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, X₀, X₂, X₃) :|: X₀ < 10
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 10 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 0 < X₁
t₈: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₂, X₃)

Preprocessing

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

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l6

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l7

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₂ ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₈: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₉: l1(X₀, X₁, X₂) → l3(X₀, X₀, X₂) :|: X₀ < 10 ∧ X₂ ≤ X₀
t₂₀: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 10 ≤ X₀ ∧ X₂ ≤ X₀
t₂₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₂₃: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9
t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 < X₁ ∧ X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9
t₂₄: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 10 ≤ X₀
t₂₅: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
t₂₆: l6(X₀, X₁, X₂) → l3(X₀, X₁+1, X₂) :|: X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l6

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l7

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₂ ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₁₉ 4⋅X₂+26 {O(n)}

TWN-Loops:

entry: t₂₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
results in twn-loop: twn:Inv: [X₂ ≤ X₀ ∧ X₂ ≤ 9 ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 0 ≤ 0 ∧ X₀ ≤ 9 ∧ X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ X₀ ≤ 0 ∧ 2⋅X₀ ≤ 0 ∧ 0 ≤ 0 ∧ X₀ ≤ 0] , (X₀,X₁,X₂) -> (X₀+1,X₀,X₂) :|: X₀ < 10 ∧ X₀ ≤ 0
order: [X₀; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₂: X₂

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₀ < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₀ < 0 ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ < 10 ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: X₀ ≤ 0
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
Stabilization-Threshold for: X₀ < 10
alphas_abs: X₀+10
M: 0
N: 1
Bound: 2⋅X₀+22 {O(n)}

relevant size-bounds w.r.t. t₂₁:
X₀: X₂ {O(n)}
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 4⋅X₂+26 {O(n)}

4⋅X₂+26 {O(n)}

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l6

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l7

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₂ ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₂₃ 4⋅X₂+26 {O(n)}

relevant size-bounds w.r.t. t₂₁:
X₀: X₂ {O(n)}
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 4⋅X₂+26 {O(n)}

4⋅X₂+26 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₂₅ 4⋅X₂+26 {O(n)}

relevant size-bounds w.r.t. t₂₁:
X₀: X₂ {O(n)}
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 4⋅X₂+26 {O(n)}

4⋅X₂+26 {O(n)}

Analysing control-flow refined program

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 18 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 1 ≤ X₀ for location n_l6___3

Found invariant X₂ ≤ 9 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 1 ≤ X₀ for location n_l6___1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l7

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₂ ≤ 9 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 1 ≤ X₀ for location n_l3___2

Found invariant X₂ ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 18 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l3

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 18 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 1 ≤ X₀ for location n_l6___3

Found invariant X₂ ≤ 9 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 1 ≤ X₀ for location n_l6___1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l7

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant X₂ ≤ 9 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 9 ∧ 1 ≤ X₀ for location n_l3___2

Found invariant X₂ ≤ X₀ for location l1

Found invariant X₂ ≤ X₀ ∧ 10 ≤ X₀ for location l4

Found invariant X₂ ≤ 9 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 18 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 18 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location l3

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 4⋅X₂+26 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: 4⋅X₂+26 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 4⋅X₂+26 {O(n)}
t₂₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 4⋅X₂+26 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: 4⋅X₂+26 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 4⋅X₂+26 {O(n)}
t₂₆: inf {Infinity}

Sizebounds

t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₀: X₂+1 {O(n)}
t₁₉, X₁: 2⋅X₂+1 {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: X₂ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: X₂ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: X₂+1 {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: X₂+1 {O(n)}
t₂₃, X₁: 2⋅X₂+1 {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₄, X₀: X₂ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₅, X₀: X₂+1 {O(n)}
t₂₅, X₁: 2⋅X₂+1 {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₆, X₀: X₂+1 {O(n)}
t₂₆, X₂: X₂ {O(n)}