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) :|: X₀ < 10
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: 10 ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ < 3
t₅: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 3 < X₀
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 3 ∧ 3 ≤ X₀
t₇: l4(X₀, X₁) → l5(X₀, X₁)
Preprocessing
Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₀ for location l5
Found invariant X₁ ≤ X₀ for location l1
Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₀ for location l4
Found invariant X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9 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) :|: X₀ < 10 ∧ X₁ ≤ X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: 10 ≤ X₀ ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ < 3 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9
t₅: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 3 < X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ ≤ 3 ∧ 3 ≤ X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9
t₇: l4(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ X₀ ∧ 10 ≤ X₀
MPRF for transition t₄: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ < 3 ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9 of depth 1:
new bound:
X₁+10 {O(n)}
MPRF:
l3 [10-X₀ ]
l1 [10-X₀ ]
MPRF for transition t₅: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 3 < X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ 9 of depth 1:
new bound:
X₁+10 {O(n)}
MPRF:
l3 [10-X₀ ]
l1 [10-X₀ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₈₉: n_l1___10→l4
Cut unsatisfiable transition t₉₀: n_l1___5→l4
Cut unsatisfiable transition t₉₂: n_l1___8→l4
Found invariant 1 ≤ 0 for location n_l1___6
Found invariant 1 ≤ 0 for location n_l3___4
Found invariant X₁ ≤ 9 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 19 ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ X₀ ≤ 6+X₁ ∧ X₀ ≤ 10 ∧ 5 ≤ X₀ for location n_l1___9
Found invariant X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 ∧ 3 ≤ X₀ for location n_l3___3
Found invariant X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 for location n_l1___10
Found invariant X₁ ≤ 3 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 6 ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 3 ≤ X₀ for location n_l1___8
Found invariant X₁ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 9 for location n_l3___11
Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₀ for location l5
Found invariant X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 ∧ 3 ≤ X₀ for location n_l1___5
Found invariant X₁ ≤ 8 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 17 ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 9 ∧ 5 ≤ X₀ for location n_l3___2
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant X₁ ≤ X₀ ∧ 10 ≤ X₀ for location l4
Found invariant X₁ ≤ 3 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 6 ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 3 ∧ 3 ≤ X₀ for location n_l3___1
Found invariant X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 for location n_l3___7
Cut unsatisfiable transition t₆₇: n_l1___6→n_l3___4
Cut unsatisfiable transition t₉₁: n_l1___6→l4
Cut unsatisfiable transition t₇₆: n_l3___4→n_l1___6
Cut unsatisfiable transition t₇₉: n_l3___7→n_l1___6
Cut unreachable locations [n_l1___6; n_l3___4] from the program graph
MPRF for transition t₆₄: n_l1___10(X₀, X₁) → n_l3___7(X₀, X₁) :|: X₁ ≤ X₀ ∧ X₀ < 10 ∧ X₀ ≤ 9 ∧ X₁ ≤ 3 ∧ X₁ ≤ X₀ ∧ X₀ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₀ < 10 ∧ X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 of depth 1:
new bound:
X₁+11 {O(n)}
MPRF:
n_l3___7 [9-X₀ ]
n_l1___10 [10-X₀ ]
MPRF for transition t₇₇: n_l3___7(X₀, X₁) → n_l1___10(X₀+1, X₁) :|: X₀ ≤ 9 ∧ X₁ ≤ X₀ ∧ X₁ ≤ 3 ∧ X₀ < 3 ∧ X₁ ≤ X₀ ∧ X₁ ≤ 2 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 5 ∧ X₀ ≤ 3 of depth 1:
new bound:
X₁+5 {O(n)}
MPRF:
n_l3___7 [4-X₀ ]
n_l1___10 [4-X₀ ]
MPRF for transition t₆₉: n_l1___9(X₀, X₁) → n_l3___2(X₀, X₁) :|: X₁ ≤ X₀ ∧ 3 < X₀ ∧ X₁ ≤ X₀ ∧ X₀ < 10 ∧ X₁ ≤ 9 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 19 ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ X₀ ≤ 6+X₁ ∧ X₀ ≤ 10 ∧ 5 ≤ X₀ of depth 1:
new bound:
21 {O(1)}
MPRF:
n_l3___2 [10-X₀ ]
n_l1___9 [11-X₀ ]
MPRF for transition t₇₄: n_l3___2(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: X₀ < 10 ∧ 3 < X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 9 ∧ 3 < X₀ ∧ X₁ ≤ 8 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 17 ∧ 4 ≤ X₁ ∧ 9 ≤ X₀+X₁ ∧ X₀ ≤ 5+X₁ ∧ X₀ ≤ 9 ∧ 5 ≤ X₀ of depth 1:
new bound:
20 {O(1)}
MPRF:
n_l3___2 [10-X₀ ]
n_l1___9 [10-X₀ ]
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+10 {O(n)}
t₅: X₁+10 {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+10 {O(n)}
t₅: X₁+10 {O(n)}
t₆: inf {Infinity}
t₇: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₂, X₀: 2⋅X₁+23 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+10 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₄, X₀: 2⋅X₁+23 {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 10 {O(1)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 3 {O(1)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: X₁+10 {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}