Initial Problem
Start: eval_speed_pldi10_ex3_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: eval_speed_pldi10_ex3_2, eval_speed_pldi10_ex3_3, eval_speed_pldi10_ex3_bb0_in, eval_speed_pldi10_ex3_bb1_in, eval_speed_pldi10_ex3_bb2_in, eval_speed_pldi10_ex3_bb3_in, eval_speed_pldi10_ex3_bb4_in, eval_speed_pldi10_ex3_start, eval_speed_pldi10_ex3_stop
Transitions:
t₈: eval_speed_pldi10_ex3_2(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_3(X₀, X₁, X₂, nondef.0, X₄)
t₉: eval_speed_pldi10_ex3_3(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb1_in(X₂, X₁, X₂, X₃, X₄) :|: 1 ≤ X₃
t₁₀: eval_speed_pldi10_ex3_3(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb2_in(X₀, X₂, X₂, X₃, X₄) :|: X₃ ≤ 0
t₁: eval_speed_pldi10_ex3_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb1_in(X₄, X₁, X₂, X₃, X₄)
t₂: eval_speed_pldi10_ex3_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb2_in(X₀, X₀, X₂, X₃, X₄) :|: 1 ≤ X₀
t₃: eval_speed_pldi10_ex3_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₅: eval_speed_pldi10_ex3_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb1_in(X₁-1, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1
t₄: eval_speed_pldi10_ex3_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb3_in(X₀, X₁, X₁-1, X₃, X₄) :|: 2 ≤ X₁
t₆: eval_speed_pldi10_ex3_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_2(X₀, X₁, X₂, X₃, X₄)
t₁₁: eval_speed_pldi10_ex3_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_stop(X₀, X₁, X₂, X₃, X₄)
t₀: eval_speed_pldi10_ex3_start(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb0_in(X₀, X₁, X₂, X₃, X₄)
Preprocessing
Found invariant X₀ ≤ X₄ ∧ X₀ ≤ 0 for location eval_speed_pldi10_ex3_bb4_in
Found invariant 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_speed_pldi10_ex3_bb3_in
Found invariant X₀ ≤ X₄ ∧ X₀ ≤ 0 for location eval_speed_pldi10_ex3_stop
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_speed_pldi10_ex3_bb2_in
Found invariant X₀ ≤ X₄ for location eval_speed_pldi10_ex3_bb1_in
Found invariant 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_speed_pldi10_ex3_2
Found invariant 2 ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_speed_pldi10_ex3_3
Problem after Preprocessing
Start: eval_speed_pldi10_ex3_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: eval_speed_pldi10_ex3_2, eval_speed_pldi10_ex3_3, eval_speed_pldi10_ex3_bb0_in, eval_speed_pldi10_ex3_bb1_in, eval_speed_pldi10_ex3_bb2_in, eval_speed_pldi10_ex3_bb3_in, eval_speed_pldi10_ex3_bb4_in, eval_speed_pldi10_ex3_start, eval_speed_pldi10_ex3_stop
Transitions:
t₈: eval_speed_pldi10_ex3_2(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_3(X₀, X₁, X₂, nondef.0, X₄) :|: X₁ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄
t₉: eval_speed_pldi10_ex3_3(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb1_in(X₂, X₁, X₂, X₃, X₄) :|: 1 ≤ X₃ ∧ X₁ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄
t₁₀: eval_speed_pldi10_ex3_3(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb2_in(X₀, X₂, X₂, X₃, X₄) :|: X₃ ≤ 0 ∧ X₁ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄
t₁: eval_speed_pldi10_ex3_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb1_in(X₄, X₁, X₂, X₃, X₄)
t₂: eval_speed_pldi10_ex3_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb2_in(X₀, X₀, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ X₀ ≤ X₄
t₃: eval_speed_pldi10_ex3_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ X₀ ≤ X₄
t₅: eval_speed_pldi10_ex3_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb1_in(X₁-1, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄
t₄: eval_speed_pldi10_ex3_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb3_in(X₀, X₁, X₁-1, X₃, X₄) :|: 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄
t₆: eval_speed_pldi10_ex3_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄
t₁₁: eval_speed_pldi10_ex3_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_stop(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ X₀ ≤ X₄
t₀: eval_speed_pldi10_ex3_start(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb0_in(X₀, X₁, X₂, X₃, X₄)
MPRF for transition t₂: eval_speed_pldi10_ex3_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb2_in(X₀, X₀, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ X₀ ≤ X₄ of depth 1:
new bound:
X₄ {O(n)}
MPRF:
• eval_speed_pldi10_ex3_2: [X₂]
• eval_speed_pldi10_ex3_3: [X₂]
• eval_speed_pldi10_ex3_bb1_in: [X₀]
• eval_speed_pldi10_ex3_bb2_in: [X₁-1]
• eval_speed_pldi10_ex3_bb3_in: [X₁-1]
MPRF for transition t₄: eval_speed_pldi10_ex3_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb3_in(X₀, X₁, X₁-1, X₃, X₄) :|: 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄ of depth 1:
new bound:
X₄ {O(n)}
MPRF:
• eval_speed_pldi10_ex3_2: [X₂]
• eval_speed_pldi10_ex3_3: [X₂]
• eval_speed_pldi10_ex3_bb1_in: [X₀]
• eval_speed_pldi10_ex3_bb2_in: [X₁]
• eval_speed_pldi10_ex3_bb3_in: [X₁-1]
MPRF for transition t₅: eval_speed_pldi10_ex3_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb1_in(X₁-1, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄ of depth 1:
new bound:
X₄ {O(n)}
MPRF:
• eval_speed_pldi10_ex3_2: [X₁]
• eval_speed_pldi10_ex3_3: [X₂]
• eval_speed_pldi10_ex3_bb1_in: [X₀]
• eval_speed_pldi10_ex3_bb2_in: [X₁]
• eval_speed_pldi10_ex3_bb3_in: [X₁]
MPRF for transition t₆: eval_speed_pldi10_ex3_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
• eval_speed_pldi10_ex3_2: [X₁-2]
• eval_speed_pldi10_ex3_3: [X₁-2]
• eval_speed_pldi10_ex3_bb1_in: [X₀-1]
• eval_speed_pldi10_ex3_bb2_in: [X₁-1]
• eval_speed_pldi10_ex3_bb3_in: [X₁-1]
MPRF for transition t₈: eval_speed_pldi10_ex3_2(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_3(X₀, X₁, X₂, nondef.0, X₄) :|: X₁ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
• eval_speed_pldi10_ex3_2: [X₁-1]
• eval_speed_pldi10_ex3_3: [X₂-1]
• eval_speed_pldi10_ex3_bb1_in: [X₀-1]
• eval_speed_pldi10_ex3_bb2_in: [X₁-1]
• eval_speed_pldi10_ex3_bb3_in: [X₂]
MPRF for transition t₉: eval_speed_pldi10_ex3_3(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb1_in(X₂, X₁, X₂, X₃, X₄) :|: 1 ≤ X₃ ∧ X₁ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄ of depth 1:
new bound:
X₄+1 {O(n)}
MPRF:
• eval_speed_pldi10_ex3_2: [X₂]
• eval_speed_pldi10_ex3_3: [X₂]
• eval_speed_pldi10_ex3_bb1_in: [X₀-1]
• eval_speed_pldi10_ex3_bb2_in: [X₁-1]
• eval_speed_pldi10_ex3_bb3_in: [X₂]
MPRF for transition t₁₀: eval_speed_pldi10_ex3_3(X₀, X₁, X₂, X₃, X₄) → eval_speed_pldi10_ex3_bb2_in(X₀, X₂, X₂, X₃, X₄) :|: X₃ ≤ 0 ∧ X₁ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₄ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₄ of depth 1:
new bound:
X₄ {O(n)}
MPRF:
• eval_speed_pldi10_ex3_2: [X₂]
• eval_speed_pldi10_ex3_3: [X₂]
• eval_speed_pldi10_ex3_bb1_in: [X₀]
• eval_speed_pldi10_ex3_bb2_in: [X₁-1]
• eval_speed_pldi10_ex3_bb3_in: [X₁-1]
All Bounds
Timebounds
Overall timebound:7⋅X₄+7 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: X₄ {O(n)}
t₆: X₄+1 {O(n)}
t₈: X₄+1 {O(n)}
t₉: X₄+1 {O(n)}
t₁₀: X₄ {O(n)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: 7⋅X₄+7 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: X₄ {O(n)}
t₆: X₄+1 {O(n)}
t₈: X₄+1 {O(n)}
t₉: X₄+1 {O(n)}
t₁₀: X₄ {O(n)}
t₁₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₄ {O(n)}
t₂, X₁: 2⋅X₄ {O(n)}
t₂, X₂: 4⋅X₄+X₂ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: X₄ {O(n)}
t₃, X₁: X₁+1 {O(n)}
t₃, X₂: 2⋅X₂+8⋅X₄ {O(n)}
t₃, X₄: 3⋅X₄ {O(n)}
t₄, X₀: X₄ {O(n)}
t₄, X₁: 2⋅X₄ {O(n)}
t₄, X₂: 4⋅X₄ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: 0 {O(1)}
t₅, X₁: 1 {O(1)}
t₅, X₂: 8⋅X₄+X₂ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₆, X₀: X₄ {O(n)}
t₆, X₁: 2⋅X₄ {O(n)}
t₆, X₂: 4⋅X₄ {O(n)}
t₆, X₄: X₄ {O(n)}
t₈, X₀: X₄ {O(n)}
t₈, X₁: 2⋅X₄ {O(n)}
t₈, X₂: 4⋅X₄ {O(n)}
t₈, X₄: X₄ {O(n)}
t₉, X₀: X₄ {O(n)}
t₉, X₁: 2⋅X₄ {O(n)}
t₉, X₂: 4⋅X₄ {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₀: X₄ {O(n)}
t₁₀, X₁: 2⋅X₄ {O(n)}
t₁₀, X₂: 4⋅X₄ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₁, X₀: X₄ {O(n)}
t₁₁, X₁: X₁+1 {O(n)}
t₁₁, X₂: 2⋅X₂+8⋅X₄ {O(n)}
t₁₁, X₄: 3⋅X₄ {O(n)}