Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₁ < X₂
t₅: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₃: l3(X₀, X₁, X₂) → l1(X₀, nondef.0, X₂)
t₈: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₆: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ < 0
t₇: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 < X₀
t₁₀: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₉: l6(X₀, X₁, X₂) → l4(X₀-1, X₁, X₂)

Preprocessing

Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l6

Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₁ < X₂
t₅: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₃: l3(X₀, X₁, X₂) → l1(X₀, nondef.0, X₂)
t₈: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₆: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ < 0 ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₇: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₁₀: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₉: l6(X₀, X₁, X₂) → l4(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂

Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l6

Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l4

Analysing control-flow refined program

Cut unsatisfiable transition t₁₀₄: n_l4___3→n_l6___2

Cut unsatisfiable transition t₁₁₉: n_l4___5→l5

Cut unreachable locations [n_l6___2] from the program graph

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l6___6

Found invariant 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l6___1

Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 for location n_l6___4

Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l4___3

Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 for location n_l4___5

Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location n_l6___7

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l4

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l6___6

Found invariant 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l6___1

Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 for location n_l6___4

Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l4___3

Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 for location n_l4___5

Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location n_l6___7

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l4

Time-Bound by TWN-Loops:

TWN-Loops: t₁₀₃ 10⋅X₂+11 {O(n)}

TWN-Loops:

entry: t₁₁₁: n_l6___6(X₀, X₁, X₂) → n_l4___3(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 0 < X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,X₁,X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 < X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 < X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁
X₂: X₂

Termination: true
Formula:

1+X₁ < X₂ ∧ 1 < 0 ∧ 0 < 1
∨ 0 < 1 ∧ 1+X₁ < X₂ ∧ 1 < 0 ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 1+X₁ < X₂ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ 1+X₁ < X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 0 < 1 ∧ 1+X₁ < X₂ ∧ 0 < X₀ ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 1+X₁ < X₂ ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 0 < 1
∨ 0 < 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ 0 < 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 < X₀ ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ < X₂ ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < X₂ ∧ 1+X₁ < X₂ ∧ 1 < 0 ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < X₂ ∧ 1+X₁ < X₂ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ X₀ < X₂ ∧ 1+X₁ < X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < X₂ ∧ 1+X₁ < X₂ ∧ 0 < X₀ ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < X₂ ∧ 1+X₁ < X₂ ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 0 < 1
∨ X₀ < X₂ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < X₂ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ X₀ < X₂ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ < X₂ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 < X₀ ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < X₂ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 1 < 0 ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 0 < X₀ ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ < X₂ ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 0 < 1
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 < X₀ ∧ 1+X₀ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀

Stabilization-Threshold for: X₀ ≤ X₂
alphas_abs: X₀+X₂
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+2 {O(n)}
Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: 1+X₀ ≤ X₂
alphas_abs: 1+X₀+X₂
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+4 {O(n)}

relevant size-bounds w.r.t. t₁₁₁:
X₀: X₂ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₁₁₁: 1 {O(1)}
Results in: 10⋅X₂+11 {O(n)}

10⋅X₂+11 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₀₈ 10⋅X₂+11 {O(n)}

relevant size-bounds w.r.t. t₁₁₁:
X₀: X₂ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₁₁₁: 1 {O(1)}
Results in: 10⋅X₂+11 {O(n)}

10⋅X₂+11 {O(n)}

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l6___6

Found invariant 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l6___1

Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 for location n_l6___4

Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l4___3

Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 for location n_l4___5

Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location n_l6___7

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l4

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: 1 {O(1)}
t₁₀: 1 {O(1)}
t₉: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: 1 {O(1)}
t₁₀: 1 {O(1)}
t₉: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₂: X₂ {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₈, X₀: 0 {O(1)}
t₈, X₂: 3⋅X₂ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₂: 4⋅X₂ {O(n)}
t₉, X₂: 2⋅X₂ {O(n)}