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) :|: 5⋅X₁ < 4⋅X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 4⋅X₀ ≤ 5⋅X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l1(2⋅X₀+4⋅X₁, 4⋅X₀, X₂, X₃, X₄)
t₅: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₁: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 5⋅X₁ < 4⋅X₀
t₁₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 4⋅X₀ ≤ 5⋅X₁
t₁₄: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₁₅: l3(X₀, X₁, X₂, X₃) → l1(2⋅X₀+4⋅X₁, 4⋅X₀, X₂, X₃)
t₁₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Chain transitions t₁₅: l3→l1 and t₁₃: l1→l4 to t₃₀: l3→l4

Chain transitions t₁₄: l2→l1 and t₁₃: l1→l4 to t₃₁: l2→l4

Chain transitions t₁₄: l2→l1 and t₁₂: l1→l3 to t₃₂: l2→l3

Chain transitions t₁₅: l3→l1 and t₁₂: l1→l3 to t₃₃: l3→l3

Analysing control-flow refined program

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 ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location n_l3___3

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

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: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₁: 1 {O(1)}
t₁₂: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₂: 2⋅X₂ {O(n)}
t₁₃, X₃: 2⋅X₃ {O(n)}
t₁₄, X₀: X₂ {O(n)}
t₁₄, X₁: 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)}