Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₆: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂
t₅: l1(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₂ ≤ 0
t₇: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₈: l2(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: D+1 ≤ X₁
t₉: l2(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₁+1 ≤ D
t₁₀: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1)
t₂: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 1 ≤ X₀
t₃: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 0
t₄: l5(X₀, X₁, X₂) → l1(X₀, D, X₀)
t₁₁: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₁: l7(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
Preprocessing
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l2
Found invariant X₀ ≤ 0 for location l6
Found invariant 1 ≤ X₀ for location l5
Found invariant X₀ ≤ 0 for location l8
Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l1
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₆: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₅: l1(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₇: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₈: l2(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: D+1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₉: l2(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₁+1 ≤ D ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₁₀: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₂: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 1 ≤ X₀
t₃: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 0
t₄: l5(X₀, X₁, X₂) → l1(X₀, D, X₀) :|: 1 ≤ X₀
t₁₁: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₀ ≤ 0
t₁: l7(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
MPRF for transition t₅: l1(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀+1 {O(n)}
MPRF:
l2 [X₀+X₂+1 ]
l3 [X₀+X₂+1 ]
l4 [2⋅X₀+1 ]
l5 [2⋅X₀+1 ]
l1 [X₀+X₂+1 ]
MPRF for transition t₇: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l2 [X₂ ]
l3 [X₂-1 ]
l4 [X₀ ]
l5 [X₀ ]
l1 [X₂ ]
MPRF for transition t₁₀: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l2 [X₂ ]
l3 [X₂ ]
l4 [X₀ ]
l5 [X₀ ]
l1 [X₂ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₄₃₀: n_l4___5→l6
Eliminate variables {NoDet0,X₁} that do not contribute to the problem
Found invariant 1 ≤ X₀ for location n_l5___1
Found invariant 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₀ for location n_l2___7
Found invariant X₀ ≤ 0 for location l6
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___6
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l1___3
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l2___2
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l4___5
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l5___4
Found invariant X₀ ≤ 0 for location l8
Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l1
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₄₅₅: l1(X₀, X₂) → n_l2___7(X₀, X₂) :|: X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l1 [X₂+1 ]
n_l2___2 [X₂ ]
n_l2___7 [X₂ ]
l3 [X₂ ]
n_l4___5 [X₀ ]
n_l5___4 [X₀ ]
n_l1___3 [X₂ ]
MPRF for transition t₄₅₇: l3(X₀, X₂) → l1(X₀, X₂-1) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l1 [X₂ ]
n_l2___2 [X₀ ]
n_l2___7 [X₂ ]
l3 [X₂ ]
n_l4___5 [X₀ ]
n_l5___4 [X₂ ]
n_l1___3 [X₀ ]
MPRF for transition t₄₆₅: n_l2___2(X₀, X₂) → l3(X₀, X₂) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l1 [X₂ ]
n_l2___2 [X₀ ]
n_l2___7 [X₂ ]
l3 [X₂-1 ]
n_l4___5 [X₀ ]
n_l5___4 [X₂ ]
n_l1___3 [X₂ ]
MPRF for transition t₄₆₆: n_l2___7(X₀, X₂) → n_l4___5(Arg0_P, Arg2_P) :|: 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ Arg2_P ≤ X₀ ∧ 1 ≤ Arg2_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ Arg0_P ≤ Arg2_P ∧ Arg2_P ≤ Arg0_P ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₂ ]
n_l2___2 [X₂-1 ]
n_l2___7 [X₂ ]
l3 [X₂-1 ]
n_l4___5 [X₀-1 ]
n_l5___4 [X₀-1 ]
n_l1___3 [X₂-1 ]
MPRF for transition t₄₆₇: n_l2___7(X₀, X₂) → n_l4___5(Arg0_P, Arg2_P) :|: 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ Arg2_P ≤ X₀ ∧ 1 ≤ Arg2_P ∧ Arg0_P ≤ Arg2_P ∧ Arg2_P ≤ Arg0_P ∧ X₂ ≤ Arg2_P ∧ Arg2_P ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF:
l1 [X₂ ]
n_l2___2 [X₀-1 ]
n_l2___7 [X₂ ]
l3 [X₂-1 ]
n_l4___5 [X₀-1 ]
n_l5___4 [X₀-1 ]
n_l1___3 [X₂-1 ]
MPRF for transition t₄₆₈: n_l2___7(X₀, X₂) → l3(X₀, X₂) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l1 [X₂ ]
n_l2___2 [X₀ ]
n_l2___7 [X₂ ]
l3 [X₂-1 ]
n_l4___5 [X₂ ]
n_l5___4 [X₂ ]
n_l1___3 [X₀ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₅: 2⋅X₀+1 {O(n)}
t₆: inf {Infinity}
t₇: X₀ {O(n)}
t₈: inf {Infinity}
t₉: inf {Infinity}
t₁₀: X₀ {O(n)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₅: 2⋅X₀+1 {O(n)}
t₆: inf {Infinity}
t₇: X₀ {O(n)}
t₈: inf {Infinity}
t₉: inf {Infinity}
t₁₀: X₀ {O(n)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₅, X₀: 0 {O(1)}
t₅, X₂: 0 {O(1)}
t₆, X₀: X₀ {O(n)}
t₆, X₂: X₀ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₂: X₀ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₂: X₀ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₂: X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₂: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₂: 2⋅X₀+X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₂: X₀ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}