Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃
Temp_Vars: O, P, Q, R
Locations: l0, l1, l2, l3
Transitions:
t₇: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → l2(X₀, 0, X₂, X₃, X₄, X₅, 0, X₇, X₈, 0, O, 0, 0, X₁₃-100⋅P) :|: 100⋅P ≤ X₁₃ ∧ X₁₃ ≤ 99+100⋅P ∧ X₅ ≤ 1
t₆: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → l3(X₀, X₁, X₂, X₃, X₄, X₅, 1, O, O, O, X₁₀, X₁₁, X₁₂, X₁₃-100⋅P) :|: 100⋅P ≤ X₁₃ ∧ X₁₃ ≤ 99+100⋅P ∧ 2 ≤ X₅
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → l1(X₀, P, X₁, O, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 0 ≤ X₀ ∧ 1 ≤ X₁
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → l1(X₀, P, X₁, O, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 0 ≤ X₀ ∧ X₁+1 ≤ 0
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → l2(X₀, 0, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, O, X₁₁, X₁₂, X₁₃) :|: 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → l1(X₀, R, P, Q, X₄, X₅, X₆, X₇, X₈, X₉, O, X₉, X₉, X₁₃) :|: X₅ ≤ 1+X₆ ∧ 1 ≤ P ∧ 0 ≤ X₄
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → l1(X₀, R, P, Q, X₄, X₅, X₆, X₇, X₈, X₉, O, X₉, X₉, X₁₃) :|: X₅ ≤ 1+X₆ ∧ P+1 ≤ 0 ∧ 0 ≤ X₄
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆+1, O, O, O, X₁₀, X₁₁, X₁₂, X₁₃) :|: 0 ≤ X₄ ∧ X₆+2 ≤ X₅

Preprocessing

Eliminate variables {O,Q,X₂,X₃,X₇,X₈,X₉,X₁₀,X₁₁,X₁₂} that do not contribute to the problem

Found invariant 0 ≤ X₆ ∧ X₅ ≤ 1+X₆ ∧ 0 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l2

Found invariant 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ X₅ ≤ 1+X₆ ∧ 1 ≤ X₄+X₆ ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 0 ≤ X₄ for location l1

Found invariant 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 2 ≤ X₅ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₄, X₅, X₆, X₁₃
Temp_Vars: P, R
Locations: l0, l1, l2, l3
Transitions:
t₁₇: l0(X₀, X₁, X₄, X₅, X₆, X₁₃) → l2(X₀, 0, X₄, X₅, 0, X₁₃-100⋅P) :|: 100⋅P ≤ X₁₃ ∧ X₁₃ ≤ 99+100⋅P ∧ X₅ ≤ 1
t₁₆: l0(X₀, X₁, X₄, X₅, X₆, X₁₃) → l3(X₀, X₁, X₄, X₅, 1, X₁₃-100⋅P) :|: 100⋅P ≤ X₁₃ ∧ X₁₃ ≤ 99+100⋅P ∧ 2 ≤ X₅
t₁₈: l1(X₀, X₁, X₄, X₅, X₆, X₁₃) → l1(X₀, P, X₄, X₅, X₆, X₁₃) :|: 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ X₅ ≤ 1+X₆ ∧ 1 ≤ X₄+X₆ ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 0 ≤ X₄
t₁₉: l1(X₀, X₁, X₄, X₅, X₆, X₁₃) → l1(X₀, P, X₄, X₅, X₆, X₁₃) :|: 0 ≤ X₀ ∧ X₁+1 ≤ 0 ∧ 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ X₅ ≤ 1+X₆ ∧ 1 ≤ X₄+X₆ ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 0 ≤ X₄
t₂₀: l1(X₀, X₁, X₄, X₅, X₆, X₁₃) → l2(X₀, 0, X₄, X₅, X₆, X₁₃) :|: 0 ≤ X₀ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ X₅ ≤ 1+X₆ ∧ 1 ≤ X₄+X₆ ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 0 ≤ X₄
t₂₂: l3(X₀, X₁, X₄, X₅, X₆, X₁₃) → l1(X₀, R, X₄, X₅, X₆, X₁₃) :|: X₅ ≤ 1+X₆ ∧ 1 ≤ P ∧ 0 ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 2 ≤ X₅
t₂₃: l3(X₀, X₁, X₄, X₅, X₆, X₁₃) → l1(X₀, R, X₄, X₅, X₆, X₁₃) :|: X₅ ≤ 1+X₆ ∧ P+1 ≤ 0 ∧ 0 ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 2 ≤ X₅
t₂₁: l3(X₀, X₁, X₄, X₅, X₆, X₁₃) → l3(X₀, X₁, X₄, X₅, X₆+1, X₁₃) :|: 0 ≤ X₄ ∧ X₆+2 ≤ X₅ ∧ 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 2 ≤ X₅

MPRF for transition t₂₁: l3(X₀, X₁, X₄, X₅, X₆, X₁₃) → l3(X₀, X₁, X₄, X₅, X₆+1, X₁₃) :|: 0 ≤ X₄ ∧ X₆+2 ≤ X₅ ∧ 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 2 ≤ X₅ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l3 [X₅-X₆ ]

Analysing control-flow refined program

Found invariant 0 ≤ X₆ ∧ X₅ ≤ 1+X₆ ∧ 0 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l2

Found invariant 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ X₅ ≤ 1+X₆ ∧ 1 ≤ X₄+X₆ ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 0 ≤ X₄ for location l1

Found invariant 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 2 ≤ X₅ for location l3

Found invariant 1+X₆ ≤ X₅ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ X₅ ≤ 1+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1 ≤ X₀+X₆ ∧ 2 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₀+X₅ ∧ 0 ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₀ for location n_l1___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: inf {Infinity}
t₂₀: 1 {O(1)}
t₂₁: X₅+1 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: inf {Infinity}
t₂₀: 1 {O(1)}
t₂₁: X₅+1 {O(n)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}

Sizebounds

t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₆, X₅: X₅ {O(n)}
t₁₆, X₆: 1 {O(1)}
t₁₆, X₁₃: 99 {O(1)}
t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: 0 {O(1)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₇, X₆: 0 {O(1)}
t₁₇, X₁₃: 99 {O(1)}
t₁₈, X₀: 8⋅X₀ {O(n)}
t₁₈, X₄: 8⋅X₄ {O(n)}
t₁₈, X₅: 8⋅X₅ {O(n)}
t₁₈, X₆: 4⋅X₅+12 {O(n)}
t₁₈, X₁₃: 792 {O(1)}
t₁₉, X₀: 8⋅X₀ {O(n)}
t₁₉, X₄: 8⋅X₄ {O(n)}
t₁₉, X₅: 8⋅X₅ {O(n)}
t₁₉, X₆: 4⋅X₅+12 {O(n)}
t₁₉, X₁₃: 792 {O(1)}
t₂₀, X₀: 20⋅X₀ {O(n)}
t₂₀, X₁: 0 {O(1)}
t₂₀, X₄: 20⋅X₄ {O(n)}
t₂₀, X₅: 20⋅X₅ {O(n)}
t₂₀, X₆: 10⋅X₅+30 {O(n)}
t₂₀, X₁₃: 1980 {O(1)}
t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₁, X₆: X₅+2 {O(n)}
t₂₁, X₁₃: 99 {O(1)}
t₂₂, X₀: 2⋅X₀ {O(n)}
t₂₂, X₄: 2⋅X₄ {O(n)}
t₂₂, X₅: 2⋅X₅ {O(n)}
t₂₂, X₆: X₅+3 {O(n)}
t₂₂, X₁₃: 198 {O(1)}
t₂₃, X₀: 2⋅X₀ {O(n)}
t₂₃, X₄: 2⋅X₄ {O(n)}
t₂₃, X₅: 2⋅X₅ {O(n)}
t₂₃, X₆: X₅+3 {O(n)}
t₂₃, X₁₃: 198 {O(1)}