, X₁)
results in twn-loop: twn:Inv: [1 ≤ X₀] , (X₀,X₁) -> (10-2⋅X₀,X₁) :|: 0 < X₀
order: [X₀]
closed-form:
X₀: X₀ * 4^n + [[n != 0]] * -10/3 * 4^n + [[n != 0]] * 10/3
Termination: true
Formula:
6⋅X₀ < 20 ∧ 10 < 3⋅X₀
∨ 10 < 3⋅X₀ ∧ 6⋅X₀ < 20 ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 10 < 3⋅X₀ ∧ 6⋅X₀ < 20 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 6⋅X₀ < 20 ∧ 0 < 7 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 < 3⋅X₀
∨ 6⋅X₀ < 20 ∧ 10 < 3⋅X₀ ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 6⋅X₀ < 20 ∧ 10 < 3⋅X₀ ∧ 0 < 7 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 6⋅X₀ < 20 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 ≤ 7 ∧ 7 ≤ 0 ∧ 10 < 3⋅X₀
∨ 6⋅X₀ < 20 ∧ 10 < 3⋅X₀ ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 ≤ 7 ∧ 7 ≤ 0 ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 6⋅X₀ < 20 ∧ 10 < 3⋅X₀ ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 0 < 10 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 6⋅X₀ < 20 ∧ 10 < 3⋅X₀
∨ 0 < 10 ∧ 6⋅X₀ < 20 ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 0 < 10 ∧ 6⋅X₀ < 20 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 6⋅X₀ < 20 ∧ 0 < 10 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 < 7 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 < 3⋅X₀
∨ 6⋅X₀ < 20 ∧ 0 < 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 6⋅X₀ < 20 ∧ 0 < 10 ∧ 0 < 7 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 6⋅X₀ < 20 ∧ 0 < 10 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 ≤ 7 ∧ 7 ≤ 0 ∧ 10 < 3⋅X₀
∨ 6⋅X₀ < 20 ∧ 0 < 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 ≤ 7 ∧ 7 ≤ 0 ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 6⋅X₀ < 20 ∧ 0 < 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 0 < 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 6⋅X₀ < 20 ∧ 10 < 3⋅X₀
∨ 0 < 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 < 3⋅X₀ ∧ 6⋅X₀ < 20 ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 0 < 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 < 3⋅X₀ ∧ 6⋅X₀ < 20 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 0 < 10 ∧ 0 < 7 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 < 3⋅X₀
∨ 0 < 10 ∧ 10 < 3⋅X₀ ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 0 < 10 ∧ 10 < 3⋅X₀ ∧ 0 < 7 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 0 < 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 ≤ 7 ∧ 7 ≤ 0 ∧ 10 < 3⋅X₀
∨ 0 < 10 ∧ 10 < 3⋅X₀ ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 ≤ 7 ∧ 7 ≤ 0 ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 0 < 10 ∧ 10 < 3⋅X₀ ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 < 10 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 6⋅X₀ < 20 ∧ 10 < 3⋅X₀
∨ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 < 10 ∧ 6⋅X₀ < 20 ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 < 10 ∧ 6⋅X₀ < 20 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 0 < 10 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 < 7 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 < 3⋅X₀
∨ 0 < 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 0 < 10 ∧ 0 < 7 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
∨ 0 < 10 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 ≤ 7 ∧ 7 ≤ 0 ∧ 10 < 3⋅X₀
∨ 0 < 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 0 ≤ 7 ∧ 7 ≤ 0 ∧ 0 < 7 ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10
∨ 0 < 10 ∧ 6⋅X₀ ≤ 20 ∧ 20 ≤ 6⋅X₀ ∧ 10 ≤ 3⋅X₀ ∧ 3⋅X₀ ≤ 10 ∧ 0 ≤ 7 ∧ 7 ≤ 0
Stabilization-Threshold for: 2⋅X₀ < 10
alphas_abs: 10
M: 0
N: 1
Bound: 22 {O(1)}
Stabilization-Threshold for: 0 < X₀
alphas_abs: 10
M: 0
N: 1
Bound: 22 {O(1)}
relevant size-bounds w.r.t. t₁:
Runtime-bound of t₁: 1 {O(1)}
Results in: 93 {O(1)}
93 {O(1)}
Time-Bound by TWN-Loops:
TWN-Loops: t₄ 93 {O(1)}
relevant size-bounds w.r.t. t₁:
Runtime-bound of t₁: 1 {O(1)}
Results in: 93 {O(1)}
93 {O(1)}
All Bounds
Timebounds
Overall timebound:190 {O(1)}
t₀: 1 {O(1)}
t₂: 93 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 93 {O(1)}
t₅: 1 {O(1)}
Costbounds
Overall costbound: 190 {O(1)}
t₀: 1 {O(1)}
t₂: 93 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 93 {O(1)}
t₅: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₂, X₀: 9903520314283042199192993792⋅X₁+2763082167684968773574845267968 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: 9903520314283042199192993793⋅X₁+2763082167684968773574845267968 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₄, X₀: 9903520314283042199192993792⋅X₁+2763082167684968773574845267968 {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 9903520314283042199192993793⋅X₁+2763082167684968773574845267968 {O(n)}
t₅, X₁: 2⋅X₁ {O(n)}