Initial Problem

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:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(0, 1, X₂, X₃, X₄, X₅)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₄
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₄ ≤ X₁
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₁ ∧ X₁ ≤ X₄
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb1_in(X₁, X₀+X₁, X₂, X₃, X₄, X₅)
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables [X₂; X₃; X₅] that do not contribute to the problem

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

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb1_in

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_stop

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ 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:
t₁₃: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(0, 1, X₂)
t₁₄: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₁₅: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₁₆: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₁₇: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₁, X₀+X₁, X₂) :|: 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁
t₁₈: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂) :|: 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁₉: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

MPRF for transition t₁₄: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₂+2 {O(n)}

MPRF:

• eval_foo_bb1_in: [2⋅X₂-1-X₀-X₁]
• eval_foo_bb2_in: [2⋅X₂-2-X₀-X₁]

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_foo_bb1_in_v1

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_foo_bb1_in_v3

Found invariant 3+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 3 ≤ X₂ ∧ 9 ≤ X₁+X₂ ∧ 7 ≤ X₀+X₂ ∧ 6 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 4 ≤ X₀ for location eval_foo_bb1_in_v2

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_stop

Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb3_in

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb2_in_v2

Found invariant X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location eval_foo_bb1_in

Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb2_in_v1

Found invariant 1+X₂ ≤ X₁ ∧ 3 ≤ X₂ ∧ 7 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ 4 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_foo_bb2_in_v3

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 2⋅X₂+2 {O(n)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 2⋅X₂+2 {O(n)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}

Sizebounds

t₁₃, X₀: 0 {O(1)}
t₁₃, X₁: 1 {O(1)}
t₁₃, X₂: X₂ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₂: 2⋅X₂ {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}