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_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_bb6_in, eval_foo_bb7_in, eval_foo_bb8_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₃, X₁, X₂, X₃, X₄)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₀, X₂, X₃, X₄) :|: 2 ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb8_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₁
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁-2, X₂, X₃, X₄)
t₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb5_in(X₀, X₁, X₁, X₃, X₄) :|: 0 ≤ X₁ ∧ X₁ ≤ 0
t₈: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb7_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ 0
t₉: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb7_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₁
t₁₁: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₂, X₁, X₂, X₃, X₄) :|: X₀ ≤ 2⋅X₂
t₁₀: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb6_in(X₀, X₁, X₂, X₃, X₄) :|: 1+2⋅X₂ ≤ X₀
t₁₂: eval_foo_bb6_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb5_in(X₀, X₁, 1+X₂, X₃, X₄)
t₁₃: eval_foo_bb7_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(1+3⋅X₀, X₁, X₂, X₃, X₄)
t₁₄: eval_foo_bb8_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

Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb5_in

Found invariant X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb7_in

Found invariant X₀ ≤ 1 for location eval_foo_stop

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb3_in

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb2_in

Found invariant X₀ ≤ 1 for location eval_foo_bb8_in

Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb6_in

Found invariant X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb4_in

Cut unsatisfiable transition [t₃₆: eval_foo_bb4_in→eval_foo_bb7_in]

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_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_bb6_in, eval_foo_bb7_in, eval_foo_bb8_in, eval_foo_start, eval_foo_stop
Transitions:
t₂₉: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₃, X₁, X₂, X₃)
t₃₀: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₀, X₂, X₃) :|: 2 ≤ X₀
t₃₁: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb8_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₃₂: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 2 ≤ X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₃₃: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb4_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₃₄: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁-2, X₂, X₃) :|: 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀
t₃₅: eval_foo_bb4_in(X₀, X₁, X₂, X₃) → eval_foo_bb5_in(X₀, X₁, X₁, X₃) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁
t₃₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃) → eval_foo_bb7_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₃₈: eval_foo_bb5_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂, X₁, X₂, X₃) :|: X₀ ≤ 2⋅X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₃₉: eval_foo_bb5_in(X₀, X₁, X₂, X₃) → eval_foo_bb6_in(X₀, X₁, X₂, X₃) :|: 1+2⋅X₂ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₄₀: eval_foo_bb6_in(X₀, X₁, X₂, X₃) → eval_foo_bb5_in(X₀, X₁, 1+X₂, X₃) :|: 1+X₂ ≤ X₀ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₄₁: eval_foo_bb7_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+3⋅X₀, X₁, X₂, X₃) :|: X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 3 ≤ X₀+X₁
t₄₂: eval_foo_bb8_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₄₃: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb1_in_v1

Found invariant X₁ ≤ 1 ∧ 9+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 11 ≤ X₀+X₁ ∧ 10 ≤ X₀ for location eval_foo_bb1_in_v2

Found invariant X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location eval_foo_bb7_in_v1

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb6_in_v1

Found invariant X₀ ≤ 1 for location eval_foo_stop

Found invariant 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb2_in_v2

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

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_foo_bb2_in_v1

Found invariant X₁ ≤ 1 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb4_in_v1

Found invariant 2+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location eval_foo_bb6_in_v2

Found invariant X₀ ≤ 1 for location eval_foo_bb8_in

Found invariant 2+X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 4 ≤ X₀ for location eval_foo_bb3_in_v2

Found invariant X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb5_in_v1

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_foo_bb3_in_v1

Found invariant 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_foo_bb5_in_v2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₉: 1 {O(1)}
t₃₀: inf {Infinity}
t₃₁: 1 {O(1)}
t₃₂: inf {Infinity}
t₃₃: inf {Infinity}
t₃₄: inf {Infinity}
t₃₅: inf {Infinity}
t₃₇: inf {Infinity}
t₃₈: inf {Infinity}
t₃₉: inf {Infinity}
t₄₀: inf {Infinity}
t₄₁: inf {Infinity}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₉: 1 {O(1)}
t₃₀: inf {Infinity}
t₃₁: 1 {O(1)}
t₃₂: inf {Infinity}
t₃₃: inf {Infinity}
t₃₄: inf {Infinity}
t₃₅: inf {Infinity}
t₃₇: inf {Infinity}
t₃₈: inf {Infinity}
t₃₉: inf {Infinity}
t₄₀: inf {Infinity}
t₄₁: inf {Infinity}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}

Sizebounds

t₂₉, X₀: X₃ {O(n)}
t₂₉, X₁: X₁ {O(n)}
t₂₉, X₂: X₂ {O(n)}
t₂₉, X₃: X₃ {O(n)}
t₃₀, X₃: X₃ {O(n)}
t₃₁, X₁: X₁ {O(n)}
t₃₁, X₃: 2⋅X₃ {O(n)}
t₃₂, X₃: X₃ {O(n)}
t₃₃, X₁: 1 {O(1)}
t₃₃, X₃: X₃ {O(n)}
t₃₄, X₃: X₃ {O(n)}
t₃₅, X₁: 0 {O(1)}
t₃₅, X₂: 0 {O(1)}
t₃₅, X₃: X₃ {O(n)}
t₃₇, X₁: 1 {O(1)}
t₃₇, X₃: X₃ {O(n)}
t₃₈, X₁: 0 {O(1)}
t₃₈, X₃: X₃ {O(n)}
t₃₉, X₁: 0 {O(1)}
t₃₉, X₃: X₃ {O(n)}
t₄₀, X₁: 0 {O(1)}
t₄₀, X₃: X₃ {O(n)}
t₄₁, X₁: 1 {O(1)}
t₄₁, X₃: X₃ {O(n)}
t₄₂, X₁: X₁ {O(n)}
t₄₂, X₃: 2⋅X₃ {O(n)}
t₄₃, X₀: X₀ {O(n)}
t₄₃, X₁: X₁ {O(n)}
t₄₃, X₂: X₂ {O(n)}
t₄₃, X₃: X₃ {O(n)}