Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l2(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₂-X₀, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 7 < X₁
t₃: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 7
t₇: l5(X₀, X₁, X₂, X₃) → l3(X₀+4, X₁, X₂, X₃) :|: X₀ < X₂
t₈: l5(X₀, X₁, X₂, X₃) → l3(X₀-4, X₁, X₂, X₃) :|: X₂ ≤ X₀
t₁: l6(X₀, X₁, X₂, X₃) → l3(X₃, X₁, X₂, X₃)

Preprocessing

Found invariant X₁ ≤ 7 for location l2

Found invariant X₁ ≤ 7 for location l7

Found invariant 8 ≤ X₁ for location l5

Found invariant 8 ≤ X₁ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 8 ≤ X₁
t₅: l2(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ 7
t₂: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₂-X₀, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 7 < X₁
t₃: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 7
t₇: l5(X₀, X₁, X₂, X₃) → l3(X₀+4, X₁, X₂, X₃) :|: X₀ < X₂ ∧ 8 ≤ X₁
t₈: l5(X₀, X₁, X₂, X₃) → l3(X₀-4, X₁, X₂, X₃) :|: X₂ ≤ X₀ ∧ 8 ≤ X₁
t₁: l6(X₀, X₁, X₂, X₃) → l3(X₃, X₁, X₂, X₃)

Chain transitions t₄: l4→l1 and t₆: l1→l5 to t₉₂: l4→l5

Chain transitions t₁: l6→l3 and t₂: l3→l4 to t₉₃: l6→l4

Chain transitions t₈: l5→l3 and t₂: l3→l4 to t₉₄: l5→l4

Chain transitions t₇: l5→l3 and t₂: l3→l4 to t₉₅: l5→l4

Chain transitions t₉₃: l6→l4 and t₉₂: l4→l5 to t₉₆: l6→l5

Chain transitions t₉₅: l5→l4 and t₉₂: l4→l5 to t₉₇: l5→l5

Chain transitions t₉₅: l5→l4 and t₃: l4→l2 to t₉₈: l5→l2

Chain transitions t₉₃: l6→l4 and t₃: l4→l2 to t₉₉: l6→l2

Chain transitions t₉₄: l5→l4 and t₃: l4→l2 to t₁₀₀: l5→l2

Chain transitions t₉₄: l5→l4 and t₉₂: l4→l5 to t₁₀₁: l5→l5

Chain transitions t₉₄: l5→l4 and t₄: l4→l1 to t₁₀₂: l5→l1

Chain transitions t₉₅: l5→l4 and t₄: l4→l1 to t₁₀₃: l5→l1

Chain transitions t₉₃: l6→l4 and t₄: l4→l1 to t₁₀₄: l6→l1

Analysing control-flow refined program

Cut unsatisfiable transition t₈: l5→l3

Cut unsatisfiable transition t₉₄: l5→l4

Cut unsatisfiable transition t₁₀₀: l5→l2

Cut unsatisfiable transition t₁₀₁: l5→l5

Cut unsatisfiable transition t₁₀₂: l5→l1

Found invariant X₃ ≤ X₀ ∧ X₂ ≤ 7+X₀ for location l2

Found invariant X₃ ≤ X₀ ∧ X₂ ≤ 7+X₀ ∧ X₁ ≤ 7 for location l7

Found invariant 8+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 8+X₀ ≤ X₂ for location l5

Found invariant 8+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 8+X₀ ≤ X₂ for location l1

Found invariant X₃ ≤ X₀ for location l4

Found invariant X₃ ≤ X₀ for location l3

MPRF for transition t₉₇: l5(X₀, X₁, X₂, X₃) -{4}> l5(4+X₀, X₂-4-X₀, X₂, X₃) :|: X₀ < X₂ ∧ 11+X₀ < X₂ ∧ 8 ≤ X₁ ∧ 12+X₀ ≤ X₂ ∧ 8+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 8+X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₃ {O(n)}

Analysing control-flow refined program

Found invariant X₃ ≤ X₀ ∧ X₁ ≤ 7 for location l2

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 8 ≤ X₁ for location n_l1___6

Found invariant 12+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 8+X₀ ≤ X₂ ∧ 8 ≤ X₁ for location n_l5___1

Found invariant 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂ ∧ 8 ≤ X₁ for location n_l3___4

Found invariant 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂ for location n_l4___3

Found invariant 8+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 8+X₀ ≤ X₂ ∧ 8 ≤ X₁ for location n_l5___5

Found invariant 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂ ∧ 8 ≤ X₁ for location n_l1___2

Found invariant X₃ ≤ X₀ ∧ X₁ ≤ 7 for location l7

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

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location n_l4___7

MPRF for transition t₁₈₁: n_l1___2(X₀, X₁, X₂, X₃) → n_l5___1(X₀, X₁, X₂, X₃) :|: 7+X₀ < X₂ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ 8 ≤ X₁ ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂ ∧ 8 ≤ X₁ of depth 1:

new bound:

X₂+X₃+5 {O(n)}

MPRF for transition t₁₈₃: n_l3___4(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₂-X₀, X₂, X₃) :|: X₀ < X₂ ∧ 8 ≤ X₁ ∧ X₀ ≤ 3+X₂ ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂ ∧ 8 ≤ X₁ of depth 1:

new bound:

X₂+X₃+4 {O(n)}

MPRF for transition t₁₈₅: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ 7 < X₁ ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₃+7 {O(n)}

MPRF for transition t₁₈₇: n_l5___1(X₀, X₁, X₂, X₃) → n_l3___4(X₀+4, X₁, X₂, X₃) :|: 8+X₀ ≤ X₂ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ X₀ < X₂ ∧ 8 ≤ X₁ ∧ 12+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 8+X₀ ≤ X₂ ∧ 8 ≤ X₁ of depth 1:

new bound:

X₂+X₃+11 {O(n)}

CFR: Improvement to new bound with the following program:

new bound:

Infinite

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l2, l3, l6, l7, n_l1___2, n_l1___6, n_l3___4, n_l4___3, n_l4___7, n_l5___1, n_l5___5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₅: l2(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ 7 ∧ X₃ ≤ X₀ ∧ X₁ ≤ 7
t₁₈₄: l3(X₀, X₁, X₂, X₃) → n_l4___7(X₀, X₂-X₀, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁: l6(X₀, X₁, X₂, X₃) → l3(X₃, X₁, X₂, X₃)
t₁₈₁: n_l1___2(X₀, X₁, X₂, X₃) → n_l5___1(X₀, X₁, X₂, X₃) :|: 7+X₀ < X₂ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ 8 ≤ X₁ ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂ ∧ 8 ≤ X₁
t₁₈₂: n_l1___6(X₀, X₁, X₂, X₃) → n_l5___5(X₀, X₁, X₂, X₃) :|: 7+X₀ < X₂ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 8 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 8 ≤ X₁
t₁₈₃: n_l3___4(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₂-X₀, X₂, X₃) :|: X₀ < X₂ ∧ 8 ≤ X₁ ∧ X₀ ≤ 3+X₂ ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂ ∧ 8 ≤ X₁
t₁₉₆: n_l4___3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 7 ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂
t₁₈₅: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ 7 < X₁ ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂
t₁₉₇: n_l4___7(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 7 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₈₆: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___6(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ 7 < X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₈₇: n_l5___1(X₀, X₁, X₂, X₃) → n_l3___4(X₀+4, X₁, X₂, X₃) :|: 8+X₀ ≤ X₂ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ X₀ < X₂ ∧ 8 ≤ X₁ ∧ 12+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 8+X₀ ≤ X₂ ∧ 8 ≤ X₁
t₁₈₈: n_l5___5(X₀, X₁, X₂, X₃) → n_l3___4(X₀+4, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ X₀ < X₂ ∧ 8 ≤ X₁ ∧ 8 ≤ X₁ ∧ 8+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 8+X₀ ≤ X₂ ∧ 8 ≤ X₁

CFR: Improvement to new bound with the following program:

new bound:

4⋅X₂+4⋅X₃+27 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l2, l3, l6, l7, n_l1___2, n_l1___6, n_l3___4, n_l4___3, n_l4___7, n_l5___1, n_l5___5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₅: l2(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₁ ≤ 7 ∧ X₃ ≤ X₀ ∧ X₁ ≤ 7
t₁₈₄: l3(X₀, X₁, X₂, X₃) → n_l4___7(X₀, X₂-X₀, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁: l6(X₀, X₁, X₂, X₃) → l3(X₃, X₁, X₂, X₃)
t₁₈₁: n_l1___2(X₀, X₁, X₂, X₃) → n_l5___1(X₀, X₁, X₂, X₃) :|: 7+X₀ < X₂ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ 8 ≤ X₁ ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂ ∧ 8 ≤ X₁
t₁₈₂: n_l1___6(X₀, X₁, X₂, X₃) → n_l5___5(X₀, X₁, X₂, X₃) :|: 7+X₀ < X₂ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 8 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 8 ≤ X₁
t₁₈₃: n_l3___4(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₂-X₀, X₂, X₃) :|: X₀ < X₂ ∧ 8 ≤ X₁ ∧ X₀ ≤ 3+X₂ ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂ ∧ 8 ≤ X₁
t₁₉₆: n_l4___3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 7 ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂
t₁₈₅: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ 7 < X₁ ∧ 8+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 4+X₀ ≤ X₂
t₁₉₇: n_l4___7(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ ≤ 7 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₈₆: n_l4___7(X₀, X₁, X₂, X₃) → n_l1___6(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ 7 < X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₈₇: n_l5___1(X₀, X₁, X₂, X₃) → n_l3___4(X₀+4, X₁, X₂, X₃) :|: 8+X₀ ≤ X₂ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ X₀ < X₂ ∧ 8 ≤ X₁ ∧ 12+X₃ ≤ X₂ ∧ 4+X₃ ≤ X₀ ∧ 8+X₀ ≤ X₂ ∧ 8 ≤ X₁
t₁₈₈: n_l5___5(X₀, X₁, X₂, X₃) → n_l3___4(X₀+4, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀+X₁ ≤ X₂ ∧ X₂ ≤ X₀+X₁ ∧ X₀ < X₂ ∧ 8 ≤ X₁ ∧ 8 ≤ X₁ ∧ 8+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 8+X₀ ≤ X₂ ∧ 8 ≤ X₁

All Bounds

Timebounds

Overall timebound:4⋅X₂+4⋅X₃+36 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 1 {O(1)}
t₁₈₁: X₂+X₃+5 {O(n)}
t₁₈₂: 1 {O(1)}
t₁₈₃: X₂+X₃+4 {O(n)}
t₁₈₄: 1 {O(1)}
t₁₈₅: X₂+X₃+7 {O(n)}
t₁₈₆: 1 {O(1)}
t₁₈₇: X₂+X₃+11 {O(n)}
t₁₈₈: 1 {O(1)}
t₁₉₆: 1 {O(1)}
t₁₉₇: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₂+4⋅X₃+36 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 1 {O(1)}
t₁₈₁: X₂+X₃+5 {O(n)}
t₁₈₂: 1 {O(1)}
t₁₈₃: X₂+X₃+4 {O(n)}
t₁₈₄: 1 {O(1)}
t₁₈₅: X₂+X₃+7 {O(n)}
t₁₈₆: 1 {O(1)}
t₁₈₇: X₂+X₃+11 {O(n)}
t₁₈₈: 1 {O(1)}
t₁₉₆: 1 {O(1)}
t₁₉₇: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₅, X₀: 4⋅X₂+6⋅X₃+48 {O(n)}
t₅, X₁: 7⋅X₂+7⋅X₃+52 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₁₈₁, X₀: 4⋅X₂+5⋅X₃+48 {O(n)}
t₁₈₁, X₁: 6⋅X₂+6⋅X₃+52 {O(n)}
t₁₈₁, X₂: X₂ {O(n)}
t₁₈₁, X₃: X₃ {O(n)}
t₁₈₂, X₀: X₃ {O(n)}
t₁₈₂, X₁: X₂+X₃ {O(n)}
t₁₈₂, X₂: X₂ {O(n)}
t₁₈₂, X₃: X₃ {O(n)}
t₁₈₃, X₀: 4⋅X₂+5⋅X₃+48 {O(n)}
t₁₈₃, X₁: 6⋅X₂+6⋅X₃+52 {O(n)}
t₁₈₃, X₂: X₂ {O(n)}
t₁₈₃, X₃: X₃ {O(n)}
t₁₈₄, X₀: X₃ {O(n)}
t₁₈₄, X₁: X₂+X₃ {O(n)}
t₁₈₄, X₂: X₂ {O(n)}
t₁₈₄, X₃: X₃ {O(n)}
t₁₈₅, X₀: 4⋅X₂+5⋅X₃+48 {O(n)}
t₁₈₅, X₁: 6⋅X₂+6⋅X₃+52 {O(n)}
t₁₈₅, X₂: X₂ {O(n)}
t₁₈₅, X₃: X₃ {O(n)}
t₁₈₆, X₀: X₃ {O(n)}
t₁₈₆, X₁: X₂+X₃ {O(n)}
t₁₈₆, X₂: X₂ {O(n)}
t₁₈₆, X₃: X₃ {O(n)}
t₁₈₇, X₀: 4⋅X₂+5⋅X₃+48 {O(n)}
t₁₈₇, X₁: 6⋅X₂+6⋅X₃+52 {O(n)}
t₁₈₇, X₂: X₂ {O(n)}
t₁₈₇, X₃: X₃ {O(n)}
t₁₈₈, X₀: X₃+4 {O(n)}
t₁₈₈, X₁: X₂+X₃ {O(n)}
t₁₈₈, X₂: X₂ {O(n)}
t₁₈₈, X₃: X₃ {O(n)}
t₁₉₆, X₀: 4⋅X₂+5⋅X₃+48 {O(n)}
t₁₉₆, X₁: 6⋅X₂+6⋅X₃+52 {O(n)}
t₁₉₆, X₂: X₂ {O(n)}
t₁₉₆, X₃: X₃ {O(n)}
t₁₉₇, X₀: X₃ {O(n)}
t₁₉₇, X₁: X₂+X₃ {O(n)}
t₁₉₇, X₂: X₂ {O(n)}
t₁₉₇, X₃: X₃ {O(n)}