Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀ ∧ X₀ < 50
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: 50 ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 20 ∧ 11 < X₀ ∧ 30 ≤ X₀ ∧ X₀ ≤ 40
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ < 20 ∧ 11 < X₀ ∧ X₀ < 30
t₇: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ < 20 ∧ 11 < X₀ ∧ 40 < X₀
t₈: l3(X₀, X₁) → l1(X₀-2, X₁) :|: X₀ < 20 ∧ X₀ ≤ 11 ∧ 31 ≤ X₀ ∧ X₀ ≤ 41
t₉: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 20 ∧ X₀ ≤ 11 ∧ X₀ < 31
t₁₀: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 20 ∧ X₀ ≤ 11 ∧ 41 < X₀
t₁₁: l3(X₀, X₁) → l1(X₀, X₁) :|: 20 ≤ X₀ ∧ 10 < X₀ ∧ 29 ≤ X₀ ∧ X₀ ≤ 39
t₁₂: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 20 ≤ X₀ ∧ 10 < X₀ ∧ X₀ < 29
t₁₃: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 20 ≤ X₀ ∧ 10 < X₀ ∧ 39 < X₀
t₁₄: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 20 ≤ X₀ ∧ X₀ ≤ 10 ∧ 30 ≤ X₀ ∧ X₀ ≤ 40
t₁₅: l3(X₀, X₁) → l1(X₀, X₁) :|: 20 ≤ X₀ ∧ X₀ ≤ 10 ∧ X₀ < 30
t₁₆: l3(X₀, X₁) → l1(X₀, X₁) :|: 20 ≤ X₀ ∧ X₀ ≤ 10 ∧ 40 < X₀
t₁₇: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Cut unsatisfiable transition t₅: l3→l1

Cut unsatisfiable transition t₇: l3→l1

Cut unsatisfiable transition t₈: l3→l1

Cut unsatisfiable transition t₁₀: l3→l1

Cut unsatisfiable transition t₁₄: l3→l1

Cut unsatisfiable transition t₁₅: l3→l1

Cut unsatisfiable transition t₁₆: l3→l1

Found invariant X₀ ≤ 49 ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀ ∧ X₀ < 50
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: 50 ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₆: l3(X₀, X₁) → l1(X₀, X₁) :|: X₀ < 20 ∧ 11 < X₀ ∧ X₀ < 30 ∧ X₀ ≤ 49 ∧ 1 ≤ X₀
t₉: l3(X₀, X₁) → l1(X₀-1, X₁) :|: X₀ < 20 ∧ X₀ ≤ 11 ∧ X₀ < 31 ∧ X₀ ≤ 49 ∧ 1 ≤ X₀
t₁₁: l3(X₀, X₁) → l1(X₀, X₁) :|: 20 ≤ X₀ ∧ 10 < X₀ ∧ 29 ≤ X₀ ∧ X₀ ≤ 39 ∧ X₀ ≤ 49 ∧ 1 ≤ X₀
t₁₂: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 20 ≤ X₀ ∧ 10 < X₀ ∧ X₀ < 29 ∧ X₀ ≤ 49 ∧ 1 ≤ X₀
t₁₃: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 20 ≤ X₀ ∧ 10 < X₀ ∧ 39 < X₀ ∧ X₀ ≤ 49 ∧ 1 ≤ X₀
t₁₇: l4(X₀, X₁) → l5(X₀, X₁)

Analysing control-flow refined program

Cut unsatisfiable transition t₁₆₂: n_l1___10→l4

Cut unsatisfiable transition t₁₆₈: n_l1___10→l4

Cut unsatisfiable transition t₁₆₃: n_l1___11→l4

Cut unsatisfiable transition t₁₆₄: n_l1___12→l4

Cut unsatisfiable transition t₁₇₀: n_l1___12→l4

Cut unsatisfiable transition t₁₆₅: n_l1___3→l4

Cut unsatisfiable transition t₁₇₁: n_l1___3→l4

Cut unsatisfiable transition t₁₇₂: n_l1___8→l4

Cut unsatisfiable transition t₁₆₇: n_l1___9→l4

Cut unsatisfiable transition t₁₇₃: n_l1___9→l4

Found invariant X₁ ≤ 19 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 38 ∧ 12 ≤ X₁ ∧ 24 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 19 ∧ 12 ≤ X₀ for location n_l1___12

Found invariant X₁ ≤ 28 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 57 ∧ 20 ≤ X₁ ∧ 41 ≤ X₀+X₁ ∧ X₀ ≤ 9+X₁ ∧ X₀ ≤ 29 ∧ 21 ≤ X₀ for location n_l3___4

Found invariant X₁ ≤ 28 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 57 ∧ 20 ≤ X₁ ∧ 41 ≤ X₀+X₁ ∧ X₀ ≤ 9+X₁ ∧ X₀ ≤ 29 ∧ 21 ≤ X₀ for location n_l1___9

Found invariant X₁ ≤ 11 ∧ X₁ ≤ 11+X₀ ∧ X₀+X₁ ≤ 21 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ for location n_l1___11

Found invariant X₁ ≤ 39 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 78 ∧ 29 ≤ X₁ ∧ 58 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 39 ∧ 29 ≤ X₀ for location n_l3___5

Found invariant X₁ ≤ 11 ∧ X₁ ≤ 10+X₀ ∧ X₀+X₁ ≤ 21 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 1 ≤ X₀ for location n_l3___6

Found invariant X₁ ≤ 39 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 78 ∧ 29 ≤ X₁ ∧ 58 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 39 ∧ 29 ≤ X₀ for location n_l1___10

Found invariant X₁ ≤ 28 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 57 ∧ X₀ ≤ 29 ∧ 29 ≤ X₀ for location n_l1___3

Found invariant X₁ ≤ 49 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 99 ∧ 40 ≤ X₁ ∧ 81 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 50 ∧ 41 ≤ X₀ for location n_l1___8

Found invariant X₁ ≤ 49 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 98 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 49 ∧ 1 ≤ X₀ for location n_l3___13

Found invariant X₁ ≤ 28 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 57 ∧ X₀ ≤ 29 ∧ 29 ≤ X₀ for location n_l3___2

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

Found invariant X₁ ≤ 48 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 97 ∧ 40 ≤ X₁ ∧ 81 ≤ X₀+X₁ ∧ X₀ ≤ 9+X₁ ∧ X₀ ≤ 49 ∧ 41 ≤ X₀ for location n_l3___1

Found invariant X₁ ≤ 19 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 38 ∧ 12 ≤ X₁ ∧ 24 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 19 ∧ 12 ≤ X₀ for location n_l3___7

MPRF for transition t₁₂₄: n_l1___11(X₀, X₁) → n_l3___6(X₀, X₁) :|: X₀ < 20 ∧ X₀ < 50 ∧ X₀ ≤ 11 ∧ X₀ ≤ 39 ∧ X₀ < 29 ∧ X₀ ≤ 49 ∧ 0 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 < X₀ ∧ X₀ < 50 ∧ X₁ ≤ 11 ∧ X₁ ≤ 11+X₀ ∧ X₀+X₁ ≤ 21 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

MPRF:

n_l3___6 [X₀ ]
n_l1___11 [X₀+1 ]

MPRF for transition t₁₄₀: n_l3___6(X₀, X₁) → n_l1___11(X₀-1, X₁) :|: X₀ ≤ 10 ∧ 0 < X₀ ∧ X₀ ≤ 11 ∧ 1 ≤ X₀ ∧ X₁ ≤ 11 ∧ X₁ ≤ 10+X₀ ∧ X₀+X₁ ≤ 21 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 1 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

MPRF:

n_l3___6 [X₀ ]
n_l1___11 [X₀ ]

MPRF for transition t₁₂₈: n_l1___8(X₀, X₁) → n_l3___1(X₀, X₁) :|: 0 < X₀ ∧ 11 < X₀ ∧ 1 ≤ X₀ ∧ 29 ≤ X₀ ∧ 20 ≤ X₀ ∧ 39 < X₀ ∧ 0 < X₀ ∧ X₀ < 50 ∧ X₁ ≤ 49 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 99 ∧ 40 ≤ X₁ ∧ 81 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 50 ∧ 41 ≤ X₀ of depth 1:

new bound:

101 {O(1)}

MPRF:

n_l3___1 [50-X₀ ]
n_l1___8 [51-X₀ ]

MPRF for transition t₁₃₀: n_l3___1(X₀, X₁) → n_l1___8(X₀+1, X₁) :|: X₀ < 50 ∧ 39 < X₀ ∧ 39 < X₀ ∧ X₀ ≤ 49 ∧ X₁ ≤ 48 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 97 ∧ 40 ≤ X₁ ∧ 81 ≤ X₀+X₁ ∧ X₀ ≤ 9+X₁ ∧ X₀ ≤ 49 ∧ 41 ≤ X₀ of depth 1:

new bound:

100 {O(1)}

MPRF:

n_l3___1 [50-X₀ ]
n_l1___8 [50-X₀ ]

MPRF for transition t₁₂₉: n_l1___9(X₀, X₁) → n_l3___4(X₀, X₁) :|: 0 < X₀ ∧ X₀ < 50 ∧ 11 < X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 39 ∧ 20 ≤ X₀ ∧ X₀ ≤ 49 ∧ 1 ≤ X₀ ∧ X₀ ≤ 49 ∧ 0 < X₀ ∧ X₀ < 50 ∧ X₁ ≤ 28 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 57 ∧ 20 ≤ X₁ ∧ 41 ≤ X₀+X₁ ∧ X₀ ≤ 9+X₁ ∧ X₀ ≤ 29 ∧ 21 ≤ X₀ of depth 1:

new bound:

59 {O(1)}

MPRF:

n_l3___4 [29-X₀ ]
n_l1___9 [30-X₀ ]

MPRF for transition t₁₃₈: n_l3___4(X₀, X₁) → n_l1___9(X₀+1, X₁) :|: X₀ ≤ 39 ∧ 20 ≤ X₀ ∧ 20 ≤ X₀ ∧ X₀ < 29 ∧ X₁ ≤ 28 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 57 ∧ 20 ≤ X₁ ∧ 41 ≤ X₀+X₁ ∧ X₀ ≤ 9+X₁ ∧ X₀ ≤ 29 ∧ 21 ≤ X₀ of depth 1:

new bound:

58 {O(1)}

MPRF:

n_l3___4 [29-X₀ ]
n_l1___9 [29-X₀ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₆: inf {Infinity}
t₉: inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: inf {Infinity}
t₁₃: inf {Infinity}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₆: inf {Infinity}
t₉: inf {Infinity}
t₁₁: inf {Infinity}
t₁₂: inf {Infinity}
t₁₃: inf {Infinity}
t₁₇: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₂, X₀: 49 {O(1)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₁+10 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₄, X₀: X₁+50 {O(n)}
t₄, X₁: 2⋅X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₆, X₀: 19 {O(1)}
t₆, X₁: X₁ {O(n)}
t₉, X₀: 10 {O(1)}
t₉, X₁: X₁ {O(n)}
t₁₁, X₀: 39 {O(1)}
t₁₁, X₁: X₁ {O(n)}
t₁₂, X₀: 29 {O(1)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: 50 {O(1)}
t₁₃, X₁: X₁ {O(n)}
t₁₇, X₀: 2⋅X₁+60 {O(n)}
t₁₇, X₁: 4⋅X₁ {O(n)}