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(X₂, X₁, X₂)
t₂: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁
t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ 0
t₄: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ X₀
t₅: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₀+X₁, 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 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location eval_foo_bb2_in

Found invariant X₂ ≤ X₀ for location eval_foo_bb1_in

Found invariant X₂ ≤ X₀ for location eval_foo_stop

Found invariant X₂ ≤ X₀ for location eval_foo_bb3_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(X₂, X₁, X₂)
t₂: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₂ ≤ X₀
t₄: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₀
t₅: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₀+X₁, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀
t₆: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂) :|: X₂ ≤ X₀
t₀: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

MPRF for transition t₂: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₁+X₂ {O(n)}

MPRF:

• eval_foo_bb1_in: [X₁-X₀]
• eval_foo_bb2_in: [X₁-1-X₀]

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

new bound:

2⋅X₁+X₂+1 {O(n)}

MPRF:

• eval_foo_bb1_in: [2⋅X₁-1-X₀]
• eval_foo_bb2_in: [X₁-X₀]

All Bounds

Timebounds

Overall timebound:2⋅X₂+3⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+X₂ {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₁+X₂+1 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₂+3⋅X₁+6 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+X₂ {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₁+X₂+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: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₁⋅X₁+X₁⋅X₂+X₁+X₂ {O(n^2)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₀: X₂ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: X₁⋅X₂+2⋅X₂+X₁ {O(n^2)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₅, X₀: X₁⋅X₂+X₁+X₂ {O(n^2)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₆, X₀: X₁⋅X₂+3⋅X₂+X₁ {O(n^2)}
t₆, X₁: 3⋅X₁ {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}