Initial Problem

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:
t₁: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb1_in(X₁, X₁)
t₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: X₀ ≤ 10
t₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: 11 ≤ X₀
t₄: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(2+X₀, X₁) :|: 7 ≤ X₀
t₅: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(X₀, X₁) :|: X₀ ≤ 6
t₆: eval_foo_bb3_in(X₀, X₁) → eval_foo_stop(X₀, X₁)
t₀: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

Preprocessing

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 for location eval_foo_bb2_in

Found invariant X₁ ≤ X₀ for location eval_foo_bb1_in

Found invariant X₁ ≤ X₀ ∧ 11 ≤ X₀ for location eval_foo_stop

Found invariant X₁ ≤ X₀ ∧ 11 ≤ 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:
t₁: eval_foo_bb0_in(X₀, X₁) → eval_foo_bb1_in(X₁, X₁)
t₂: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb2_in(X₀, X₁) :|: X₀ ≤ 10 ∧ X₁ ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁) → eval_foo_bb3_in(X₀, X₁) :|: 11 ≤ X₀ ∧ X₁ ≤ X₀
t₄: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(2+X₀, X₁) :|: 7 ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀
t₅: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(X₀, X₁) :|: X₀ ≤ 6 ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀
t₆: eval_foo_bb3_in(X₀, X₁) → eval_foo_stop(X₀, X₁) :|: 11 ≤ X₀ ∧ X₁ ≤ X₀
t₀: eval_foo_start(X₀, X₁) → eval_foo_bb0_in(X₀, X₁)

MPRF for transition t₄: eval_foo_bb2_in(X₀, X₁) → eval_foo_bb1_in(2+X₀, X₁) :|: 7 ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₁+11 {O(n)}

• eval_foo_bb1_in: [11-X₀]
• eval_foo_bb2_in: [11-X₀]

Found invariant X₁ ≤ 6 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 12 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 6 for location eval_foo_bb1_in_v1

Found invariant X₁ ≤ 8 ∧ 4+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 7 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 12 ∧ 11 ≤ X₀ for location eval_foo_bb1_in_v3

Found invariant X₁ ≤ 10 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 22 ∧ 7 ≤ X₁ ∧ 16 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 12 ∧ 9 ≤ X₀ for location eval_foo_bb1_in_v2

Found invariant X₁ ≤ X₀ ∧ 7 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ 11 ≤ X₀ for location eval_foo_stop

Found invariant X₁ ≤ X₀ ∧ 7 ≤ X₁ ∧ 18 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ 11 ≤ X₀ for location eval_foo_bb3_in

Found invariant X₁ ≤ 8 ∧ 2+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 18 ∧ 7 ≤ X₁ ∧ 16 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 10 ∧ 9 ≤ X₀ for location eval_foo_bb2_in_v2

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

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 for location eval_foo_bb2_in_v1

Found invariant X₁ ≤ 6 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 12 ∧ X₀ ≤ X₁ ∧ X₀ ≤ 6 for location eval_foo_bb2_in_v3

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: X₁+11 {O(n)}
t₅: inf {Infinity}
t₆: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: X₁+11 {O(n)}
t₅: inf {Infinity}
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: X₁+12 {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+12 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₄, X₀: 12 {O(1)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: X₁+12 {O(n)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: X₁+12 {O(n)}
t₆, X₁: 2⋅X₁ {O(n)}