Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H, I, J
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(H, I, J, 0, X₄, X₅, X₆)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃+1, X₄, X₅, X₆) :|: X₃+1 ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₀, 0, H) :|: X₂ ≤ X₃
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅+1, X₆) :|: X₅+1 ≤ X₄
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₄ ≤ X₅

Preprocessing

Eliminate variables {I,X₁,X₆} that do not contribute to the problem

Found invariant 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l2

Found invariant 0 ≤ X₂ for location l1

Found invariant 0 ≤ X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: H, J
Locations: l0, l1, l2, l3
Transitions:
t₁₁: l0(X₀, X₁, X₂, X₃, X₄) → l1(H, J, 0, X₃, X₄)
t₁₂: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂+1, X₃, X₄) :|: X₂+1 ≤ X₁ ∧ 0 ≤ X₂
t₁₃: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₀, 0) :|: X₁ ≤ X₂ ∧ 0 ≤ X₂
t₁₄: l2(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄+1) :|: X₄+1 ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂
t₁₅: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂

Analysing control-flow refined program

Found invariant 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l2

Found invariant X₂ ≤ 0 ∧ 0 ≤ X₂ for location l1

Found invariant 0 ≤ X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l3

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

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₄ ≤ 0 ∧ X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l2

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location n_l2___1

Found invariant 0 ≤ X₂ for location l1

Found invariant 0 ≤ X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l3

Solv. Size Bound: t₉₃: n_l2___1→n_l2___1 for X₀

Solv. Size Bound: t₉₃: n_l2___1→n_l2___1 for X₁

Solv. Size Bound: t₉₃: n_l2___1→n_l2___1 for X₂

Solv. Size Bound: t₉₃: n_l2___1→n_l2___1 for X₃

cycle: [t₉₃: n_l2___1→n_l2___1]
loop: (1 ≤ X₄ ∧ X₄ ≤ X₀ ∧ 1+X₄ ≤ X₀,(X₀,X₃) -> (X₀,X₀)
overappr. closed-form: 2⋅X₀ {O(n)}
runtime bound: X₀+X₄+2 {O(n)}

Solv. Size Bound - Lifting for t₉₃: n_l2___1→n_l2___1 and X₃: inf {Infinity}

Solv. Size Bound: t₉₃: n_l2___1→n_l2___1 for X₀

Solv. Size Bound: t₉₃: n_l2___1→n_l2___1 for X₁

Solv. Size Bound: t₉₃: n_l2___1→n_l2___1 for X₂

Solv. Size Bound - Lifting for t₉₃: n_l2___1→n_l2___1 and X₃: inf {Infinity}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: inf {Infinity}
t₁₅: 1 {O(1)}

Sizebounds

t₁₁, X₂: 0 {O(1)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₃, X₄: 0 {O(1)}