Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
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) → eval_foo_bb1_in(X₁, X₁, X₂) :|: 1 ≤ 2⋅X₂
t₂: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₂ ≤ 0
t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 0 ≤ X₀
t₄: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: 1+X₀ ≤ 0
t₅: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀-2⋅X₂, X₁, X₂)
t₆: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂)
t₀: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

Preprocessing

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb2_in

Found invariant 1 ≤ X₂ ∧ X₀ ≤ X₁ for location eval_foo_bb1_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
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) → eval_foo_bb1_in(X₁, X₁, X₂) :|: 1 ≤ 2⋅X₂
t₂: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₂ ≤ 0
t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₄: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: 1+X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₅: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀-2⋅X₂, X₁, X₂) :|: 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₆: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂)
t₀: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

MPRF for transition t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [X₀]

MPRF for transition t₅: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀-2⋅X₂, X₁, X₂) :|: 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

2⋅X₂+X₁+1 {O(n)}

MPRF:

• eval_foo_bb1_in: [X₀+2⋅X₂-1]
• eval_foo_bb2_in: [1+X₀]

All Bounds

Timebounds

Overall timebound:2⋅X₁+2⋅X₂+7 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₁+1 {O(n)}
t₄: 1 {O(1)}
t₅: 2⋅X₂+X₁+1 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁+2⋅X₂+7 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: X₁+1 {O(n)}
t₄: 1 {O(1)}
t₅: 2⋅X₂+X₁+1 {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: 2⋅X₁⋅X₂+2⋅X₁+4⋅X₂+2 {O(n^2)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: 2⋅X₁⋅X₂+3⋅X₁+4⋅X₂+2 {O(n^2)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₅, X₀: 2⋅X₁⋅X₂+2⋅X₁+4⋅X₂+2 {O(n^2)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₀: 2⋅X₁⋅X₂+3⋅X₁+4⋅X₂+X₀+2 {O(n^2)}
t₆, X₁: 3⋅X₁ {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}