Initial Problem

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

Preprocessing

Cut unreachable locations [l4; l5] from the program graph

Eliminate variables {X₁,X₃} that do not contribute to the problem

Found invariant X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: E
Locations: l0, l1, l2, l3
Transitions:
t₁₄: l0(X₀, X₁) → l1(E, X₁)
t₁₅: l1(X₀, X₁) → l2(X₀, E) :|: X₀ ≤ 0
t₁₆: l1(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ X₀
t₁₇: l2(X₀, X₁) → l1(E, X₁) :|: X₁ ≤ 0 ∧ X₀ ≤ 0
t₁₈: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₉: l3(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ X₀

Chain transitions t₁₇: l2→l1 and t₁₆: l1→l3 to t₄₇: l2→l3

Chain transitions t₁₄: l0→l1 and t₁₆: l1→l3 to t₄₈: l0→l3

Chain transitions t₁₄: l0→l1 and t₁₅: l1→l2 to t₄₉: l0→l2

Chain transitions t₁₇: l2→l1 and t₁₅: l1→l2 to t₅₀: l2→l2

Analysing control-flow refined program

Found invariant X₀ ≤ 0 for location l2

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 X₁ ≤ 0 for location n_l1___2

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l2___1

Found invariant X₀ ≤ 0 for location n_l2___3

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 X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₀ for location l3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₁₄, X₁: X₁ {O(n)}