Initial Problem
Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_foo_bb1_in(X₇, X₈, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₂
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₁ ≤ X₃
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_foo_bb1_in(1+X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
Preprocessing
Eliminate variables [X₄; X₅; X₆] that do not contribute to the problem
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location eval_foo_bb2_in
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location eval_foo_bb1_in
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location eval_foo_stop
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location eval_foo_bb3_in
Problem after Preprocessing
Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₃: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅)
t₁₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₁₅: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₁₆: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₁₇: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(1+X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀ ∧ X₅ ≤ X₁
t₁₈: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₅ ≤ X₁
t₁₉: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)
MPRF for transition t₁₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ of depth 1:
new bound:
X₂+X₄ {O(n)}
MPRF:
• eval_foo_bb1_in: [X₂-X₀]
• eval_foo_bb2_in: [X₂-1-X₀]
MPRF for transition t₁₅: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ of depth 1:
new bound:
X₃+X₅ {O(n)}
MPRF:
• eval_foo_bb1_in: [X₃-X₁]
• eval_foo_bb2_in: [X₃-1-X₁]
TWN: t₁₄: eval_foo_bb1_in→eval_foo_bb2_in
cycle: [t₁₄: eval_foo_bb1_in→eval_foo_bb2_in; t₁₅: eval_foo_bb1_in→eval_foo_bb2_in; t₁₇: eval_foo_bb2_in→eval_foo_bb1_in]
loop: (1+X₀ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ ∨ 1+X₁ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁,(X₀,X₁,X₂,X₃,X₄,X₅) -> (1+X₀,1+X₁,X₂,X₃,X₄,X₅))
order: [X₅; X₄; X₃; X₂; X₁; X₀]
closed-form:X₅: X₅
X₄: X₄
X₃: X₃
X₂: X₂
X₁: X₁ + [[n != 0]]⋅n^1
X₀: X₀ + [[n != 0]]⋅n^1
Termination: true
Formula:
0 ≤ 1 ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 1+X₀ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
∨ 0 ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ 0 ∧ 1+X₁ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2+X₀ ≤ X₂ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2+X₁ ≤ X₃ ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
∨ 1 ≤ 0 ∧ X₄ ≤ X₀ ∧ X₅ ≤ X₁
Stabilization-Threshold for: 1+X₁ ≤ X₃
alphas_abs: X₁+X₃
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₃+2 {O(n)}
Stabilization-Threshold for: 1+X₀ ≤ X₂
alphas_abs: X₀+X₂
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+2 {O(n)}
TWN - Lifting for [14: eval_foo_bb1_in->eval_foo_bb2_in; 15: eval_foo_bb1_in->eval_foo_bb2_in; 17: eval_foo_bb2_in->eval_foo_bb1_in] of 2⋅X₀+2⋅X₁+2⋅X₂+2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₁₃: eval_foo_bb0_in→eval_foo_bb1_in:
X₀: X₄ {O(n)}
X₁: X₅ {O(n)}
X₂: X₂ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₁₃: 1 {O(1)}
Results in: 2⋅X₂+2⋅X₃+2⋅X₄+2⋅X₅+6 {O(n)}
All Bounds
Timebounds
Overall timebound:3⋅X₂+3⋅X₃+3⋅X₄+3⋅X₅+10 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₂+X₄ {O(n)}
t₁₅: X₃+X₅ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 2⋅X₂+2⋅X₃+2⋅X₄+2⋅X₅+6 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
Costbounds
Overall costbound: 3⋅X₂+3⋅X₃+3⋅X₄+3⋅X₅+10 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₂+X₄ {O(n)}
t₁₅: X₃+X₅ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 2⋅X₂+2⋅X₃+2⋅X₄+2⋅X₅+6 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
Sizebounds
t₁₃, X₀: X₄ {O(n)}
t₁₃, X₁: X₅ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₄, X₀: 2⋅X₂+2⋅X₃+2⋅X₅+3⋅X₄+6 {O(n)}
t₁₄, X₁: 2⋅X₂+2⋅X₃+2⋅X₄+3⋅X₅+6 {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₅, X₀: 2⋅X₂+2⋅X₃+2⋅X₅+3⋅X₄+6 {O(n)}
t₁₅, X₁: 2⋅X₂+2⋅X₃+2⋅X₄+3⋅X₅+6 {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₆, X₀: 2⋅X₂+2⋅X₃+2⋅X₅+4⋅X₄+6 {O(n)}
t₁₆, X₁: 2⋅X₂+2⋅X₃+2⋅X₄+4⋅X₅+6 {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₆, X₅: 2⋅X₅ {O(n)}
t₁₇, X₀: 2⋅X₂+2⋅X₃+2⋅X₅+3⋅X₄+6 {O(n)}
t₁₇, X₁: 2⋅X₂+2⋅X₃+2⋅X₄+3⋅X₅+6 {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₈, X₀: 2⋅X₂+2⋅X₃+2⋅X₅+4⋅X₄+6 {O(n)}
t₁₈, X₁: 2⋅X₂+2⋅X₃+2⋅X₄+4⋅X₅+6 {O(n)}
t₁₈, X₂: 2⋅X₂ {O(n)}
t₁₈, X₃: 2⋅X₃ {O(n)}
t₁₈, X₄: 2⋅X₄ {O(n)}
t₁₈, X₅: 2⋅X₅ {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₅ {O(n)}