Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₃: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₉: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃
t₁₀: l11(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ < X₂
t₁₅: l12(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃)
t₁₁: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂+2, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, 0, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l11(X₀, X₁, 0, X₃) :|: X₁ ≤ X₃
t₈: l7(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₃ < X₁
t₁₄: l8(X₀, X₁, X₂, X₃) → l7(X₀, X₀, X₂, X₃)
t₁₂: l9(X₀, X₁, X₂, X₃) → l10(X₁+2, X₁, X₂, X₃)
Preprocessing
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l11
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₁ for location l12
Found invariant 0 ≤ X₁ for location l7
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l13
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ 2+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ 2 ≤ X₀ for location l8
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ 2+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ 2 ≤ X₀ for location l10
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l9
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₁ for location l14
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₃: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ 2+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ 2 ≤ X₀
t₉: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁₀: l11(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ < X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁₅: l12(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₁
t₁₁: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂+2, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, 0, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l11(X₀, X₁, 0, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₁
t₈: l7(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₃ < X₁ ∧ 0 ≤ X₁
t₁₄: l8(X₀, X₁, X₂, X₃) → l7(X₀, X₀, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ 2+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ 2 ≤ X₀
t₁₂: l9(X₀, X₁, X₂, X₃) → l10(X₁+2, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁
MPRF for transition t₇: l7(X₀, X₁, X₂, X₃) → l11(X₀, X₁, 0, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF for transition t₁₀: l11(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ < X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₃+2 {O(n)}
MPRF for transition t₁₂: l9(X₀, X₁, X₂, X₃) → l10(X₁+2, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF for transition t₁₃: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ 2+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₃+2 {O(n)}
MPRF for transition t₁₄: l8(X₀, X₁, X₂, X₃) → l7(X₀, X₀, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ 2+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₃+1 {O(n)}
TWN: t₉: l11→l13
cycle: [t₉: l11→l13; t₁₁: l13→l11]
loop: (X₂ ≤ X₃,(X₂,X₃) -> (X₂+2,X₃)
order: [X₂; X₃]
closed-form:
X₂: X₂ + [[n != 0]] * 2 * n^1
X₃: X₃
Termination: true
Formula:
2 < 0
∨ X₂ < X₃ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂
Stabilization-Threshold for: X₂ ≤ X₃
alphas_abs: X₂+X₃
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₃+2 {O(n)}
TWN - Lifting for t₉: l11→l13 of 2⋅X₂+2⋅X₃+4 {O(n)}
relevant size-bounds w.r.t. t₇:
X₂: 0 {O(1)}
X₃: X₃ {O(n)}
Runtime-bound of t₇: X₃+1 {O(n)}
Results in: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
TWN: t₁₁: l13→l11
TWN - Lifting for t₁₁: l13→l11 of 2⋅X₂+2⋅X₃+4 {O(n)}
relevant size-bounds w.r.t. t₇:
X₂: 0 {O(1)}
X₃: X₃ {O(n)}
Runtime-bound of t₇: X₃+1 {O(n)}
Results in: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
Chain transitions t₁₂: l9→l10 and t₁₃: l10→l8 to t₈₉: l9→l8
Chain transitions t₇: l7→l11 and t₁₀: l11→l9 to t₉₀: l7→l9
Chain transitions t₁₁: l13→l11 and t₁₀: l11→l9 to t₉₁: l13→l9
Chain transitions t₁₁: l13→l11 and t₉: l11→l13 to t₉₂: l13→l13
Chain transitions t₇: l7→l11 and t₉: l11→l13 to t₉₃: l7→l13
Chain transitions t₁₄: l8→l7 and t₉₀: l7→l9 to t₉₄: l8→l9
Chain transitions t₆: l6→l7 and t₉₀: l7→l9 to t₉₅: l6→l9
Chain transitions t₆: l6→l7 and t₉₃: l7→l13 to t₉₆: l6→l13
Chain transitions t₁₄: l8→l7 and t₉₃: l7→l13 to t₉₇: l8→l13
Chain transitions t₆: l6→l7 and t₈: l7→l12 to t₉₈: l6→l12
Chain transitions t₁₄: l8→l7 and t₈: l7→l12 to t₉₉: l8→l12
Chain transitions t₆: l6→l7 and t₇: l7→l11 to t₁₀₀: l6→l11
Chain transitions t₁₄: l8→l7 and t₇: l7→l11 to t₁₀₁: l8→l11
Chain transitions t₈₉: l9→l8 and t₉₄: l8→l9 to t₁₀₂: l9→l9
Chain transitions t₈₉: l9→l8 and t₁₄: l8→l7 to t₁₀₃: l9→l7
Chain transitions t₈₉: l9→l8 and t₉₇: l8→l13 to t₁₀₄: l9→l13
Chain transitions t₈₉: l9→l8 and t₉₉: l8→l12 to t₁₀₅: l9→l12
Chain transitions t₈₉: l9→l8 and t₁₀₁: l8→l11 to t₁₀₆: l9→l11
Analysing control-flow refined program
Cut unsatisfiable transition t₉₅: l6→l9
Cut unsatisfiable transition t₁₀₂: l9→l9
Eliminate variables {X₀} that do not contribute to the problem
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l11
Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ X₀ for location l12
Found invariant 0 ≤ X₀ for location l7
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l13
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l8
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l10
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l9
Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ X₀ for location l14
MPRF for transition t₁₄₈: l13(X₀, X₁, X₂) -{2}> l9(X₀, 2+X₁, X₂) :|: X₂ < X₁+2 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF for transition t₁₆₀: l9(X₀, X₁, X₂) -{5}> l13(2+X₀, 0, X₂) :|: 2+X₀ ≤ X₂ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 2+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+1 {O(n)}
TWN: t₁₄₇: l13→l13
cycle: [t₁₄₇: l13→l13]
loop: (2+X₁ ≤ X₂,(X₁,X₂) -> (2+X₁,X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁ + [[n != 0]] * 2 * n^1
X₂: X₂
Termination: true
Formula:
2 < 0
∨ 2+X₁ < X₂ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2+X₁ ≤ X₂ ∧ X₂ ≤ 2+X₁
Stabilization-Threshold for: 2+X₁ ≤ X₂
alphas_abs: 2+X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+6 {O(n)}
loop: (2+X₁ ≤ X₂,(X₁,X₂) -> (2+X₁,X₂)
order: [X₁; X₂]
closed-form:
X₁: X₁ + [[n != 0]] * 2 * n^1
X₂: X₂
Termination: true
Formula:
2 < 0
∨ 2+X₁ < X₂ ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2+X₁ ≤ X₂ ∧ X₂ ≤ 2+X₁
Stabilization-Threshold for: 2+X₁ ≤ X₂
alphas_abs: 2+X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+6 {O(n)}
TWN - Lifting for t₁₄₇: l13→l13 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₆₀:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₁₆₀: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+10⋅X₂+8 {O(n^2)}
TWN - Lifting for t₁₄₇: l13→l13 of 2⋅X₁+2⋅X₂+8 {O(n)}
relevant size-bounds w.r.t. t₁₅₅:
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₁₅₅: 1 {O(1)}
Results in: 2⋅X₂+8 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀: l11→l9
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l11
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l13___3
Found invariant 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l13___1
Found invariant 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location n_l11___2
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₁ for location l12
Found invariant 0 ≤ X₁ for location l7
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ 2+X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ 2 ≤ X₀ for location l8
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ 2+X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ 2 ≤ X₀ for location l10
Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location l9
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₁ for location l14
knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₂₂₄: l11(X₀, X₁, X₂, X₃) → n_l13___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₂₂₆: n_l13___3(X₀, X₁, X₂, X₃) → n_l11___2(X₀, X₁, X₂+2, X₃) :|: X₂ ≤ 0 ∧ X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
MPRF for transition t₂₂₃: n_l11___2(X₀, X₁, X₂, X₃) → n_l13___1(X₀, X₁, X₂, X₃) :|: 2 ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₃⋅X₃+5⋅X₃+4 {O(n^2)}
MPRF for transition t₂₂₅: n_l13___1(X₀, X₁, X₂, X₃) → n_l11___2(X₀, X₁, X₂+2, X₃) :|: 2 ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₃⋅X₃+6⋅X₃+4 {O(n^2)}
MPRF for transition t₂₃₀: n_l11___2(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ < X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ 2+X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:
new bound:
X₃+1 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₃⋅X₃+17⋅X₃+24 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₃+1 {O(n)}
t₈: 1 {O(1)}
t₉: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₀: X₃+2 {O(n)}
t₁₁: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₂: X₃+1 {O(n)}
t₁₃: X₃+2 {O(n)}
t₁₄: X₃+1 {O(n)}
t₁₅: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₃⋅X₃+17⋅X₃+24 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: X₃+1 {O(n)}
t₈: 1 {O(1)}
t₉: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₀: X₃+2 {O(n)}
t₁₁: 2⋅X₃⋅X₃+6⋅X₃+4 {O(n^2)}
t₁₂: X₃+1 {O(n)}
t₁₃: X₃+2 {O(n)}
t₁₄: X₃+1 {O(n)}
t₁₅: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 0 {O(1)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: 2⋅X₃+X₀+2 {O(n)}
t₇, X₁: 2⋅X₃+2 {O(n)}
t₇, X₂: 0 {O(1)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: 2⋅X₃+X₀+2 {O(n)}
t₈, X₁: 2⋅X₃+2 {O(n)}
t₈, X₂: 4⋅X₃⋅X₃+12⋅X₃+X₂+8 {O(n^2)}
t₈, X₃: 2⋅X₃ {O(n)}
t₉, X₀: 2⋅X₃+X₀+2 {O(n)}
t₉, X₁: 2⋅X₃+2 {O(n)}
t₉, X₂: 4⋅X₃⋅X₃+12⋅X₃+8 {O(n^2)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₀: 2⋅X₃+X₀+2 {O(n)}
t₁₀, X₁: 2⋅X₃+2 {O(n)}
t₁₀, X₂: 4⋅X₃⋅X₃+12⋅X₃+8 {O(n^2)}
t₁₀, X₃: X₃ {O(n)}
t₁₁, X₀: 2⋅X₃+X₀+2 {O(n)}
t₁₁, X₁: 2⋅X₃+2 {O(n)}
t₁₁, X₂: 4⋅X₃⋅X₃+12⋅X₃+8 {O(n^2)}
t₁₁, X₃: X₃ {O(n)}
t₁₂, X₀: 2⋅X₃+2 {O(n)}
t₁₂, X₁: 2⋅X₃+2 {O(n)}
t₁₂, X₂: 4⋅X₃⋅X₃+12⋅X₃+8 {O(n^2)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₀: 2⋅X₃+2 {O(n)}
t₁₃, X₁: 2⋅X₃+2 {O(n)}
t₁₃, X₂: 4⋅X₃⋅X₃+12⋅X₃+8 {O(n^2)}
t₁₃, X₃: X₃ {O(n)}
t₁₄, X₀: 2⋅X₃+2 {O(n)}
t₁₄, X₁: 2⋅X₃+2 {O(n)}
t₁₄, X₂: 4⋅X₃⋅X₃+12⋅X₃+8 {O(n^2)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₀: 2⋅X₃+X₀+2 {O(n)}
t₁₅, X₁: 2⋅X₃+2 {O(n)}
t₁₅, X₂: 4⋅X₃⋅X₃+12⋅X₃+X₂+8 {O(n^2)}
t₁₅, X₃: 2⋅X₃ {O(n)}