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 ≤ 0 ∧ X₀ ≤ 0
t₃: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ X₀ ≤ 0
t₄: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1+X₀ ≤ 0 ∧ 2 ≤ X₀
t₅: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1 ≤ X₀ ∧ 2 ≤ X₀
t₆: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₀ ≤ 1 ∧ 1 ≤ X₀
t₇: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ X₀ ≤ 0
t₈: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₀-2, X₁, X₂)
t₉: 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

Cut unsatisfiable transition [t₃: eval_foo_bb1_in→eval_foo_bb2_in; t₄: eval_foo_bb1_in→eval_foo_bb2_in]

Eliminate variables [X₁] that do not contribute to the problem

Found invariant X₀ ≤ X₁ for location eval_foo_bb2_in

Found invariant X₀ ≤ X₁ for location eval_foo_bb1_in

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

Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 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:
t₂₁: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb1_in(X₁, X₁)
t₂₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: 1+X₀ ≤ 0 ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁
t₂₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ X₁
t₂₄: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁
t₂₅: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁
t₂₆: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(X₀-2, X₁) :|: X₀ ≤ X₁
t₂₇: eval_foo_bb3_in(X₀, X₁) → eval_foo_stop(X₀, X₁) :|: X₀ ≤ 1 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₁
t₂₈: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

MPRF for transition t₂₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

• eval_foo_bb1_in: [X₀]
• eval_foo_bb2_in: [X₀-2]

Found invariant 1+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ X₁ ∧ 3+X₀ ≤ 0 for location eval_foo_bb1_in_v1

Found invariant 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb1_in_v2

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

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

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

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

Found invariant 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_foo_bb2_in_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: X₁ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: inf {Infinity}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: X₁ {O(n)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: inf {Infinity}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}

Sizebounds

t₂₁, X₀: X₁ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₄, X₀: 1 {O(1)}
t₂₄, X₁: 2⋅X₁ {O(n)}
t₂₅, X₀: 0 {O(1)}
t₂₅, X₁: 2⋅X₁ {O(n)}
t₂₆, X₁: X₁ {O(n)}
t₂₇, X₀: 1 {O(1)}
t₂₇, X₁: 4⋅X₁ {O(n)}
t₂₈, X₀: X₀ {O(n)}
t₂₈, X₁: X₁ {O(n)}