Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(E, 0, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l3(X₀-1, X₁+1, X₂, X₃) :|: 1 ≤ X₀
t₈: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂-1, 0) :|: 1 ≤ X₂
t₄: l2(X₀, X₁, X₂, X₃) → l2(X₀-1, X₁+1, X₂-1, E) :|: 1 ≤ X₂ ∧ E+1 ≤ 0
t₅: l2(X₀, X₁, X₂, X₃) → l2(X₀-1, X₁+1, X₂-1, E) :|: 1 ≤ X₂ ∧ 1 ≤ E
t₆: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁-1, X₀-1, X₃) :|: 1 ≤ X₁
Preprocessing
Eliminate variables {X₃} that do not contribute to the problem
Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant X₁ ≤ 0 ∧ 0 ≤ X₁ for location l1
Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: E
Locations: l0, l1, l2, l3, l4
Transitions:
t₁₇: l0(X₀, X₁, X₂) → l1(E, 0, X₂)
t₁₈: l1(X₀, X₁, X₂) → l3(X₀-1, X₁+1, X₂) :|: 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
t₁₉: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
t₂₀: l2(X₀, X₁, X₂) → l2(X₀, X₁, X₂-1) :|: 1 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₁: l2(X₀, X₁, X₂) → l2(X₀-1, X₁+1, X₂-1) :|: 1 ≤ X₂ ∧ E+1 ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₂: l2(X₀, X₁, X₂) → l2(X₀-1, X₁+1, X₂-1) :|: 1 ≤ X₂ ∧ 1 ≤ E ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₃: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₄: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₅: l3(X₀, X₁, X₂) → l2(X₀, X₁-1, X₀-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
Chain transitions t₂₄: l3→l1 and t₁₉: l1→l4 to t₉₈: l3→l4
Chain transitions t₁₇: l0→l1 and t₁₉: l1→l4 to t₉₉: l0→l4
Chain transitions t₁₇: l0→l1 and t₁₈: l1→l3 to t₁₀₀: l0→l3
Chain transitions t₂₄: l3→l1 and t₁₈: l1→l3 to t₁₀₁: l3→l3
Analysing control-flow refined program
Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant X₁ ≤ 0 ∧ 0 ≤ X₁ for location l1
Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₂₄₃: n_l1___5→l4
Found invariant 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___6
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___4
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location n_l1___2
Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___11
Found invariant 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___12
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location n_l2___3
Found invariant 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___9
Found invariant X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l3___14
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___8
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___5
Found invariant X₁ ≤ 0 ∧ 0 ≤ X₁ for location l1
Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___1
Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___13
Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location n_l3___10
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___7
MPRF for transition t₁₉₀: n_l1___2(X₀, X₁, X₂) → n_l3___1(X₀-1, 1, X₂) :|: X₀ ≤ 2 ∧ 0 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ of depth 1:
new bound:
4 {O(1)}
MPRF for transition t₂₁₂: n_l3___1(X₀, X₁, X₂) → n_l2___3(X₀, X₁-1, X₀-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 1 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:
new bound:
2 {O(1)}
MPRF for transition t₂₁₃: n_l3___10(X₀, X₁, X₂) → n_l1___2(X₀, 0, X₂) :|: X₀ ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ 0 ∧ X₁ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ of depth 1:
new bound:
4 {O(1)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: inf {Infinity}
Sizebounds
t₁₇, X₁: 0 {O(1)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₁: 1 {O(1)}
t₁₈, X₂: X₂+1 {O(n)}
t₁₉, X₁: 0 {O(1)}
t₁₉, X₂: X₂+1 {O(n)}
t₂₃, X₂: 1 {O(1)}
t₂₄, X₁: 0 {O(1)}
t₂₄, X₂: 1 {O(1)}