Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₄: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₆: l6(X₀, X₁, X₂) → l7(X₂, X₁, X₂)
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₀ < X₁
t₈: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₁ < X₀
t₉: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁₀: l8(X₀, X₁, X₂) → l7(X₀+1, X₁, X₂)
t₁₁: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂)

Preprocessing

Found invariant X₂ ≤ X₀ for location l7

Found invariant X₂ ≤ X₀ for location l8

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l10

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₂: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₄: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₅: l5(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₆: l6(X₀, X₁, X₂) → l7(X₂, X₁, X₂)
t₇: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₂ ≤ X₀
t₈: l7(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₂ ≤ X₀
t₉: l7(X₀, X₁, X₂) → l9(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀
t₁₀: l8(X₀, X₁, X₂) → l7(X₀+1, X₁, X₂) :|: X₂ ≤ X₀
t₁₁: l9(X₀, X₁, X₂) → l10(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁

Found invariant X₂ ≤ X₀ for location l7

Found invariant X₂ ≤ X₀ for location l8

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l10

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l9

Analysing control-flow refined program

Cut unsatisfiable transition t₁₂₆: n_l7___2→l9

Cut unsatisfiable transition t₁₁₂: n_l7___5→n_l8___3

Cut unreachable locations [n_l8___3] from the program graph

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l8___1

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l8___7

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l8___6

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

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l7___2

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l8___4

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l10

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l9

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l7___5

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l8___1

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l8___7

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l8___6

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

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l7___2

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l8___4

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l10

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l9

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l7___5

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l8___1

Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l8___7

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l8___6

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

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l7___2

Found invariant 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l8___4

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l10

Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l9

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l7___5

Time-Bound by TWN-Loops:

TWN-Loops: t₁₁₃ 10⋅X₂+2⋅X₁+16 {O(n)}

TWN-Loops:

entry: t₁₂₀: n_l8___7(X₀, X₁, X₂) → n_l7___5(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁
results in twn-loop: twn:Inv: [1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁] , (X₀,X₁,X₂) -> (X₀+1,X₁,X₂) :|: X₂ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₀ < X₁ ∧ X₀ < X₁ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * n^1
X₁: X₁
X₂: X₂

Termination: true
Formula:

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

Stabilization-Threshold for: X₂ ≤ X₀
alphas_abs: X₀+X₂
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+2 {O(n)}
Stabilization-Threshold for: 1+X₂ ≤ X₀
alphas_abs: 1+X₀+X₂
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+4 {O(n)}
Stabilization-Threshold for: X₀ < X₁
alphas_abs: X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₁₂₀:
X₀: X₂+1 {O(n)}
X₁: X₁ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₁₂₀: 1 {O(1)}
Results in: 10⋅X₂+2⋅X₁+16 {O(n)}

10⋅X₂+2⋅X₁+16 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₁₁₈ 10⋅X₂+2⋅X₁+16 {O(n)}

relevant size-bounds w.r.t. t₁₂₀:
X₀: X₂+1 {O(n)}
X₁: X₁ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₁₂₀: 1 {O(1)}
Results in: 10⋅X₂+2⋅X₁+16 {O(n)}

10⋅X₂+2⋅X₁+16 {O(n)}

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: inf {Infinity}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₀: X₂ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₉, X₁: 3⋅X₁ {O(n)}
t₉, X₂: 3⋅X₂ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₁, X₁: 3⋅X₁ {O(n)}
t₁₁, X₂: 3⋅X₂ {O(n)}