Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 5
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 5 < X₀
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 5 ∧ 5 ≤ X₀
t₇: l4(X₀, X₁) → l5(X₀, X₁)
Preprocessing
Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5
Found invariant X₀ ≤ X₁ for location l1
Found invariant X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ X₀ ≤ X₁
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 5 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 5 < X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 5 ∧ 5 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₀ ≤ 0
MPRF for transition t₄: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 5 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
l3 [X₀ ]
l1 [X₀ ]
MPRF for transition t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 5 < X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+5 {O(n)}
MPRF:
l3 [X₀-5 ]
l1 [X₀-5 ]
Analysing control-flow refined program
Cut unsatisfiable transition t₉₂: n_l1___4→l4
Cut unsatisfiable transition t₉₄: n_l1___8→l4
Cut unsatisfiable transition t₉₅: n_l1___9→l4
Found invariant 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 5 ≤ X₀ for location n_l1___9
Found invariant 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location n_l1___4
Found invariant 1 ≤ 0 for location n_l3___3
Found invariant 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 5 ≤ X₀ for location n_l3___6
Found invariant X₁ ≤ 4 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 7 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀ for location n_l1___10
Found invariant X₁ ≤ 5 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10 ∧ 5 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location n_l1___8
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___11
Found invariant X₁ ≤ 4 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5
Found invariant 1 ≤ 0 for location n_l1___5
Found invariant 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location n_l3___2
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant X₁ ≤ 4 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant X₁ ≤ 5 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 10 ∧ 5 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 5 ∧ 5 ≤ X₀ for location n_l3___1
Found invariant X₁ ≤ 4 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 7 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 1 ≤ X₀ for location n_l3___7
Cut unsatisfiable transition t₆₉: n_l1___5→n_l3___3
Cut unsatisfiable transition t₉₃: n_l1___5→l4
Cut unsatisfiable transition t₇₇: n_l3___3→n_l1___5
Cut unsatisfiable transition t₇₉: n_l3___6→n_l1___5
Cut unreachable locations [n_l1___5; n_l3___3] from the program graph
MPRF for transition t₆₆: n_l1___10(X₀, X₁) → n_l3___7(X₀, X₁) :|: X₀ < 5 ∧ X₀ ≤ X₁ ∧ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ 4 ∧ X₁ ≤ 4+X₀ ∧ X₀+X₁ ≤ 7 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀ of depth 1:
new bound:
4 {O(1)}
MPRF:
n_l3___7 [X₀ ]
n_l1___10 [X₀+1 ]
MPRF for transition t₈₁: n_l3___7(X₀, X₁) → n_l1___10(X₀-1, X₁) :|: X₀ < 5 ∧ 0 < X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ < 5 ∧ X₁ ≤ 4 ∧ X₁ ≤ 3+X₀ ∧ X₀+X₁ ≤ 7 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 1 ≤ X₀ of depth 1:
new bound:
3 {O(1)}
MPRF:
n_l3___7 [X₀ ]
n_l1___10 [X₀ ]
MPRF for transition t₇₁: n_l1___9(X₀, X₁) → n_l3___6(X₀, X₁) :|: 0 < X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 5 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 < X₀ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 5 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF:
n_l3___6 [X₀-1 ]
n_l1___9 [X₀ ]
MPRF for transition t₈₀: n_l3___6(X₀, X₁) → n_l1___9(X₀-1, X₁) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 5 ≤ X₁ ∧ 5 < X₀ ∧ X₀ ≤ X₁ ∧ 6 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 5 ≤ X₀ of depth 1:
new bound:
X₁+5 {O(n)}
MPRF:
n_l3___6 [X₀-5 ]
n_l1___9 [X₀-5 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: X₁+5 {O(n)}
t₆: inf {Infinity}
t₇: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: X₁+5 {O(n)}
t₆: inf {Infinity}
t₇: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₂, X₀: X₁+8 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+3 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₄, X₀: 3 {O(1)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: X₁+8 {O(n)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 5 {O(1)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: X₁+3 {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}