Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, 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)
t₁₁: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₁-1, X₂, X₃) :|: 0 < X₁ ∧ 0 < X₁
t₁₂: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₀, X₂, X₃) :|: 0 < X₁ ∧ X₁ ≤ 0
t₁₃: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₁-1, X₂-1, X₃) :|: X₁ ≤ 0 ∧ 0 < X₁
t₁₄: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₀, X₂-1, X₃) :|: X₁ ≤ 0 ∧ X₁ ≤ 0
t₁₅: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, 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, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₃, X₀, X₃)
t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: 0 < X₂
t₁₀: l9(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
Preprocessing
Cut unsatisfiable transition t₁₂: l10→l9
Cut unsatisfiable transition t₁₃: l10→l9
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₀ for location l11
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₀ for location l12
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l10
Found invariant X₂ ≤ X₀ for location l9
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, 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)
t₁₁: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₁-1, X₂, X₃) :|: 0 < X₁ ∧ 0 < X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₁₄: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₀, X₂-1, X₃) :|: X₁ ≤ 0 ∧ X₁ ≤ 0 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₁₅: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₂ ≤ X₀
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, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₃, X₀, X₃)
t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₂ ≤ X₀
t₁₀: l9(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ X₂ ≤ X₀
MPRF for transition t₁₄: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₀, X₂-1, X₃) :|: X₁ ≤ 0 ∧ X₁ ≤ 0 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l9 [X₂ ]
l10 [X₂ ]
MPRF for transition t₁₁: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₁-1, X₂, X₃) :|: 0 < X₁ ∧ 0 < X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀⋅X₀+X₃ {O(n^2)}
MPRF:
l9 [X₁ ]
l10 [X₁ ]
knowledge_propagation leads to new time bound X₀⋅X₀+X₀+X₃+1 {O(n^2)} for transition t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₂ ≤ X₀
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀₆: n_l9___2→l11
Cut unsatisfiable transition t₁₀₈: n_l9___6→l11
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₀ for location l11
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l10___3
Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location n_l10___1
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l10___4
Found invariant X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ for location n_l9___2
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₀ for location l12
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l9___6
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l9
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l10___7
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l9___5
MPRF for transition t₉₀: n_l10___1(X₀, X₁, X₂, X₃) → n_l9___6(X₀, X₁-1, X₂, X₃) :|: 0 < X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
4⋅X₀+1 {O(n)}
MPRF:
n_l9___2 [X₂+1 ]
n_l10___1 [X₂+1 ]
n_l9___5 [X₀+X₂+1-X₁ ]
n_l10___3 [X₀+X₂+1-X₁ ]
n_l9___6 [X₂ ]
n_l10___4 [X₂ ]
MPRF for transition t₉₁: n_l10___3(X₀, X₁, X₂, X₃) → n_l9___2(X₀, X₁-1, X₂, X₃) :|: 1+X₂ ≤ X₀ ∧ 0 < X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
4⋅X₀+1 {O(n)}
MPRF:
n_l9___2 [X₂-1 ]
n_l10___1 [X₂-1 ]
n_l9___5 [X₁+X₂-X₀ ]
n_l10___3 [X₂ ]
n_l9___6 [X₂-1 ]
n_l10___4 [X₂-1 ]
MPRF for transition t₉₂: n_l10___4(X₀, X₁, X₂, X₃) → n_l9___5(X₀, X₀, X₂-1, X₃) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ 0 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀ {O(n)}
MPRF:
n_l9___2 [X₂ ]
n_l10___1 [X₂ ]
n_l9___5 [X₂ ]
n_l10___3 [X₂ ]
n_l9___6 [X₂ ]
n_l10___4 [X₂ ]
MPRF for transition t₉₆: n_l9___2(X₀, X₁, X₂, X₃) → n_l10___1(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₂ ≤ X₀ ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 < X₂ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀+1 {O(n)}
MPRF:
n_l9___2 [X₂+1 ]
n_l10___1 [X₂ ]
n_l9___5 [X₂+1 ]
n_l10___3 [X₂+1 ]
n_l9___6 [X₂ ]
n_l10___4 [X₂ ]
MPRF for transition t₉₇: n_l9___5(X₀, X₁, X₂, X₃) → n_l10___3(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 < X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀+1 {O(n)}
MPRF:
n_l9___2 [X₂ ]
n_l10___1 [X₂ ]
n_l9___5 [X₂+1 ]
n_l10___3 [X₂ ]
n_l9___6 [X₂ ]
n_l10___4 [X₂ ]
MPRF for transition t₉₃: n_l10___4(X₀, X₁, X₂, X₃) → n_l9___6(X₀, X₁-1, X₂, X₃) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
6⋅X₀⋅X₀+3⋅X₀+X₃+1 {O(n^2)}
MPRF:
n_l10___3 [X₁ ]
n_l9___5 [0 ]
n_l9___2 [X₁ ]
n_l10___1 [X₁ ]
n_l9___6 [X₁+1 ]
n_l10___4 [X₁+1 ]
MPRF for transition t₉₈: n_l9___6(X₀, X₁, X₂, X₃) → n_l10___4(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀ ∧ 0 < X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 < X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
20⋅X₀⋅X₀+10⋅X₀+X₃+1 {O(n^2)}
MPRF:
n_l10___3 [2⋅X₁+X₂-X₀ ]
n_l9___5 [0 ]
n_l9___2 [2⋅X₁+X₂-X₀ ]
n_l10___1 [X₁+X₂-1 ]
n_l9___6 [X₁+1 ]
n_l10___4 [X₁ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:2⋅X₀⋅X₀+2⋅X₀+2⋅X₃+12 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: X₀⋅X₀+X₃ {O(n^2)}
t₁₄: X₀ {O(n)}
t₁₅: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₀⋅X₀+X₀+X₃+1 {O(n^2)}
t₁₀: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₀⋅X₀+2⋅X₀+2⋅X₃+12 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: X₀⋅X₀+X₃ {O(n^2)}
t₁₄: X₀ {O(n)}
t₁₅: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₀⋅X₀+X₀+X₃+1 {O(n^2)}
t₁₀: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₀+X₃ {O(n)}
t₁₁, X₂: X₀ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₀ {O(n)}
t₁₄, X₂: X₀ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₀: 2⋅X₀ {O(n)}
t₁₅, X₁: X₀+X₃ {O(n)}
t₁₅, X₂: 2⋅X₀ {O(n)}
t₁₅, X₃: 2⋅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)}
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: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₃ {O(n)}
t₈, X₂: X₀ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₀+X₃ {O(n)}
t₉, X₂: X₀ {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₀: 2⋅X₀ {O(n)}
t₁₀, X₁: X₀+X₃ {O(n)}
t₁₀, X₂: 2⋅X₀ {O(n)}
t₁₀, X₃: 2⋅X₃ {O(n)}