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(X₂, X₃, X₂, X₃, X₄)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₁, X₀, X₂, X₃, X₄) :|: 1+X₀ ≤ 0 ∧ 1+X₁ ≤ 0
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₁, X₀, X₂, X₃, X₄) :|: 1+X₀ ≤ 0 ∧ 1 ≤ X₁
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₁, X₀, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ 0
t₅: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₁, X₀, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₆: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₇: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₁ ∧ X₁ ≤ 0
t₈: 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 [X₄] that do not contribute to the problem

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:
t₃₆: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂, X₃, X₂, X₃)
t₃₇: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₁, X₀, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ 1+X₁ ≤ 0
t₃₈: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₁, X₀, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ 1 ≤ X₁
t₃₉: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₁, X₀, X₂, X₃) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ 0
t₄₀: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₁, X₀, X₂, X₃) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₄₁: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₄₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ 0
t₄₃: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃)
t₄₄: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb1_in_v1

Found invariant X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location eval_foo_bb1_in_v3

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location eval_foo_bb1_in_v2

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

Found invariant 1+X₃ ≤ 0 ∧ 2+X₂+X₃ ≤ 0 ∧ 2+X₁+X₃ ≤ 0 ∧ 2+X₀+X₃ ≤ 0 ∧ 1+X₂ ≤ 0 ∧ 2+X₁+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location eval_foo_bb1_in_v4

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

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

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₃₆: 1 {O(1)}
t₃₇: inf {Infinity}
t₃₈: inf {Infinity}
t₃₉: inf {Infinity}
t₄₀: inf {Infinity}
t₄₁: 1 {O(1)}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}
t₄₄: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₃₆: 1 {O(1)}
t₃₇: inf {Infinity}
t₃₈: inf {Infinity}
t₃₉: inf {Infinity}
t₄₀: inf {Infinity}
t₄₁: 1 {O(1)}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}
t₄₄: 1 {O(1)}

Sizebounds

t₃₆, X₀: X₂ {O(n)}
t₃₆, X₁: X₃ {O(n)}
t₃₆, X₂: X₂ {O(n)}
t₃₆, X₃: X₃ {O(n)}
t₃₇, X₀: X₂+X₃ {O(n)}
t₃₇, X₁: X₂+X₃ {O(n)}
t₃₇, X₂: X₂ {O(n)}
t₃₇, X₃: X₃ {O(n)}
t₃₈, X₀: X₂+X₃ {O(n)}
t₃₈, X₁: X₂+X₃ {O(n)}
t₃₈, X₂: X₂ {O(n)}
t₃₈, X₃: X₃ {O(n)}
t₃₉, X₀: X₂+X₃ {O(n)}
t₃₉, X₁: X₂+X₃ {O(n)}
t₃₉, X₂: X₂ {O(n)}
t₃₉, X₃: X₃ {O(n)}
t₄₀, X₀: X₂+X₃ {O(n)}
t₄₀, X₁: X₂+X₃ {O(n)}
t₄₀, X₂: X₂ {O(n)}
t₄₀, X₃: X₃ {O(n)}
t₄₁, X₀: 0 {O(1)}
t₄₁, X₁: X₃ {O(n)}
t₄₁, X₂: X₂ {O(n)}
t₄₁, X₃: X₃ {O(n)}
t₄₂, X₀: X₂ {O(n)}
t₄₂, X₁: 0 {O(1)}
t₄₂, X₂: X₂ {O(n)}
t₄₂, X₃: X₃ {O(n)}
t₄₃, X₀: X₂ {O(n)}
t₄₃, X₁: X₃ {O(n)}
t₄₃, X₂: 2⋅X₂ {O(n)}
t₄₃, X₃: 2⋅X₃ {O(n)}
t₄₄, X₀: X₀ {O(n)}
t₄₄, X₁: X₁ {O(n)}
t₄₄, X₂: X₂ {O(n)}
t₄₄, X₃: X₃ {O(n)}