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_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₃, X₄, X₂, X₃, X₄)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₁, X₃, X₄) :|: 1 ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂-1, X₃, X₄)
t₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₀-1, X₂, X₂, X₃, X₄)
t₈: eval_foo_bb5_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
Found invariant X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₀ ≤ 0 for location eval_foo_bb5_in
Found invariant X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₀ for location eval_foo_bb2_in
Found invariant X₁ ≤ X₄ ∧ X₀ ≤ X₃ for location eval_foo_bb1_in
Found invariant X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₀ ≤ 0 for location eval_foo_stop
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb3_in
Found invariant X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ for location eval_foo_bb4_in
Problem after Preprocessing
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_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₃, X₄, X₂, X₃, X₄)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₁, X₃, X₄) :|: 1 ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₄
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₄
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₄
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₄
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂-1, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₄
t₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₀-1, X₂, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₄
t₈: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₄
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄)
MPRF for transition t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₁, X₃, X₄) :|: 1 ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₄ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
• eval_foo_bb1_in: [X₀]
• eval_foo_bb2_in: [X₀-1]
• eval_foo_bb3_in: [X₀-1]
• eval_foo_bb4_in: [X₀-1]
MPRF for transition t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₄ of depth 1:
new bound:
X₄ {O(n)}
MPRF:
• eval_foo_bb1_in: [X₁]
• eval_foo_bb2_in: [X₂]
• eval_foo_bb3_in: [X₂-1]
• eval_foo_bb4_in: [X₂]
MPRF for transition t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₄ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
• eval_foo_bb1_in: [X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₀]
• eval_foo_bb4_in: [X₀-1]
MPRF for transition t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂-1, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₄ of depth 1:
new bound:
X₄ {O(n)}
MPRF:
• eval_foo_bb1_in: [X₁]
• eval_foo_bb2_in: [X₂]
• eval_foo_bb3_in: [X₂]
• eval_foo_bb4_in: [X₂]
MPRF for transition t₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₀-1, X₂, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₄ of depth 1:
new bound:
X₃ {O(n)}
MPRF:
• eval_foo_bb1_in: [X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₀]
• eval_foo_bb4_in: [X₀]
All Bounds
Timebounds
Overall timebound:2⋅X₄+3⋅X₃+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: X₃ {O(n)}
t₆: X₄ {O(n)}
t₇: X₃ {O(n)}
t₈: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₄+3⋅X₃+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃ {O(n)}
t₃: 1 {O(1)}
t₄: X₄ {O(n)}
t₅: X₃ {O(n)}
t₆: X₄ {O(n)}
t₇: X₃ {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)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₃ {O(n)}
t₂, X₁: 2⋅X₄ {O(n)}
t₂, X₂: X₄ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 2⋅X₃ {O(n)}
t₃, X₁: 2⋅X₄ {O(n)}
t₃, X₂: X₂+X₄ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: X₃ {O(n)}
t₄, X₁: 2⋅X₄ {O(n)}
t₄, X₂: X₄ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₃ {O(n)}
t₅, X₁: 4⋅X₄ {O(n)}
t₅, X₂: X₄ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₃ {O(n)}
t₆, X₁: 2⋅X₄ {O(n)}
t₆, X₂: X₄ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: X₃ {O(n)}
t₇, X₁: X₄ {O(n)}
t₇, X₂: X₄ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: 2⋅X₃ {O(n)}
t₈, X₁: 2⋅X₄ {O(n)}
t₈, X₂: X₂+X₄ {O(n)}
t₈, X₃: 2⋅X₃ {O(n)}
t₈, X₄: 2⋅X₄ {O(n)}