Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_bb6_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb1_in(X₅, X₆, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₁
t₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₇ ∧ X₁ ≤ X₇
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₀
t₆: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₇
t₇: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb5_in(X₀, X₁, X₀-1, X₁, X₄, X₅, X₆, X₇)
t₈: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb5_in(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆, X₇) :|: 1+X₇ ≤ X₁
t₉: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb5_in(X₀, X₁, X₀, X₁, X₄, X₅, X₆, X₇) :|: X₁ ≤ X₇
t₁₀: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb1_in(X₂, X₃, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₁: eval_foo_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Eliminate variables [X₄] that do not contribute to the problem

Found invariant X₃ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₂ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ 1+X₂ for location eval_foo_bb5_in

Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location eval_foo_stop

Found invariant 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location eval_foo_bb3_in

Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location eval_foo_bb2_in

Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location eval_foo_bb1_in

Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location eval_foo_bb6_in

Found invariant X₀ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_bb6_in, eval_foo_start, eval_foo_stop
Transitions:
t₂₃: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₄, X₅, X₂, X₃, X₄, X₅, X₆)
t₂₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅
t₂₅: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅
t₂₆: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅
t₂₇: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅
t₂₈: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅
t₂₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₀-1, X₁, X₄, X₅, X₆) :|: 1+X₆ ≤ X₀ ∧ 1+X₆ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅
t₃₀: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆) :|: 1+X₆ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₆ ∧ X₁ ≤ X₅
t₃₁: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₁ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₆ ∧ X₁ ≤ X₅
t₃₂: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₂, X₃, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₂ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₅
t₃₃: eval_foo_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₄ ∧ X₀ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₁ ≤ X₆
t₃₄: eval_foo_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₂₇: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅ of depth 1:

new bound:

X₄+X₆ {O(n)}

• eval_foo_bb1_in: [X₀-X₆]
• eval_foo_bb2_in: [X₀-X₆]
• eval_foo_bb3_in: [X₀-1-X₆]
• eval_foo_bb4_in: [X₀-X₆]
• eval_foo_bb5_in: [X₂-X₆]

MPRF for transition t₂₉: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₀-1, X₁, X₄, X₅, X₆) :|: 1+X₆ ≤ X₀ ∧ 1+X₆ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅ of depth 1:

new bound:

X₄+X₆ {O(n)}

• eval_foo_bb1_in: [X₀-X₆]
• eval_foo_bb2_in: [X₀-X₆]
• eval_foo_bb3_in: [X₀-X₆]
• eval_foo_bb4_in: [X₀-X₆]
• eval_foo_bb5_in: [X₂-X₆]

MPRF for transition t₃₀: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₀, X₁-1, X₄, X₅, X₆) :|: 1+X₆ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₆ ∧ X₁ ≤ X₅ of depth 1:

new bound:

X₅+X₆ {O(n)}

• eval_foo_bb1_in: [X₁-X₆]
• eval_foo_bb2_in: [X₁-X₆]
• eval_foo_bb3_in: [X₁-X₆]
• eval_foo_bb4_in: [X₁-X₆]
• eval_foo_bb5_in: [X₃-X₆]

MPRF for transition t₂₅: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅ of depth 1:

new bound:

2⋅X₆+X₄+X₅+1 {O(n)}

• eval_foo_bb1_in: [1]
• eval_foo_bb2_in: [1+X₆-X₁]
• eval_foo_bb3_in: [1]
• eval_foo_bb4_in: [1+X₆-X₁]
• eval_foo_bb5_in: [1]

MPRF for transition t₂₈: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅ of depth 1:

new bound:

2⋅X₆⋅X₆+3⋅X₅⋅X₆+X₄⋅X₅+X₄⋅X₆+X₅⋅X₅+2⋅X₅+3⋅X₆+X₄+1 {O(n^2)}

• eval_foo_bb1_in: [1+X₅-X₆]
• eval_foo_bb2_in: [2+X₅-X₁]
• eval_foo_bb3_in: [1+X₅-X₆]
• eval_foo_bb4_in: [1+X₅-X₁]
• eval_foo_bb5_in: [1+X₅-X₆]

MPRF for transition t₃₁: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₁ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₆ ∧ X₁ ≤ X₅ of depth 1:

new bound:

2⋅X₆⋅X₆+3⋅X₅⋅X₆+X₄⋅X₅+X₄⋅X₆+X₅⋅X₅+X₅+X₆ {O(n^2)}

• eval_foo_bb1_in: [X₅-X₆]
• eval_foo_bb2_in: [1+X₅-X₁]
• eval_foo_bb3_in: [X₅-X₆]
• eval_foo_bb4_in: [1+X₅-X₁]
• eval_foo_bb5_in: [X₅-X₆]

MPRF for transition t₃₂: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb1_in(X₂, X₃, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ 1+X₂ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₅ of depth 1:

new bound:

2⋅X₆+X₄+X₅ {O(n)}

• eval_foo_bb1_in: [0]
• eval_foo_bb2_in: [1+X₆-X₁]
• eval_foo_bb3_in: [1]
• eval_foo_bb4_in: [1+X₆-X₁]
• eval_foo_bb5_in: [1]

knowledge_propagation leads to new time bound 2⋅X₆+X₄+X₅+1 {O(n)} for transition t₂₄: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅

knowledge_propagation leads to new time bound 2⋅X₆+X₄+X₅+1 {O(n)} for transition t₂₈: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₅

knowledge_propagation leads to new time bound 2⋅X₆+X₄+X₅+1 {O(n)} for transition t₃₁: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_foo_bb5_in(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₁ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₆ ∧ X₁ ≤ X₅

All Bounds

Timebounds

Overall timebound:13⋅X₆+6⋅X₅+7⋅X₄+8 {O(n)}
t₂₃: 1 {O(1)}
t₂₄: 2⋅X₆+X₄+X₅+1 {O(n)}
t₂₅: 2⋅X₆+X₄+X₅+1 {O(n)}
t₂₆: 1 {O(1)}
t₂₇: X₄+X₆ {O(n)}
t₂₈: 2⋅X₆+X₄+X₅+1 {O(n)}
t₂₉: X₄+X₆ {O(n)}
t₃₀: X₅+X₆ {O(n)}
t₃₁: 2⋅X₆+X₄+X₅+1 {O(n)}
t₃₂: 2⋅X₆+X₄+X₅ {O(n)}
t₃₃: 1 {O(1)}
t₃₄: 1 {O(1)}

Costbounds

Overall costbound: 13⋅X₆+6⋅X₅+7⋅X₄+8 {O(n)}
t₂₃: 1 {O(1)}
t₂₄: 2⋅X₆+X₄+X₅+1 {O(n)}
t₂₅: 2⋅X₆+X₄+X₅+1 {O(n)}
t₂₆: 1 {O(1)}
t₂₇: X₄+X₆ {O(n)}
t₂₈: 2⋅X₆+X₄+X₅+1 {O(n)}
t₂₉: X₄+X₆ {O(n)}
t₃₀: X₅+X₆ {O(n)}
t₃₁: 2⋅X₆+X₄+X₅+1 {O(n)}
t₃₂: 2⋅X₆+X₄+X₅ {O(n)}
t₃₃: 1 {O(1)}
t₃₄: 1 {O(1)}

Sizebounds

t₂₃, X₀: X₄ {O(n)}
t₂₃, X₁: X₅ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₃, X₆: X₆ {O(n)}
t₂₄, X₀: 2⋅X₄+2⋅X₆+X₅ {O(n)}
t₂₄, X₁: 2⋅X₅+2⋅X₆+X₄ {O(n)}
t₂₄, X₂: 3⋅X₅+6⋅X₄+6⋅X₆+X₂+1 {O(n)}
t₂₄, X₃: 3⋅X₄+6⋅X₅+6⋅X₆+X₃+1 {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₄, X₆: X₆ {O(n)}
t₂₅, X₀: 2⋅X₄+2⋅X₆+X₅ {O(n)}
t₂₅, X₁: 2⋅X₅+2⋅X₆+X₄ {O(n)}
t₂₅, X₂: 3⋅X₅+6⋅X₄+6⋅X₆+X₂+1 {O(n)}
t₂₅, X₃: 3⋅X₄+6⋅X₅+6⋅X₆+X₃+1 {O(n)}
t₂₅, X₄: X₄ {O(n)}
t₂₅, X₅: X₅ {O(n)}
t₂₅, X₆: X₆ {O(n)}
t₂₆, X₀: 2⋅X₆+3⋅X₄+X₅ {O(n)}
t₂₆, X₁: 2⋅X₆+3⋅X₅+X₄ {O(n)}
t₂₆, X₂: 3⋅X₅+6⋅X₄+6⋅X₆+X₂+1 {O(n)}
t₂₆, X₃: 3⋅X₄+6⋅X₅+6⋅X₆+X₃+1 {O(n)}
t₂₆, X₄: 2⋅X₄ {O(n)}
t₂₆, X₅: 2⋅X₅ {O(n)}
t₂₆, X₆: 2⋅X₆ {O(n)}
t₂₇, X₀: 2⋅X₄+2⋅X₆+X₅ {O(n)}
t₂₇, X₁: 2⋅X₅+2⋅X₆+X₄ {O(n)}
t₂₇, X₂: 12⋅X₄+12⋅X₆+2⋅X₂+6⋅X₅+2 {O(n)}
t₂₇, X₃: 12⋅X₅+12⋅X₆+2⋅X₃+6⋅X₄+2 {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₇, X₆: X₆ {O(n)}
t₂₈, X₀: 2⋅X₄+2⋅X₆+X₅ {O(n)}
t₂₈, X₁: 2⋅X₅+2⋅X₆+X₄ {O(n)}
t₂₈, X₂: 3⋅X₅+6⋅X₄+6⋅X₆+X₂+1 {O(n)}
t₂₈, X₃: 3⋅X₄+6⋅X₅+6⋅X₆+X₃+1 {O(n)}
t₂₈, X₄: X₄ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₈, X₆: X₆ {O(n)}
t₂₉, X₀: 2⋅X₄+2⋅X₆+X₅ {O(n)}
t₂₉, X₁: 2⋅X₅+2⋅X₆+X₄ {O(n)}
t₂₉, X₂: 2⋅X₄+2⋅X₆+X₅+1 {O(n)}
t₂₉, X₃: 2⋅X₅+2⋅X₆+X₄ {O(n)}
t₂₉, X₄: X₄ {O(n)}
t₂₉, X₅: X₅ {O(n)}
t₂₉, X₆: X₆ {O(n)}
t₃₀, X₀: 2⋅X₄+2⋅X₆+X₅ {O(n)}
t₃₀, X₁: 2⋅X₅+2⋅X₆+X₄ {O(n)}
t₃₀, X₂: 2⋅X₄+2⋅X₆+X₅ {O(n)}
t₃₀, X₃: 2⋅X₅+2⋅X₆+X₄+1 {O(n)}
t₃₀, X₄: X₄ {O(n)}
t₃₀, X₅: X₅ {O(n)}
t₃₀, X₆: X₆ {O(n)}
t₃₁, X₀: 2⋅X₄+2⋅X₆+X₅ {O(n)}
t₃₁, X₁: 2⋅X₅+2⋅X₆+X₄ {O(n)}
t₃₁, X₂: 2⋅X₄+2⋅X₆+X₅ {O(n)}
t₃₁, X₃: 2⋅X₅+2⋅X₆+X₄ {O(n)}
t₃₁, X₄: X₄ {O(n)}
t₃₁, X₅: X₅ {O(n)}
t₃₁, X₆: X₆ {O(n)}
t₃₂, X₀: 2⋅X₄+2⋅X₆+X₅ {O(n)}
t₃₂, X₁: 2⋅X₅+2⋅X₆+X₄ {O(n)}
t₃₂, X₂: 3⋅X₅+6⋅X₄+6⋅X₆+1 {O(n)}
t₃₂, X₃: 3⋅X₄+6⋅X₅+6⋅X₆+1 {O(n)}
t₃₂, X₄: X₄ {O(n)}
t₃₂, X₅: X₅ {O(n)}
t₃₂, X₆: X₆ {O(n)}
t₃₃, X₀: 2⋅X₆+3⋅X₄+X₅ {O(n)}
t₃₃, X₁: 2⋅X₆+3⋅X₅+X₄ {O(n)}
t₃₃, X₂: 3⋅X₅+6⋅X₄+6⋅X₆+X₂+1 {O(n)}
t₃₃, X₃: 3⋅X₄+6⋅X₅+6⋅X₆+X₃+1 {O(n)}
t₃₃, X₄: 2⋅X₄ {O(n)}
t₃₃, X₅: 2⋅X₅ {O(n)}
t₃₃, X₆: 2⋅X₆ {O(n)}
t₃₄, X₀: X₀ {O(n)}
t₃₄, X₁: X₁ {O(n)}
t₃₄, X₂: X₂ {O(n)}
t₃₄, X₃: X₃ {O(n)}
t₃₄, X₄: X₄ {O(n)}
t₃₄, X₅: X₅ {O(n)}
t₃₄, X₆: X₆ {O(n)}