Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₄: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂) :|: X₂+1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂+1) :|: X₂+1 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l2(X₀-1, X₁, X₂) :|: X₀ ≤ X₂
t₀: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀

Preprocessing

Found invariant 1+X₁ ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₄: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁: l1(X₀, X₁, X₂) → l2(X₀, X₁+1, X₂) :|: X₂+1 ≤ X₀ ∧ 1+X₁ ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂+1) :|: X₂+1 ≤ X₀ ∧ 1+X₁ ≤ X₀
t₃: l1(X₀, X₁, X₂) → l2(X₀-1, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₀: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: X₁+1 ≤ X₀

Analysing control-flow refined program

Found invariant 1+X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location n_l2___6

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l2___5

Found invariant 1+X₁ ≤ X₀ for location n_l1___7

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l1___2

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l1___3

Found invariant 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___1

Found invariant 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l2___4

Found invariant 1+X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location n_l2___6

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l2___5

Found invariant 1+X₁ ≤ X₀ for location n_l1___7

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l1___2

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l1___3

Found invariant 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___1

Found invariant 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l2___4

Found invariant 1+X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location n_l2___6

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l2___5

Found invariant 1+X₁ ≤ X₀ for location n_l1___7

Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l1___2

Found invariant 1+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location n_l1___3

Found invariant 2+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l1___1

Found invariant 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l2___4

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₄: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
t₃: inf {Infinity}
t₀: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₄: 1 {O(1)}
t₁: inf {Infinity}
t₂: inf {Infinity}
t₃: inf {Infinity}
t₀: inf {Infinity}

Sizebounds

t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}