Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₃, X₄, X₂, X₃, X₄)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₁, X₀, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Eliminate variables [X₂] that do not contribute to the problem

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location eval_foo_bb2_in

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ for location eval_foo_bb1_in

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

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₀: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂, X₃, X₂, X₃)
t₁₁: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₁, X₀, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁
t₁₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁
t₁₃: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁
t₁₄: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₁: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₁, X₀, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₃ ≤ X₁

All Bounds

Timebounds

Overall timebound:5 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}

Costbounds

Overall costbound: 5 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}

Sizebounds

t₁₀, X₀: X₂ {O(n)}
t₁₀, X₁: X₃ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₁, X₀: X₃ {O(n)}
t₁₁, X₁: X₂ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₂, X₀: X₂+X₃ {O(n)}
t₁₂, X₁: X₂+X₃ {O(n)}
t₁₂, X₂: 2⋅X₂ {O(n)}
t₁₂, X₃: 2⋅X₃ {O(n)}
t₁₃, X₀: X₂+X₃ {O(n)}
t₁₃, X₁: X₂+X₃ {O(n)}
t₁₃, X₂: 2⋅X₂ {O(n)}
t₁₃, X₃: 2⋅X₃ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}