Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0 ∧ X₁ < 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁-1, X₀-1, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Eliminate variables {X₂} that do not contribute to the problem

Found invariant 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l5

Found invariant 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₃: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₄: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀
t₁₅: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁
t₁₆: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ < 0
t₁₇: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₁₈: l3(X₀, X₁, X₂, X₃) → l1(X₁-1, X₀-1, X₂, X₃)
t₁₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0

Chain transitions t₁₈: l3→l1 and t₁₆: l1→l4 to t₅₄: l3→l4

Chain transitions t₁₇: l2→l1 and t₁₆: l1→l4 to t₅₅: l2→l4

Chain transitions t₁₇: l2→l1 and t₁₅: l1→l3 to t₅₆: l2→l3

Chain transitions t₁₈: l3→l1 and t₁₅: l1→l3 to t₅₇: l3→l3

Chain transitions t₁₇: l2→l1 and t₁₄: l1→l3 to t₅₈: l2→l3

Chain transitions t₁₈: l3→l1 and t₁₄: l1→l3 to t₅₉: l3→l3

Analysing control-flow refined program

Found invariant 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l5

Found invariant 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l4

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ for location n_l3___4

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l3___5

Found invariant 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l5

Found invariant 0 ≤ X₀ for location n_l3___2

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l4

Found invariant 0 ≤ X₁ for location n_l3___1

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: 1 {O(1)}

Sizebounds

t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₇, X₀: X₂ {O(n)}
t₁₇, X₁: X₃ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₂: 2⋅X₂ {O(n)}
t₁₉, X₃: 2⋅X₃ {O(n)}