Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: eval_foo_.critedge_in, eval_foo_2, eval_foo_3, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₀: eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄)
t₈: eval_foo_2(X₀, X₁, X₂, X₃, X₄) → eval_foo_3(X₀, X₁, nondef.0, X₃, X₄)
t₉: eval_foo_3(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₂, X₀, X₂, X₃, X₄)
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₄, X₃, X₂, X₃, X₄)
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ 2⋅X₀+X₁
t₅: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄) :|: 1+2⋅X₀+X₁ ≤ 0
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₀ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 2⋅X₀+X₁ ≤ 0
t₆: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_2(X₀, X₁, X₂, X₃, X₄)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀ for location eval_foo_2

Found invariant 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀ for location eval_foo_bb2_in

Found invariant X₃ ≤ X₁ for location eval_foo_bb1_in

Found invariant X₃ ≤ X₁ for location eval_foo_stop

Found invariant X₃ ≤ X₁ for location eval_foo_.critedge_in

Found invariant 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀ for location eval_foo_3

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: eval_foo_.critedge_in, eval_foo_2, eval_foo_3, eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₀: eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₁
t₈: eval_foo_2(X₀, X₁, X₂, X₃, X₄) → eval_foo_3(X₀, X₁, nondef.0, X₃, X₄) :|: 2 ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 4+X₃ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 6+X₃ ≤ X₀ ∧ 8+X₁+X₃ ≤ 0 ∧ X₃ ≤ X₁
t₉: eval_foo_3(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₂, X₀, X₂, X₃, X₄) :|: 2 ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 4+X₃ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 6+X₃ ≤ X₀ ∧ 8+X₁+X₃ ≤ 0 ∧ X₃ ≤ X₁
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₄, X₃, X₂, X₃, X₄)
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1 ∧ X₃ ≤ X₁
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ 2⋅X₀+X₁ ∧ X₃ ≤ X₁
t₅: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_.critedge_in(X₀, X₁, X₂, X₃, X₄) :|: 1+2⋅X₀+X₁ ≤ 0 ∧ X₃ ≤ X₁
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₀ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 2⋅X₀+X₁ ≤ 0 ∧ X₃ ≤ X₁
t₆: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_2(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 4+X₃ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 6+X₃ ≤ X₀ ∧ 8+X₁+X₃ ≤ 0 ∧ X₃ ≤ X₁
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄)

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₀ ∧ 0 ≤ 2⋅X₀+X₁ ∧ 2⋅X₀+X₁ ≤ 0 ∧ X₃ ≤ X₁

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₆: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_2(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 4+X₃ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 6+X₃ ≤ X₀ ∧ 8+X₁+X₃ ≤ 0 ∧ X₃ ≤ X₁

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₈: eval_foo_2(X₀, X₁, X₂, X₃, X₄) → eval_foo_3(X₀, X₁, nondef.0, X₃, X₄) :|: 2 ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 4+X₃ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 6+X₃ ≤ X₀ ∧ 8+X₁+X₃ ≤ 0 ∧ X₃ ≤ X₁

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₉: eval_foo_3(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₂, X₀, X₂, X₃, X₄) :|: 2 ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 4+X₃ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 6+X₃ ≤ X₀ ∧ 8+X₁+X₃ ≤ 0 ∧ X₃ ≤ X₁

All Bounds

Timebounds

Overall timebound:10 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 10 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₄ {O(n)}
t₂, X₁: X₃ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₁: X₃+X₄ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₁: X₃+X₄ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₅, X₁: X₃+X₄ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₆, X₀: X₄ {O(n)}
t₆, X₁: X₃ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₈, X₀: X₄ {O(n)}
t₈, X₁: X₃ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₉, X₁: X₄ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₁: 3⋅X₃+3⋅X₄ {O(n)}
t₁₀, X₃: 6⋅X₃ {O(n)}
t₁₀, X₄: 6⋅X₄ {O(n)}