Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁
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) → eval_foo_bb1_in(X₁, X₁)
t₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: X₀ ≤ 2147483647
t₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: 2147483648 ≤ X₀
t₄: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(1+X₀, X₁)
t₅: eval_foo_bb3_in(X₀, X₁) → eval_foo_stop(X₀, X₁)
t₀: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

Preprocessing

Found invariant X₁ ≤ 2147483647 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4294967294 ∧ X₀ ≤ 2147483647 for location eval_foo_bb2_in

Found invariant X₁ ≤ X₀ for location eval_foo_bb1_in

Found invariant X₁ ≤ X₀ ∧ 2147483648 ≤ X₀ for location eval_foo_stop

Found invariant X₁ ≤ X₀ ∧ 2147483648 ≤ X₀ for location eval_foo_bb3_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁
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) → eval_foo_bb1_in(X₁, X₁)
t₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: X₀ ≤ 2147483647 ∧ X₁ ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: 2147483648 ≤ X₀ ∧ X₁ ≤ X₀
t₄: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(1+X₀, X₁) :|: X₀+X₁ ≤ 4294967294 ∧ X₀ ≤ 2147483647 ∧ X₁ ≤ 2147483647 ∧ X₁ ≤ X₀
t₅: eval_foo_bb3_in(X₀, X₁) → eval_foo_stop(X₀, X₁) :|: 2147483648 ≤ X₀ ∧ X₁ ≤ X₀
t₀: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

MPRF for transition t₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: X₀ ≤ 2147483647 ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₁+2147483648 {O(n)}

• eval_foo_bb1_in: [2147483648-X₀]
• eval_foo_bb2_in: [2147483647-X₀]

MPRF for transition t₄: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(1+X₀, X₁) :|: X₀+X₁ ≤ 4294967294 ∧ X₀ ≤ 2147483647 ∧ X₁ ≤ 2147483647 ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₁+2147483648 {O(n)}

• eval_foo_bb1_in: [2147483648-X₀]
• eval_foo_bb2_in: [2147483648-X₀]

All Bounds

Timebounds

Overall timebound:2⋅X₁+4294967300 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2147483648 {O(n)}
t₃: 1 {O(1)}
t₄: X₁+2147483648 {O(n)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+4294967300 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2147483648 {O(n)}
t₃: 1 {O(1)}
t₄: X₁+2147483648 {O(n)}
t₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: 2⋅X₁+2147483649 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: 3⋅X₁+2147483648 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₄, X₀: 2⋅X₁+2147483648 {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 3⋅X₁+2147483648 {O(n)}
t₅, X₁: 2⋅X₁ {O(n)}