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) :|: 0 < X₃
t₁₀: l11(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₁₅: l12(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃)
t₁₁: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃-1)
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, X₁, X₁, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₁) :|: 0 < X₂
t₈: l7(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₁₄: l8(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₀, X₃)
t₁₂: l9(X₀, X₁, X₂, X₃) → l10(X₂-1, X₁, X₂, X₃)
Preprocessing
Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l11
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l12
Found invariant X₂ ≤ X₁ for location l7
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l13
Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l8
Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l10
Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l9
Found invariant X₂ ≤ 0 ∧ X₂ ≤ 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) :|: X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₉: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: 0 < X₃ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₀: l11(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₅: l12(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁
t₁₁: l13(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃-1) :|: X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ 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, X₁, X₁, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₁) :|: 0 < X₂ ∧ X₂ ≤ X₁
t₈: l7(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁
t₁₄: l8(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₀, X₃) :|: X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₂: l9(X₀, X₁, X₂, X₃) → l10(X₂-1, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
MPRF for transition t₇: l7(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₁) :|: 0 < X₂ ∧ X₂ ≤ X₁ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₁₀: l11(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₁₂: l9(X₀, X₁, X₂, X₃) → l10(X₂-1, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₁₃: l10(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₁₄: l8(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₀, X₃) :|: X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
TWN: t₉: l11→l13
cycle: [t₉: l11→l13; t₁₁: l13→l11]
loop: (0 < X₃,(X₃) -> (X₃-1)
order: [X₃]
closed-form:
X₃: X₃ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ 0 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: 0 < X₃
alphas_abs: X₃
M: 0
N: 1
Bound: 2⋅X₃+2 {O(n)}
TWN - Lifting for t₉: l11→l13 of 2⋅X₃+4 {O(n)}
relevant size-bounds w.r.t. t₇:
X₃: 2⋅X₁ {O(n)}
Runtime-bound of t₇: X₁ {O(n)}
Results in: 4⋅X₁⋅X₁+4⋅X₁ {O(n^2)}
TWN: t₁₁: l13→l11
TWN - Lifting for t₁₁: l13→l11 of 2⋅X₃+4 {O(n)}
relevant size-bounds w.r.t. t₇:
X₃: 2⋅X₁ {O(n)}
Runtime-bound of t₇: X₁ {O(n)}
Results in: 4⋅X₁⋅X₁+4⋅X₁ {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 X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l11
Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ for location l12
Found invariant X₁ ≤ X₀ for location l7
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l13
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l8
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l10
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l9
Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ for location l14
MPRF for transition t₁₄₈: l13(X₀, X₁, X₂) -{2}> l9(X₀, X₁, X₂-1) :|: X₂ ≤ 1 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₁₆₀: l9(X₀, X₁, X₂) -{5}> l13(X₀, X₁-1, X₀) :|: 1 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
TWN: t₁₄₇: l13→l13
cycle: [t₁₄₇: l13→l13]
loop: (1 < X₂,(X₂) -> (X₂-1)
order: [X₂]
closed-form:
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ 1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: 1 < X₂
alphas_abs: 1+X₂
M: 0
N: 1
Bound: 2⋅X₂+4 {O(n)}
loop: (1 < X₂,(X₂) -> (X₂-1)
order: [X₂]
closed-form:
X₂: X₂ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
1 < 0
∨ 1 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: 1 < X₂
alphas_abs: 1+X₂
M: 0
N: 1
Bound: 2⋅X₂+4 {O(n)}
TWN - Lifting for t₁₄₇: l13→l13 of 2⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₁₆₀:
X₂: X₀ {O(n)}
Runtime-bound of t₁₆₀: X₀ {O(n)}
Results in: 2⋅X₀⋅X₀+6⋅X₀ {O(n^2)}
TWN - Lifting for t₁₄₇: l13→l13 of 2⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₁₅₅:
X₂: X₀ {O(n)}
Runtime-bound of t₁₅₅: 1 {O(1)}
Results in: 2⋅X₀+6 {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 X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l11
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l13___3
Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location n_l13___1
Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l11___2
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l12
Found invariant X₂ ≤ X₁ for location l7
Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l8
Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l10
Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l9
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ for location l14
knowledge_propagation leads to new time bound X₁ {O(n)} for transition t₂₂₄: l11(X₀, X₁, X₂, X₃) → n_l13___3(X₀, X₁, X₂, X₃) :|: 0 < X₃ ∧ 0 < X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
knowledge_propagation leads to new time bound X₁ {O(n)} for transition t₂₂₆: n_l13___3(X₀, X₁, X₂, X₃) → n_l11___2(X₀, X₁, X₂, X₃-1) :|: 0 < X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
MPRF for transition t₂₂₃: n_l11___2(X₀, X₁, X₂, X₃) → n_l13___1(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 0 < X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
2⋅X₁⋅X₁+X₁ {O(n^2)}
MPRF for transition t₂₂₅: n_l13___1(X₀, X₁, X₂, X₃) → n_l11___2(X₀, X₁, X₂, X₃-1) :|: 1+X₃ ≤ X₁ ∧ 0 < X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₁ of depth 1:
new bound:
2⋅X₁⋅X₁ {O(n^2)}
MPRF for transition t₂₃₀: n_l11___2(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁ {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:8⋅X₁⋅X₁+13⋅X₁+10 {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: X₁ {O(n)}
t₈: 1 {O(1)}
t₉: 4⋅X₁⋅X₁+4⋅X₁ {O(n^2)}
t₁₀: X₁ {O(n)}
t₁₁: 4⋅X₁⋅X₁+4⋅X₁ {O(n^2)}
t₁₂: X₁ {O(n)}
t₁₃: X₁+1 {O(n)}
t₁₄: X₁ {O(n)}
t₁₅: 1 {O(1)}
Costbounds
Overall costbound: 8⋅X₁⋅X₁+13⋅X₁+10 {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: X₁ {O(n)}
t₈: 1 {O(1)}
t₉: 4⋅X₁⋅X₁+4⋅X₁ {O(n^2)}
t₁₀: X₁ {O(n)}
t₁₁: 4⋅X₁⋅X₁+4⋅X₁ {O(n^2)}
t₁₂: X₁ {O(n)}
t₁₃: X₁+1 {O(n)}
t₁₄: X₁ {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: X₁ {O(n)}
t₆, X₂: X₁ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀+X₁ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁ {O(n)}
t₇, X₃: 2⋅X₁ {O(n)}
t₈, X₀: X₀+X₁ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₁ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₀+X₁ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₁ {O(n)}
t₉, X₃: 2⋅X₁ {O(n)}
t₁₀, X₀: X₀+X₁ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁ {O(n)}
t₁₀, X₃: 0 {O(1)}
t₁₁, X₀: X₀+X₁ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₁ {O(n)}
t₁₁, X₃: 2⋅X₁ {O(n)}
t₁₂, X₀: X₁ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₁ {O(n)}
t₁₂, X₃: 0 {O(1)}
t₁₃, X₀: X₁ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₁ {O(n)}
t₁₃, X₃: 0 {O(1)}
t₁₄, X₀: X₁ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₁ {O(n)}
t₁₄, X₃: 0 {O(1)}
t₁₅, X₀: X₀+X₁ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₅, X₂: 2⋅X₁ {O(n)}
t₁₅, X₃: X₃ {O(n)}