Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁-1, X₂, X₃) :|: 0 ≤ X₁
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁, X₂, X₃) :|: X₁ < 0
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Preprocessing
Found invariant X₁ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l5
Found invariant X₁ ≤ X₃ for location l1
Found invariant X₁ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l4
Found invariant X₁ ≤ X₃ ∧ 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ ≤ X₃
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁-1, X₂, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁, X₂, X₃) :|: X₁ < 0 ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₀ ≤ 0
MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁-1, X₂, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF:
l3 [X₁+1 ]
l1 [X₁+1 ]
Found invariant 1 ≤ 0 for location l5
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l4
Found invariant 1 ≤ 0 for location l3
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l5
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l1
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l4
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location l3
MPRF for transition t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃ of depth 1:
new bound:
X₃⋅X₃⋅X₃+5⋅X₃⋅X₃+X₂⋅X₃+2⋅X₂+9⋅X₃+7 {O(n^3)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+2 ]
MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁, X₂, X₃) :|: X₁ < 0 ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃⋅X₃+5⋅X₃⋅X₃+X₂⋅X₃+2⋅X₂+8⋅X₃+5 {O(n^3)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+1 ]
Analysing control-flow refined program
Cut unsatisfiable transition t₈₉: n_l1___4→l4
Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___4
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l3___5
Found invariant X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l5
Found invariant X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___2
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1
Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l4
Found invariant X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₀ for location n_l3___1
MPRF for transition t₇₅: n_l1___4(X₀, X₁, X₂, X₃) → n_l3___2(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ 1+X₁ ∧ 1+X₁ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃+3 {O(n)}
MPRF:
n_l3___2 [X₁+1 ]
n_l1___4 [X₁+2 ]
MPRF for transition t₇₉: n_l3___2(X₀, X₁, X₂, X₃) → n_l1___4(X₀+X₁, X₁-1, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃+3 {O(n)}
MPRF:
n_l3___2 [X₁+2 ]
n_l1___4 [X₁+2 ]
MPRF for transition t₇₄: n_l1___3(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ X₁ < 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ of depth 1:
new bound:
2^(X₃+3)⋅X₂+2^(X₃+3)⋅X₃+X₂+X₃+3 {O(EXP)}
MPRF:
n_l3___1 [X₀ ]
n_l1___3 [X₀+1 ]
MPRF for transition t₇₇: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀+X₁, X₁, X₂, X₃) :|: X₁ < 0 ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₁ < 0 ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₀ of depth 1:
new bound:
2^(X₃+3)⋅X₂+2^(X₃+3)⋅X₃+2⋅X₃+X₂+2 {O(EXP)}
MPRF:
n_l3___1 [X₀+1 ]
n_l1___3 [X₀-X₁ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:2⋅X₃⋅X₃⋅X₃+10⋅X₃⋅X₃+2⋅X₂⋅X₃+18⋅X₃+4⋅X₂+17 {O(n^3)}
t₀: 1 {O(1)}
t₂: X₃⋅X₃⋅X₃+5⋅X₃⋅X₃+X₂⋅X₃+2⋅X₂+9⋅X₃+7 {O(n^3)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₃+1 {O(n)}
t₅: X₃⋅X₃⋅X₃+5⋅X₃⋅X₃+X₂⋅X₃+2⋅X₂+8⋅X₃+5 {O(n^3)}
t₆: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₃⋅X₃⋅X₃+10⋅X₃⋅X₃+2⋅X₂⋅X₃+18⋅X₃+4⋅X₂+17 {O(n^3)}
t₀: 1 {O(1)}
t₂: X₃⋅X₃⋅X₃+5⋅X₃⋅X₃+X₂⋅X₃+2⋅X₂+9⋅X₃+7 {O(n^3)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₃+1 {O(n)}
t₅: X₃⋅X₃⋅X₃+5⋅X₃⋅X₃+X₂⋅X₃+2⋅X₂+8⋅X₃+5 {O(n^3)}
t₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: X₃⋅X₃+4⋅X₃+X₂+3 {O(n^2)}
t₂, X₁: X₃+1 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₃⋅X₃+2⋅X₂+4⋅X₃+3 {O(n^2)}
t₃, X₁: 2⋅X₃+1 {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₄, X₀: X₃⋅X₃+4⋅X₃+X₂+3 {O(n^2)}
t₄, X₁: X₃+1 {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₃⋅X₃+4⋅X₃+X₂+3 {O(n^2)}
t₅, X₁: X₃+1 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₃⋅X₃+2⋅X₂+4⋅X₃+3 {O(n^2)}
t₆, X₁: 2⋅X₃+1 {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 2⋅X₃ {O(n)}