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 < X₂
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) :|: X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁-X₀-5, 2⋅X₁, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ 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 < X₂
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) :|: X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁-X₀-5, 2⋅X₁, X₂, X₃, X₄) :|: 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3

Analysing control-flow refined program

Cut unsatisfiable transition t₁₀₃: n_l1___2→l4

Found invariant 6+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location n_l1___4

Found invariant 7 ≤ X₄ ∧ 8 ≤ X₃+X₄ ∧ 9 ≤ X₂+X₄ ∧ 21 ≤ X₁+X₄ ∧ 8 ≤ X₀+X₄ ∧ 6+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 15 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 16 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 14 ≤ X₁ ∧ 15 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___3

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l3___5

Found invariant 7 ≤ X₄ ∧ 8 ≤ X₃+X₄ ∧ 9 ≤ X₂+X₄ ∧ 35 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 29 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 30 ≤ X₁+X₂ ∧ 10 ≤ X₀+X₂ ∧ 28 ≤ X₁ ∧ 36 ≤ X₀+X₁ ∧ 20+X₀ ≤ X₁ for location n_l1___2

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1

Found invariant 7 ≤ X₄ ∧ 8 ≤ X₃+X₄ ∧ 13 ≤ X₂+X₄ ∧ 35 ≤ X₁+X₄ ∧ 8 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 7 ≤ X₂+X₃ ∧ 29 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 6 ≤ X₂ ∧ 37 ≤ X₁+X₂ ∧ 10 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 28 ≤ X₁ ∧ 36 ≤ X₀+X₁ ∧ 20+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1

MPRF for transition t₉₃: n_l1___2(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 8+2⋅X₀+2⋅X₂ ∧ 12+2⋅X₀ ≤ X₁ ∧ 0 < X₀ ∧ X₀ < X₂ ∧ 7 ≤ X₄ ∧ 8 ≤ X₃+X₄ ∧ 9 ≤ X₂+X₄ ∧ 35 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 29 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 30 ≤ X₁+X₂ ∧ 10 ≤ X₀+X₂ ∧ 28 ≤ X₁ ∧ 36 ≤ X₀+X₁ ∧ 20+X₀ ≤ X₁ of depth 1:

new bound:

11⋅X₂+14⋅X₄+20 {O(n)}

MPRF:

n_l3___1 [11⋅X₂+15-X₀-5⋅X₁ ]
n_l1___2 [X₀+11⋅X₂+20-3⋅X₁ ]

MPRF for transition t₉₆: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l1___2(X₁-X₀-5, 2⋅X₁, X₂, X₃, X₄) :|: X₀ < X₂ ∧ 1 ≤ X₀ ∧ X₁ ≤ 8+2⋅X₀+2⋅X₂ ∧ 12+2⋅X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 7 ≤ X₄ ∧ 8 ≤ X₃+X₄ ∧ 13 ≤ X₂+X₄ ∧ 35 ≤ X₁+X₄ ∧ 8 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 7 ≤ X₂+X₃ ∧ 29 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 6 ≤ X₂ ∧ 37 ≤ X₁+X₂ ∧ 10 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 28 ≤ X₁ ∧ 36 ≤ X₀+X₁ ∧ 20+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

4⋅X₂+4⋅X₄+7 {O(n)}

MPRF:

n_l3___1 [4⋅X₂+7-X₁ ]
n_l1___2 [4⋅X₂+7-X₁ ]

CFR: Improvement to new bound with the following program:

new bound:

15⋅X₂+18⋅X₄+27 {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_l1___4, n_l3___1, n_l3___3, n_l3___5
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 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₉₅: l1(X₀, X₁, X₂, X₃, X₄) → n_l3___5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 < X₀ ∧ X₀ < X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₁₀₅: n_l1___2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ 7 ≤ X₄ ∧ 8 ≤ X₃+X₄ ∧ 9 ≤ X₂+X₄ ∧ 35 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 29 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 30 ≤ X₁+X₂ ∧ 10 ≤ X₀+X₂ ∧ 28 ≤ X₁ ∧ 36 ≤ X₀+X₁ ∧ 20+X₀ ≤ X₁
t₉₃: n_l1___2(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 8+2⋅X₀+2⋅X₂ ∧ 12+2⋅X₀ ≤ X₁ ∧ 0 < X₀ ∧ X₀ < X₂ ∧ 7 ≤ X₄ ∧ 8 ≤ X₃+X₄ ∧ 9 ≤ X₂+X₄ ∧ 35 ≤ X₁+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 29 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 30 ≤ X₁+X₂ ∧ 10 ≤ X₀+X₂ ∧ 28 ≤ X₁ ∧ 36 ≤ X₀+X₁ ∧ 20+X₀ ≤ X₁
t₁₀₄: n_l1___4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 6+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₂
t₁₀₆: n_l1___4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ 6+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₂
t₉₄: n_l1___4(X₀, X₁, X₂, X₃, X₄) → n_l3___3(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 8+2⋅X₀+2⋅X₂ ∧ 12+2⋅X₀ ≤ X₁ ∧ 0 < X₀ ∧ X₀ < X₂ ∧ 6+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₂
t₉₆: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l1___2(X₁-X₀-5, 2⋅X₁, X₂, X₃, X₄) :|: X₀ < X₂ ∧ 1 ≤ X₀ ∧ X₁ ≤ 8+2⋅X₀+2⋅X₂ ∧ 12+2⋅X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 7 ≤ X₄ ∧ 8 ≤ X₃+X₄ ∧ 13 ≤ X₂+X₄ ∧ 35 ≤ X₁+X₄ ∧ 8 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 7 ≤ X₂+X₃ ∧ 29 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 6 ≤ X₂ ∧ 37 ≤ X₁+X₂ ∧ 10 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 28 ≤ X₁ ∧ 36 ≤ X₀+X₁ ∧ 20+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₉₇: n_l3___3(X₀, X₁, X₂, X₃, X₄) → n_l1___2(X₁-X₀-5, 2⋅X₁, X₂, X₃, X₄) :|: X₀ < X₂ ∧ 0 < X₀ ∧ X₁ ≤ 8+2⋅X₀+2⋅X₂ ∧ 12+2⋅X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 7 ≤ X₄ ∧ 8 ≤ X₃+X₄ ∧ 9 ≤ X₂+X₄ ∧ 21 ≤ X₁+X₄ ∧ 8 ≤ X₀+X₄ ∧ 6+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 15 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 16 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 14 ≤ X₁ ∧ 15 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉₈: n_l3___5(X₀, X₁, X₂, X₃, X₄) → n_l1___4(X₁-X₀-5, 2⋅X₁, X₂, X₃, X₄) :|: X₀ < X₂ ∧ 0 < X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀

All Bounds

Timebounds

Overall timebound:15⋅X₂+18⋅X₄+39 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₉₅: 1 {O(1)}
t₁: 1 {O(1)}
t₆: 1 {O(1)}
t₉₃: 11⋅X₂+14⋅X₄+20 {O(n)}
t₁₀₅: 1 {O(1)}
t₉₄: 1 {O(1)}
t₁₀₄: 1 {O(1)}
t₁₀₆: 1 {O(1)}
t₉₆: 4⋅X₂+4⋅X₄+7 {O(n)}
t₉₇: 1 {O(1)}
t₉₈: 1 {O(1)}

Costbounds

Overall costbound: 15⋅X₂+18⋅X₄+39 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₉₅: 1 {O(1)}
t₁: 1 {O(1)}
t₆: 1 {O(1)}
t₉₃: 11⋅X₂+14⋅X₄+20 {O(n)}
t₁₀₅: 1 {O(1)}
t₉₄: 1 {O(1)}
t₁₀₄: 1 {O(1)}
t₁₀₆: 1 {O(1)}
t₉₆: 4⋅X₂+4⋅X₄+7 {O(n)}
t₉₇: 1 {O(1)}
t₉₈: 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: X₃ {O(n)}
t₃, X₁: X₄ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: X₃ {O(n)}
t₄, X₁: X₄ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₉₅, X₀: X₃ {O(n)}
t₉₅, X₁: X₄ {O(n)}
t₉₅, X₂: X₂ {O(n)}
t₉₅, X₃: X₃ {O(n)}
t₉₅, X₄: X₄ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₆, X₀: 2^(4⋅X₂+4⋅X₄+7)⋅4⋅X₄+4⋅X₃+4⋅X₄+10 {O(EXP)}
t₆, X₁: 2^(4⋅X₂+4⋅X₄+7)⋅4⋅X₄+10⋅X₄ {O(EXP)}
t₆, X₂: 6⋅X₂ {O(n)}
t₆, X₃: 6⋅X₃ {O(n)}
t₆, X₄: 6⋅X₄ {O(n)}
t₉₃, X₀: 2^(4⋅X₂+4⋅X₄+7)⋅4⋅X₄+2⋅X₄ {O(EXP)}
t₉₃, X₁: 2^(4⋅X₂+4⋅X₄+7)⋅4⋅X₄ {O(EXP)}
t₉₃, X₂: X₂ {O(n)}
t₉₃, X₃: X₃ {O(n)}
t₉₃, X₄: X₄ {O(n)}
t₁₀₅, X₀: 2^(4⋅X₂+4⋅X₄+7)⋅4⋅X₄+2⋅X₄ {O(EXP)}
t₁₀₅, X₁: 2^(4⋅X₂+4⋅X₄+7)⋅4⋅X₄+4⋅X₄ {O(EXP)}
t₁₀₅, X₂: 2⋅X₂ {O(n)}
t₁₀₅, X₃: 2⋅X₃ {O(n)}
t₁₀₅, X₄: 2⋅X₄ {O(n)}
t₉₄, X₀: X₃+X₄+5 {O(n)}
t₉₄, X₁: 2⋅X₄ {O(n)}
t₉₄, X₂: X₂ {O(n)}
t₉₄, X₃: X₃ {O(n)}
t₉₄, X₄: X₄ {O(n)}
t₁₀₄, X₀: X₃+X₄+5 {O(n)}
t₁₀₄, X₁: 2⋅X₄ {O(n)}
t₁₀₄, X₂: X₂ {O(n)}
t₁₀₄, X₃: X₃ {O(n)}
t₁₀₄, X₄: X₄ {O(n)}
t₁₀₆, X₀: X₃+X₄+5 {O(n)}
t₁₀₆, X₁: 2⋅X₄ {O(n)}
t₁₀₆, X₂: X₂ {O(n)}
t₁₀₆, X₃: X₃ {O(n)}
t₁₀₆, X₄: X₄ {O(n)}
t₉₆, X₀: 2^(4⋅X₂+4⋅X₄+7)⋅4⋅X₄ {O(EXP)}
t₉₆, X₁: 2^(4⋅X₂+4⋅X₄+7)⋅4⋅X₄ {O(EXP)}
t₉₆, X₂: X₂ {O(n)}
t₉₆, X₃: X₃ {O(n)}
t₉₆, X₄: X₄ {O(n)}
t₉₇, X₀: 2⋅X₄ {O(n)}
t₉₇, X₁: 4⋅X₄ {O(n)}
t₉₇, X₂: X₂ {O(n)}
t₉₇, X₃: X₃ {O(n)}
t₉₇, X₄: X₄ {O(n)}
t₉₈, X₀: X₃+X₄+5 {O(n)}
t₉₈, X₁: 2⋅X₄ {O(n)}
t₉₈, X₂: X₂ {O(n)}
t₉₈, X₃: X₃ {O(n)}
t₉₈, X₄: X₄ {O(n)}