Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(1, X₄, nondef.0, X₃, X₄) :|: 1 ≤ nondef.0
t₂: l2(X₀, X₁, X₂, X₃, X₄) → l1(-1, X₄, nondef.0, X₃, X₄) :|: nondef.0 < 1
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁+X₀, X₂, X₃, X₄) :|: 1 ≤ X₂
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁-X₀, X₂, X₃, X₄) :|: X₂ < 1
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 for location l5

Found invariant X₀ ≤ 1 for location l1

Found invariant 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 for location l4

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ 1 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃ ∧ X₀ ≤ 1
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₁ ∧ X₀ ≤ 1
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(1, X₄, nondef.0, X₃, X₄) :|: 1 ≤ nondef.0
t₂: l2(X₀, X₁, X₂, X₃, X₄) → l1(-1, X₄, nondef.0, X₃, X₄) :|: nondef.0 < 1
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁+X₀, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁-X₀, X₂, X₃, X₄) :|: X₂ < 1 ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₁ ∧ X₀ ≤ 1

Analysing control-flow refined program

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___4

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___3

Found invariant 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 for location l5

Found invariant 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___2

Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l1

Found invariant 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l4

Found invariant X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location n_l3___1

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___4

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___3

Found invariant 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l5

Found invariant 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___2

Found invariant X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l1

Found invariant 1+X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location l4

Found invariant X₁ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ 1+X₀ ∧ X₀+X₂ ≤ 1 ∧ X₀ ≤ 1 ∧ 0 ≤ 1+X₀ for location n_l3___1

MPRF for transition t₁₄₇: n_l1___3(X₀, X₁, X₂, X₃, X₄) → n_l3___2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀+X₃ ∧ X₀ ≤ 1 ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃+X₄+2 {O(n)}

MPRF:

n_l3___2 [X₃-X₁ ]
n_l1___3 [X₃+1-X₁ ]

MPRF for transition t₁₅₁: n_l3___2(X₀, X₁, X₂, X₃, X₄) → n_l1___3(X₀, X₀+X₁, X₂, X₃, X₄) :|: X₀ ≤ 1 ∧ X₁ ≤ X₀+X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃+X₄+2 {O(n)}

MPRF:

n_l3___2 [X₃+1-X₁ ]
n_l1___3 [X₀+X₃-X₁ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₃: inf {Infinity}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: inf {Infinity}
t₆: inf {Infinity}
t₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₃: inf {Infinity}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: inf {Infinity}
t₆: inf {Infinity}
t₇: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₃, X₀: 2 {O(1)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: 6 {O(1)}
t₄, X₃: 6⋅X₃ {O(n)}
t₄, X₄: 6⋅X₄ {O(n)}
t₁, X₀: 1 {O(1)}
t₁, X₁: X₄ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: 1 {O(1)}
t₂, X₁: X₄ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₅, X₀: 2 {O(1)}
t₅, X₃: 2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₆, X₀: 2 {O(1)}
t₆, X₃: 2⋅X₃ {O(n)}
t₆, X₄: 2⋅X₄ {O(n)}
t₇, X₀: 6 {O(1)}
t₇, X₃: 6⋅X₃ {O(n)}
t₇, X₄: 6⋅X₄ {O(n)}