Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ X₀ ≤ X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(2⋅X₀+X₁, X₁+1, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant X₃ ≤ X₁ for location l5

Found invariant X₃ ≤ X₁ for location l1

Found invariant X₃ ≤ X₁ for location l4

Found invariant 0 ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0 ∧ X₃ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₀ ∧ X₃ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(2⋅X₀+X₁, X₁+1, X₂, X₃, X₄) :|: 0 ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₁

Analysing control-flow refined program

Found invariant 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l3___3

Found invariant 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ 1+X₀ for location n_l1___2

Found invariant X₃ ≤ X₁ for location l5

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₃ ≤ X₁ for location l4

Found invariant 0 ≤ X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₀ for location n_l3___1

MPRF for transition t₄₅: n_l1___2(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁+2⋅X₄ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ 1+X₀ of depth 1:

new bound:

X₃+X₄+3 {O(n)}

MPRF:

n_l3___1 [X₄+1-X₁ ]
n_l1___2 [X₄+2-X₁ ]

MPRF for transition t₄₇: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l1___2(2⋅X₀+X₁, X₁+1, X₂, X₃, X₄) :|: X₀ ≤ X₄ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁+2⋅X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₃+X₄+3 {O(n)}

MPRF:

n_l3___1 [X₄+2-X₁ ]
n_l1___2 [X₄+2-X₁ ]

CFR: Improvement to new bound with the following program:

new bound:

2⋅X₃+2⋅X₄+6 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___2, n_l3___1, n_l3___3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0 ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₄₆: l1(X₀, X₁, X₂, X₃, X₄) → n_l3___3(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₁
t₅₃: n_l1___2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ 1+X₀
t₅₄: n_l1___2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ 1+X₀
t₄₅: n_l1___2(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 1+X₀ ≤ X₁+2⋅X₄ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ 1+X₀
t₄₇: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l1___2(2⋅X₀+X₁, X₁+1, X₂, X₃, X₄) :|: X₀ ≤ X₄ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ 1+X₀ ≤ X₁+2⋅X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ 1+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₀
t₄₈: n_l3___3(X₀, X₁, X₂, X₃, X₄) → n_l1___2(2⋅X₀+X₁, X₁+1, X₂, X₃, X₄) :|: X₂ ≤ X₄ ∧ 0 ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₂+X₄ ∧ X₂ ≤ X₄ ∧ 0 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀

All Bounds

Timebounds

Overall timebound:2⋅X₃+2⋅X₄+15 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₄₆: 1 {O(1)}
t₁: 1 {O(1)}
t₆: 1 {O(1)}
t₄₅: X₃+X₄+3 {O(n)}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₄₇: X₃+X₄+3 {O(n)}
t₄₈: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+2⋅X₄+15 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₄₆: 1 {O(1)}
t₁: 1 {O(1)}
t₆: 1 {O(1)}
t₄₅: X₃+X₄+3 {O(n)}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₄₇: X₃+X₄+3 {O(n)}
t₄₈: 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: X₂ {O(n)}
t₃, X₁: X₃ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄₆, X₀: X₂ {O(n)}
t₄₆, X₁: X₃ {O(n)}
t₄₆, X₂: X₂ {O(n)}
t₄₆, X₃: X₃ {O(n)}
t₄₆, X₄: X₄ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₆, X₀: 16⋅2^(X₃+X₄+3)⋅X₄+2⋅2^(X₃+X₄+3)⋅X₄⋅X₄+28⋅2^(X₃+X₄+3)⋅X₃+2^(X₃+X₄+3)⋅32+2^(X₃+X₄+3)⋅4⋅X₂+2^(X₃+X₄+3)⋅4⋅X₃⋅X₃+2^(X₃+X₄+3)⋅6⋅X₃⋅X₄+4⋅X₃+6⋅X₂ {O(EXP)}
t₆, X₁: 2⋅X₄+8⋅X₃+10 {O(n)}
t₆, X₂: 6⋅X₂ {O(n)}
t₆, X₃: 6⋅X₃ {O(n)}
t₆, X₄: 6⋅X₄ {O(n)}
t₄₅, X₀: 14⋅2^(X₃+X₄+3)⋅X₃+16⋅2^(X₃+X₄+3)+2⋅2^(X₃+X₄+3)⋅X₂+2⋅2^(X₃+X₄+3)⋅X₃⋅X₃+2^(X₃+X₄+3)⋅3⋅X₃⋅X₄+2^(X₃+X₄+3)⋅8⋅X₄+2^(X₃+X₄+3)⋅X₄⋅X₄ {O(EXP)}
t₄₅, X₁: 2⋅X₃+X₄+4 {O(n)}
t₄₅, X₂: X₂ {O(n)}
t₄₅, X₃: X₃ {O(n)}
t₄₅, X₄: X₄ {O(n)}
t₅₃, X₀: 14⋅2^(X₃+X₄+3)⋅X₃+16⋅2^(X₃+X₄+3)+2⋅2^(X₃+X₄+3)⋅X₂+2⋅2^(X₃+X₄+3)⋅X₃⋅X₃+2^(X₃+X₄+3)⋅3⋅X₃⋅X₄+2^(X₃+X₄+3)⋅8⋅X₄+2^(X₃+X₄+3)⋅X₄⋅X₄+2⋅X₂+2⋅X₃ {O(EXP)}
t₅₃, X₁: 3⋅X₃+X₄+5 {O(n)}
t₅₃, X₂: 2⋅X₂ {O(n)}
t₅₃, X₃: 2⋅X₃ {O(n)}
t₅₃, X₄: 2⋅X₄ {O(n)}
t₅₄, X₀: 14⋅2^(X₃+X₄+3)⋅X₃+16⋅2^(X₃+X₄+3)+2⋅2^(X₃+X₄+3)⋅X₂+2⋅2^(X₃+X₄+3)⋅X₃⋅X₃+2^(X₃+X₄+3)⋅3⋅X₃⋅X₄+2^(X₃+X₄+3)⋅8⋅X₄+2^(X₃+X₄+3)⋅X₄⋅X₄+2⋅X₂+2⋅X₃ {O(EXP)}
t₅₄, X₁: 3⋅X₃+X₄+5 {O(n)}
t₅₄, X₂: 2⋅X₂ {O(n)}
t₅₄, X₃: 2⋅X₃ {O(n)}
t₅₄, X₄: 2⋅X₄ {O(n)}
t₄₇, X₀: 14⋅2^(X₃+X₄+3)⋅X₃+16⋅2^(X₃+X₄+3)+2⋅2^(X₃+X₄+3)⋅X₂+2⋅2^(X₃+X₄+3)⋅X₃⋅X₃+2^(X₃+X₄+3)⋅3⋅X₃⋅X₄+2^(X₃+X₄+3)⋅8⋅X₄+2^(X₃+X₄+3)⋅X₄⋅X₄ {O(EXP)}
t₄₇, X₁: 2⋅X₃+X₄+4 {O(n)}
t₄₇, X₂: X₂ {O(n)}
t₄₇, X₃: X₃ {O(n)}
t₄₇, X₄: X₄ {O(n)}
t₄₈, X₀: 2⋅X₂+2⋅X₃ {O(n)}
t₄₈, X₁: X₃+1 {O(n)}
t₄₈, X₂: X₂ {O(n)}
t₄₈, X₃: X₃ {O(n)}
t₄₈, X₄: X₄ {O(n)}