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) :|: X₁ < X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₄ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(1, 1, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₀*X₁, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Eliminate variables {X₂,X₃} that do not contribute to the problem

Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₀ for location l1

Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ for location l4

Found invariant 1 ≤ X₀ for location l3

Problem after Preprocessing

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

Chain transitions t₁₈: l3→l1 and t₁₆: l1→l4 to t₅₈: l3→l4

Chain transitions t₁₇: l2→l1 and t₁₆: l1→l4 to t₅₉: l2→l4

Chain transitions t₁₇: l2→l1 and t₁₅: l1→l3 to t₆₀: l2→l3

Chain transitions t₁₈: l3→l1 and t₁₅: l1→l3 to t₆₁: l3→l3

Chain transitions t₁₇: l2→l1 and t₁₄: l1→l3 to t₆₂: l2→l3

Chain transitions t₁₈: l3→l1 and t₁₄: l1→l3 to t₆₃: l3→l3

Analysing control-flow refined program

Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₀ for location l1

Found invariant 1 ≤ X₀ for location l4

Found invariant 1 ≤ 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

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₁+X₂ ≤ 1 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 1 ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 2 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___4

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 2 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___5

Found invariant 2 ≤ X₀ for location n_l1___3

Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ for location l5

Found invariant 1+X₁ ≤ X₂ ∧ 2 ≤ X₀ for location n_l3___2

Found invariant X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 2 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l1

Found invariant X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ for location l4

Found invariant 1+X₂ ≤ X₁ ∧ 2 ≤ X₀ 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)}
t₁₄, X₂: X₂ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₇, X₀: 1 {O(1)}
t₁₇, X₁: 1 {O(1)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₂: 2⋅X₂ {O(n)}