Initial Problem

Start: eval_speed_popl10_sequential_single_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef.0
Locations: eval_speed_popl10_sequential_single_0, eval_speed_popl10_sequential_single_1, eval_speed_popl10_sequential_single_bb0_in, eval_speed_popl10_sequential_single_bb1_in, eval_speed_popl10_sequential_single_bb2_in, eval_speed_popl10_sequential_single_bb3_in, eval_speed_popl10_sequential_single_bb4_in, eval_speed_popl10_sequential_single_bb5_in, eval_speed_popl10_sequential_single_bb6_in, eval_speed_popl10_sequential_single_start, eval_speed_popl10_sequential_single_stop
Transitions:
t₆: eval_speed_popl10_sequential_single_0(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_1(nondef.0, X₁, X₂, X₃)
t₈: eval_speed_popl10_sequential_single_1(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb3_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₇: eval_speed_popl10_sequential_single_1(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, X₂) :|: 1 ≤ X₀
t₁: eval_speed_popl10_sequential_single_bb0_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb1_in(X₀, X₁, 0, X₃)
t₂: eval_speed_popl10_sequential_single_bb1_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁
t₃: eval_speed_popl10_sequential_single_bb1_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, X₂) :|: X₁ ≤ X₂
t₄: eval_speed_popl10_sequential_single_bb2_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_0(X₀, X₁, X₂, X₃)
t₉: eval_speed_popl10_sequential_single_bb3_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb1_in(X₀, X₁, 1+X₂, X₃)
t₁₀: eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb5_in(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁
t₁₁: eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb6_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃
t₁₂: eval_speed_popl10_sequential_single_bb5_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, 1+X₃)
t₁₃: eval_speed_popl10_sequential_single_bb6_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_stop(X₀, X₁, X₂, X₃)
t₀: eval_speed_popl10_sequential_single_start(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_speed_popl10_sequential_single_1

Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_speed_popl10_sequential_single_0

Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_speed_popl10_sequential_single_bb2_in

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_speed_popl10_sequential_single_bb5_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ for location eval_speed_popl10_sequential_single_bb6_in

Found invariant 0 ≤ X₂ for location eval_speed_popl10_sequential_single_bb1_in

Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location eval_speed_popl10_sequential_single_bb3_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location eval_speed_popl10_sequential_single_bb4_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ for location eval_speed_popl10_sequential_single_stop

Problem after Preprocessing

Start: eval_speed_popl10_sequential_single_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef.0
Locations: eval_speed_popl10_sequential_single_0, eval_speed_popl10_sequential_single_1, eval_speed_popl10_sequential_single_bb0_in, eval_speed_popl10_sequential_single_bb1_in, eval_speed_popl10_sequential_single_bb2_in, eval_speed_popl10_sequential_single_bb3_in, eval_speed_popl10_sequential_single_bb4_in, eval_speed_popl10_sequential_single_bb5_in, eval_speed_popl10_sequential_single_bb6_in, eval_speed_popl10_sequential_single_start, eval_speed_popl10_sequential_single_stop
Transitions:
t₆: eval_speed_popl10_sequential_single_0(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_1(nondef.0, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂
t₈: eval_speed_popl10_sequential_single_1(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb3_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂
t₇: eval_speed_popl10_sequential_single_1(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, X₂) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂
t₁: eval_speed_popl10_sequential_single_bb0_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb1_in(X₀, X₁, 0, X₃)
t₂: eval_speed_popl10_sequential_single_bb1_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂
t₃: eval_speed_popl10_sequential_single_bb1_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, X₂) :|: X₁ ≤ X₂ ∧ 0 ≤ X₂
t₄: eval_speed_popl10_sequential_single_bb2_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_0(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂
t₉: eval_speed_popl10_sequential_single_bb3_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb1_in(X₀, X₁, 1+X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂
t₁₀: eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb5_in(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₁₁: eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb6_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₁₂: eval_speed_popl10_sequential_single_bb5_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, 1+X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₁₃: eval_speed_popl10_sequential_single_bb6_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_stop(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₀: eval_speed_popl10_sequential_single_start(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₂: eval_speed_popl10_sequential_single_bb1_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb2_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁ {O(n)}

• eval_speed_popl10_sequential_single_0: [X₁-1-X₂]
• eval_speed_popl10_sequential_single_1: [X₁-1-X₂]
• eval_speed_popl10_sequential_single_bb1_in: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb2_in: [X₁-1-X₂]
• eval_speed_popl10_sequential_single_bb3_in: [X₁-1-X₂]

MPRF for transition t₄: eval_speed_popl10_sequential_single_bb2_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_0(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁ {O(n)}

• eval_speed_popl10_sequential_single_0: [X₁-1-X₂]
• eval_speed_popl10_sequential_single_1: [X₁-1-X₂]
• eval_speed_popl10_sequential_single_bb1_in: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb2_in: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb3_in: [X₁-1-X₂]

MPRF for transition t₆: eval_speed_popl10_sequential_single_0(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_1(nondef.0, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁ {O(n)}

• eval_speed_popl10_sequential_single_0: [X₁-X₂]
• eval_speed_popl10_sequential_single_1: [X₁-1-X₂]
• eval_speed_popl10_sequential_single_bb1_in: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb2_in: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb3_in: [X₁-1-X₂]

MPRF for transition t₈: eval_speed_popl10_sequential_single_1(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb3_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁ {O(n)}

• eval_speed_popl10_sequential_single_0: [X₁-X₂]
• eval_speed_popl10_sequential_single_1: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb1_in: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb2_in: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb3_in: [X₁-1-X₂]

MPRF for transition t₉: eval_speed_popl10_sequential_single_bb3_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb1_in(X₀, X₁, 1+X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁ {O(n)}

• eval_speed_popl10_sequential_single_0: [X₁-X₂]
• eval_speed_popl10_sequential_single_1: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb1_in: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb2_in: [X₁-X₂]
• eval_speed_popl10_sequential_single_bb3_in: [X₁-X₂]

MPRF for transition t₁₀: eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb5_in(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₁ {O(n)}

• eval_speed_popl10_sequential_single_bb4_in: [X₁-X₃]
• eval_speed_popl10_sequential_single_bb5_in: [X₁-1-X₃]

MPRF for transition t₁₂: eval_speed_popl10_sequential_single_bb5_in(X₀, X₁, X₂, X₃) → eval_speed_popl10_sequential_single_bb4_in(X₀, X₁, X₂, 1+X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₁ {O(n)}

• eval_speed_popl10_sequential_single_bb4_in: [X₁-X₃]
• eval_speed_popl10_sequential_single_bb5_in: [X₁-X₃]

All Bounds

Timebounds

Overall timebound:9⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₄: X₁ {O(n)}
t₆: X₁ {O(n)}
t₇: 1 {O(1)}
t₈: X₁ {O(n)}
t₉: X₁ {O(n)}
t₁₀: 2⋅X₁ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₁ {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 9⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₄: X₁ {O(n)}
t₆: X₁ {O(n)}
t₇: 1 {O(1)}
t₈: X₁ {O(n)}
t₉: X₁ {O(n)}
t₁₀: 2⋅X₁ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₁ {O(n)}
t₁₃: 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: X₃ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₁ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: X₁ {O(n)}
t₃, X₃: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁ {O(n)}
t₄, X₃: X₃ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₁ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁ {O(n)}
t₇, X₃: X₁ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₁ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₁ {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁ {O(n)}
t₁₀, X₃: 3⋅X₁ {O(n)}
t₁₁, X₁: 3⋅X₁ {O(n)}
t₁₁, X₂: 2⋅X₁ {O(n)}
t₁₁, X₃: 4⋅X₁ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₁ {O(n)}
t₁₂, X₃: 3⋅X₁ {O(n)}
t₁₃, X₁: 3⋅X₁ {O(n)}
t₁₃, X₂: 2⋅X₁ {O(n)}
t₁₃, X₃: 4⋅X₁ {O(n)}