Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l1(X₀-1, D, X₂) :|: 1 ≤ D ∧ 0 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l1(X₀-1, D, X₂) :|: D+1 ≤ 0 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l1(X₀, 0, X₂) :|: 0 ≤ X₀
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₀+1 ≤ 0
Preprocessing
Eliminate variables {X₁,X₂} that do not contribute to the problem
Found invariant 1+X₀ ≤ 0 for location l2
Problem after Preprocessing
Start: l0
Program_Vars: X₀
Temp_Vars: D
Locations: l0, l1, l2
Transitions:
t₁₂: l0(X₀) → l1(X₀)
t₁₃: l1(X₀) → l1(X₀-1) :|: 1 ≤ D ∧ 0 ≤ X₀
t₁₄: l1(X₀) → l1(X₀-1) :|: D+1 ≤ 0 ∧ 0 ≤ X₀
t₁₅: l1(X₀) → l1(X₀) :|: 0 ≤ X₀
t₁₆: l1(X₀) → l2(X₀) :|: X₀+1 ≤ 0
MPRF for transition t₁₃: l1(X₀) → l1(X₀-1) :|: 1 ≤ D ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₀+1 ]
MPRF for transition t₁₄: l1(X₀) → l1(X₀-1) :|: D+1 ≤ 0 ∧ 0 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₀+1 ]
Found invariant 1 ≤ 0 for location l2
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l2
Found invariant 1 ≤ 0 for location l1
Found invariant 1+X₀ ≤ 0 for location l2
Analysing control-flow refined program
Cut unsatisfiable transition t₉₈: n_l1___1→l2
Found invariant 1+X₀ ≤ 0 for location l2
Found invariant 0 ≤ 1+X₀ for location n_l1___2
Found invariant 0 ≤ X₀ for location n_l1___1
MPRF for transition t₇₈: n_l1___1(X₀) → n_l1___2(Arg0_P) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 0 ≤ X₀ of depth 1:
new bound:
3⋅X₀+5 {O(n)}
MPRF:
n_l1___1 [X₀+1 ]
n_l1___2 [X₀+1 ]
MPRF for transition t₇₉: n_l1___1(X₀) → n_l1___2(Arg0_P) :|: 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 0 ≤ X₀ of depth 1:
new bound:
3⋅X₀+5 {O(n)}
MPRF:
n_l1___1 [X₀+1 ]
n_l1___2 [X₀+1 ]
MPRF for transition t₈₀: n_l1___2(X₀) → n_l1___1(X₀) :|: 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
3⋅X₀+7 {O(n)}
MPRF:
n_l1___1 [X₀+1 ]
n_l1___2 [X₀+2 ]
MPRF for transition t₈₁: n_l1___2(X₀) → n_l1___2(Arg0_P) :|: 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
3⋅X₀+7 {O(n)}
MPRF:
n_l1___1 [X₀+1 ]
n_l1___2 [X₀+2 ]
MPRF for transition t₈₂: n_l1___2(X₀) → n_l1___2(Arg0_P) :|: 0 ≤ 1+X₀ ∧ 0 ≤ 1+X₀ ∧ 0 ≤ 1+Arg0_P ∧ X₀ ≤ Arg0_P+1 ∧ 1+Arg0_P ≤ X₀ ∧ 0 ≤ 1+X₀ of depth 1:
new bound:
3⋅X₀+7 {O(n)}
MPRF:
n_l1___1 [X₀+1 ]
n_l1___2 [X₀+2 ]
Found invariant 1+X₀ ≤ 0 for location l2
Found invariant 0 ≤ 1+X₀ for location n_l1___2
Found invariant 0 ≤ X₀ for location n_l1___1
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: X₀+1 {O(n)}
t₁₄: X₀+1 {O(n)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: X₀+1 {O(n)}
t₁₄: X₀+1 {O(n)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
Sizebounds
t₁₂, X₀: X₀ {O(n)}
t₁₃, X₀: 3⋅X₀+1 {O(n)}
t₁₄, X₀: 3⋅X₀+1 {O(n)}
t₁₅, X₀: 3⋅X₀+1 {O(n)}
t₁₆, X₀: 7⋅X₀+2 {O(n)}