Initial Problem

Start: eval_speedSimpleMultipleDep_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_speedSimpleMultipleDep_bb0_in, eval_speedSimpleMultipleDep_bb1_in, eval_speedSimpleMultipleDep_bb2_in, eval_speedSimpleMultipleDep_bb3_in, eval_speedSimpleMultipleDep_start, eval_speedSimpleMultipleDep_stop
Transitions:
t₁: eval_speedSimpleMultipleDep_bb0_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 0, 0)
t₂: eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁
t₃: eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂
t₄: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, 1+X₃) :|: 1+X₃ ≤ X₀
t₅: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 1+X₂, 1+X₃) :|: 1+X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₆: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, 0) :|: 1+X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₇: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 1+X₂, 0) :|: X₀ ≤ X₃
t₈: eval_speedSimpleMultipleDep_bb3_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_stop(X₀, X₁, X₂, X₃)
t₀: eval_speedSimpleMultipleDep_start(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Cut unsatisfiable transition [t₅: eval_speedSimpleMultipleDep_bb2_in→eval_speedSimpleMultipleDep_bb1_in; t₆: eval_speedSimpleMultipleDep_bb2_in→eval_speedSimpleMultipleDep_bb1_in]

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_speedSimpleMultipleDep_bb2_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location eval_speedSimpleMultipleDep_stop

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location eval_speedSimpleMultipleDep_bb1_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location eval_speedSimpleMultipleDep_bb3_in

Problem after Preprocessing

Start: eval_speedSimpleMultipleDep_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_speedSimpleMultipleDep_bb0_in, eval_speedSimpleMultipleDep_bb1_in, eval_speedSimpleMultipleDep_bb2_in, eval_speedSimpleMultipleDep_bb3_in, eval_speedSimpleMultipleDep_start, eval_speedSimpleMultipleDep_stop
Transitions:
t₁: eval_speedSimpleMultipleDep_bb0_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 0, 0)
t₂: eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₃: eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₄: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, 1+X₃) :|: 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₇: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 1+X₂, 0) :|: X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₈: eval_speedSimpleMultipleDep_bb3_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_stop(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₀: eval_speedSimpleMultipleDep_start(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₇: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, 1+X₂, 0) :|: X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₁ {O(n)}

• eval_speedSimpleMultipleDep_bb1_in: [X₁-X₂]
• eval_speedSimpleMultipleDep_bb2_in: [X₁-X₂]

MPRF for transition t₄: eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, 1+X₃) :|: 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₀⋅X₁+X₀ {O(n^2)}

• eval_speedSimpleMultipleDep_bb1_in: [X₀-X₃]
• eval_speedSimpleMultipleDep_bb2_in: [X₀-X₃]

knowledge_propagation leads to new time bound X₀⋅X₁+X₀+X₁+1 {O(n^2)} for transition t₂: eval_speedSimpleMultipleDep_bb1_in(X₀, X₁, X₂, X₃) → eval_speedSimpleMultipleDep_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃

Found invariant X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 3+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 2+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_speedSimpleMultipleDep_bb2_in_v6

Found invariant X₃ ≤ 0 ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_speedSimpleMultipleDep_bb1_in_v5

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_speedSimpleMultipleDep_bb2_in_v1

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb2_in_v2

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location eval_speedSimpleMultipleDep_bb1_in

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb1_in_v3

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 1 ∧ 1+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₀+X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_speedSimpleMultipleDep_bb1_in_v1

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb1_in_v2

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb2_in_v3

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₂+X₃ ≤ 1 ∧ 2+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ X₀+X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_speedSimpleMultipleDep_bb2_in_v5

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location eval_speedSimpleMultipleDep_stop

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb1_in_v4

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speedSimpleMultipleDep_bb2_in_v4

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location eval_speedSimpleMultipleDep_bb3_in

Cut unsatisfiable transition [t₅₅: eval_speedSimpleMultipleDep_bb2_in_v5→eval_speedSimpleMultipleDep_bb1_in_v4]

All Bounds

Timebounds

Overall timebound:2⋅X₀⋅X₁+2⋅X₀+2⋅X₁+5 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀⋅X₁+X₀+X₁+1 {O(n^2)}
t₃: 1 {O(1)}
t₄: X₀⋅X₁+X₀ {O(n^2)}
t₇: X₁ {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₀⋅X₁+2⋅X₀+2⋅X₁+5 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀⋅X₁+X₀+X₁+1 {O(n^2)}
t₃: 1 {O(1)}
t₄: X₀⋅X₁+X₀ {O(n^2)}
t₇: X₁ {O(n)}
t₈: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 0 {O(1)}
t₁, X₃: 0 {O(1)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₁ {O(n)}
t₂, X₃: 2⋅X₀+4 {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: X₁ {O(n)}
t₃, X₃: 0 {O(1)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁ {O(n)}
t₄, X₃: 2⋅X₀+4 {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁ {O(n)}
t₇, X₃: 0 {O(1)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: X₁ {O(n)}
t₈, X₃: 0 {O(1)}