Initial Problem

Start: eval_twn16_start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: eval_twn16_bb0_in, eval_twn16_bb1_in, eval_twn16_bb2_in, eval_twn16_bb3_in, eval_twn16_start, eval_twn16_stop
Transitions:
t₁: eval_twn16_bb0_in(X₀, X₁) → eval_twn16_bb1_in(X₁, X₁)
t₂: eval_twn16_bb1_in(X₀, X₁) → eval_twn16_bb2_in(X₀, X₁) :|: X₀ ≤ 42 ∧ 1 ≤ X₀
t₃: eval_twn16_bb1_in(X₀, X₁) → eval_twn16_bb3_in(X₀, X₁) :|: 43 ≤ X₀
t₄: eval_twn16_bb1_in(X₀, X₁) → eval_twn16_bb3_in(X₀, X₁) :|: X₀ ≤ 0
t₅: eval_twn16_bb2_in(X₀, X₁) → eval_twn16_bb1_in(2⋅X₀, X₁)
t₆: eval_twn16_bb3_in(X₀, X₁) → eval_twn16_stop(X₀, X₁)
t₀: eval_twn16_start(X₀, X₁) → eval_twn16_bb0_in(X₀, X₁)

Preprocessing

Found invariant X₁ ≤ X₀ for location eval_twn16_bb1_in

Found invariant X₁ ≤ X₀ for location eval_twn16_bb3_in

Found invariant X₁ ≤ X₀ for location eval_twn16_stop

Found invariant X₁ ≤ 42 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 84 ∧ X₀ ≤ 42 ∧ 1 ≤ X₀ for location eval_twn16_bb2_in

Problem after Preprocessing

Start: eval_twn16_start
Program_Vars: X₀, X₁
Temp_Vars:
Locations: eval_twn16_bb0_in, eval_twn16_bb1_in, eval_twn16_bb2_in, eval_twn16_bb3_in, eval_twn16_start, eval_twn16_stop
Transitions:
t₁: eval_twn16_bb0_in(X₀, X₁) → eval_twn16_bb1_in(X₁, X₁)
t₂: eval_twn16_bb1_in(X₀, X₁) → eval_twn16_bb2_in(X₀, X₁) :|: X₀ ≤ 42 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀
t₃: eval_twn16_bb1_in(X₀, X₁) → eval_twn16_bb3_in(X₀, X₁) :|: 43 ≤ X₀ ∧ X₁ ≤ X₀
t₄: eval_twn16_bb1_in(X₀, X₁) → eval_twn16_bb3_in(X₀, X₁) :|: X₀ ≤ 0 ∧ X₁ ≤ X₀
t₅: eval_twn16_bb2_in(X₀, X₁) → eval_twn16_bb1_in(2⋅X₀, X₁) :|: X₀+X₁ ≤ 84 ∧ X₀ ≤ 42 ∧ X₁ ≤ 42 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀
t₆: eval_twn16_bb3_in(X₀, X₁) → eval_twn16_stop(X₀, X₁) :|: X₁ ≤ X₀
t₀: eval_twn16_start(X₀, X₁) → eval_twn16_bb0_in(X₀, X₁)

MPRF for transition t₂: eval_twn16_bb1_in(X₀, X₁) → eval_twn16_bb2_in(X₀, X₁) :|: X₀ ≤ 42 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₁+43 {O(n)}

• eval_twn16_bb1_in: [43-X₀]
• eval_twn16_bb2_in: [42-X₀]

MPRF for transition t₅: eval_twn16_bb2_in(X₀, X₁) → eval_twn16_bb1_in(2⋅X₀, X₁) :|: X₀+X₁ ≤ 84 ∧ X₀ ≤ 42 ∧ X₁ ≤ 42 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₁+84 {O(n)}

• eval_twn16_bb1_in: [84-X₀]
• eval_twn16_bb2_in: [85-2⋅X₀]

All Bounds

Timebounds

Overall timebound:2⋅X₁+132 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+43 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₁+84 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+132 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+43 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₁+84 {O(n)}
t₆: 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: 42 {O(1)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+84 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: 84 {O(1)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 2⋅X₁+84 {O(n)}
t₆, X₁: 3⋅X₁ {O(n)}