Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
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) → l2(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0
t₇: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ E
t₈: l1(X₀, X₁, X₂, X₃) → l3(X₂, X₃, X₂, X₃)
t₉: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃-1)
t₂: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₀
t₃: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₀-1, X₁-1)
t₁₀: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁: l6(X₀, X₁, X₂, X₃) → l3(X₁, X₀, X₂, X₃)

Preprocessing

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
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) → l2(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l1(X₀, X₁, X₂, X₃) → l3(X₂, X₃, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃-1) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₀
t₃: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₀-1, X₁-1) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁: l6(X₀, X₁, X₂, X₃) → l3(X₁, X₀, X₂, X₃)

MPRF for transition t₈: l1(X₀, X₁, X₂, X₃) → l3(X₂, X₃, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l2 [X₁ ]
l3 [X₁ ]
l4 [X₁ ]
l1 [X₁ ]

MPRF for transition t₂: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l2 [X₁ ]
l3 [X₁+1 ]
l4 [X₁ ]
l1 [X₁ ]

MPRF for transition t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₀-1, X₁-1) :|: 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l2 [X₁-1 ]
l3 [X₁ ]
l4 [X₁ ]
l1 [X₁-1 ]

Analysing control-flow refined program

Found invariant 2+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___2

Found invariant 2+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___1

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___3

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₈₀: l1(X₀, X₁, X₂, X₃) → n_l2___3(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂+X₃ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ 1+X₃ ≤ X₁ ∧ X₀ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂+X₃ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₈₁: l1(X₀, X₁, X₂, X₃) → n_l2___3(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂+X₃ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1+X₃ ∧ 1+X₃ ≤ X₁ ∧ X₀ ≤ 1+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1+X₂ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂+X₃ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound 2⋅X₀ {O(n)} for transition t₈₃: n_l2___3(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁, X₂+1, X₃-1) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃+1 ∧ 1+X₃ ≤ X₁ ∧ X₀ ≤ X₂+1 ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₈₉: n_l1___2(X₀, X₁, X₂, X₃) → l3(X₂, X₃, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 2+X₃ ≤ X₁ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l4 [X₁ ]
l1 [X₀+X₃-X₂ ]
l3 [X₁ ]
n_l2___1 [X₁ ]
n_l2___3 [X₁ ]
n_l1___2 [X₁ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: X₀ {O(n)}
t₉: inf {Infinity}
t₂: X₀+1 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₀ {O(n)}
t₁₀: 1 {O(1)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: X₀ {O(n)}
t₉: inf {Infinity}
t₂: X₀+1 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₀ {O(n)}
t₁₀: 1 {O(1)}
t₁: 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: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}