Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁₁: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₃, X₂-1, X₃) :|: 2 ≤ X₂
t₁₂: l1(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1
t₃: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0
t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E
t₅: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, 0) :|: X₀ ≤ X₁+1
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁+1) :|: X₁+2 ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, 0)
t₉: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁-1) :|: 2 ≤ X₁
t₈: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1
t₁₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₁: l7(X₀, X₁, X₂, X₃) → l2(X₀, 0, X₀, X₃) :|: 1 ≤ X₀
t₂: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0

Preprocessing

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

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5

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

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁₁: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₃, X₂-1, X₃) :|: 2 ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₂: l1(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ X₃ ≤ 1+X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, 0) :|: X₀ ≤ X₁+1 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁+1) :|: X₁+2 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, 0) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁-1) :|: 2 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₁: l7(X₀, X₁, X₂, X₃) → l2(X₀, 0, X₀, X₃) :|: 1 ≤ X₀
t₂: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0

MPRF for transition t₁₁: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₃, X₂-1, X₃) :|: 2 ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+1 {O(n)}

MPRF:

l2 [X₁+2⋅X₂+1 ]
l3 [X₁+2⋅X₂+1 ]
l4 [2⋅X₂ ]
l5 [X₁+2⋅X₂ ]
l1 [2⋅X₂+X₃ ]

MPRF for transition t₃: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: E+1 ≤ 0 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+1 {O(n)}

MPRF:

l2 [X₁+2⋅X₂-1 ]
l3 [X₁+2⋅X₂-2 ]
l4 [2⋅X₂-1 ]
l5 [X₁+2⋅X₂-1 ]
l1 [2⋅X₂+X₃-3 ]

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀+1 {O(n)}

MPRF:

l2 [X₁+2⋅X₂-1 ]
l3 [X₁+2⋅X₂-2 ]
l4 [2⋅X₂-1 ]
l5 [X₁+2⋅X₂-1 ]
l1 [2⋅X₂+X₃-3 ]

MPRF for transition t₅: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l2 [X₂ ]
l3 [X₂-1 ]
l4 [X₂-1 ]
l5 [X₂-1 ]
l1 [X₂-1 ]

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, 0) :|: X₀ ≤ X₁+1 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l2 [X₂ ]
l3 [X₂ ]
l4 [X₂ ]
l5 [X₂ ]
l1 [X₂-1 ]

MPRF for transition t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁+1) :|: X₁+2 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l2 [X₂ ]
l3 [X₂ ]
l4 [X₂ ]
l5 [X₂ ]
l1 [X₂-1 ]

MPRF for transition t₁₀: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, 0) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ 1 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l2 [X₂+1 ]
l3 [X₂ ]
l4 [X₂+1 ]
l5 [X₂+1 ]
l1 [X₂ ]

MPRF for transition t₈: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1 ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l2 [X₂ ]
l3 [X₂ ]
l4 [X₂-1 ]
l5 [X₂ ]
l1 [X₂-1 ]

MPRF for transition t₉: l5(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₁-1) :|: 2 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀ {O(n)}

MPRF:

l2 [X₀+X₁+X₂ ]
l3 [X₀+X₁+X₂ ]
l4 [X₀+X₂ ]
l5 [X₀+X₁+X₂ ]
l1 [X₀+X₂+X₃-1 ]

All Bounds

Timebounds

Overall timebound:13⋅X₀+9 {O(n)}
t₀: 1 {O(1)}
t₁₁: 2⋅X₀+1 {O(n)}
t₁₂: 1 {O(1)}
t₃: 2⋅X₀+1 {O(n)}
t₄: 2⋅X₀+1 {O(n)}
t₅: X₀ {O(n)}
t₆: X₀ {O(n)}
t₇: X₀ {O(n)}
t₁₀: X₀+1 {O(n)}
t₈: X₀ {O(n)}
t₉: 2⋅X₀ {O(n)}
t₁₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: 13⋅X₀+9 {O(n)}
t₀: 1 {O(1)}
t₁₁: 2⋅X₀+1 {O(n)}
t₁₂: 1 {O(1)}
t₃: 2⋅X₀+1 {O(n)}
t₄: 2⋅X₀+1 {O(n)}
t₅: X₀ {O(n)}
t₆: X₀ {O(n)}
t₇: X₀ {O(n)}
t₁₀: X₀+1 {O(n)}
t₈: X₀ {O(n)}
t₉: 2⋅X₀ {O(n)}
t₁₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁₁, X₀: 3⋅X₀ {O(n)}
t₁₁, X₁: 2⋅X₀+2 {O(n)}
t₁₁, X₂: 3⋅X₀ {O(n)}
t₁₁, X₃: 6⋅X₀+8 {O(n)}
t₁₂, X₀: 12⋅X₀ {O(n)}
t₁₂, X₁: 6⋅X₀+7 {O(n)}
t₁₂, X₂: 1 {O(1)}
t₁₂, X₃: 6⋅X₀+8 {O(n)}
t₃, X₀: 3⋅X₀ {O(n)}
t₃, X₁: 2⋅X₀+2 {O(n)}
t₃, X₂: 3⋅X₀ {O(n)}
t₃, X₃: 6⋅X₀+X₃+8 {O(n)}
t₄, X₀: 3⋅X₀ {O(n)}
t₄, X₁: 2⋅X₀+2 {O(n)}
t₄, X₂: 3⋅X₀ {O(n)}
t₄, X₃: 6⋅X₀+X₃+8 {O(n)}
t₅, X₀: 3⋅X₀ {O(n)}
t₅, X₁: 2⋅X₀+2 {O(n)}
t₅, X₂: 3⋅X₀ {O(n)}
t₅, X₃: 6⋅X₀+X₃+8 {O(n)}
t₆, X₀: 3⋅X₀ {O(n)}
t₆, X₁: 2⋅X₀+2 {O(n)}
t₆, X₂: 3⋅X₀ {O(n)}
t₆, X₃: 0 {O(1)}
t₇, X₀: 3⋅X₀ {O(n)}
t₇, X₁: 2⋅X₀+2 {O(n)}
t₇, X₂: 3⋅X₀ {O(n)}
t₇, X₃: 4⋅X₀+6 {O(n)}
t₁₀, X₀: 3⋅X₀ {O(n)}
t₁₀, X₁: 1 {O(1)}
t₁₀, X₂: 3⋅X₀ {O(n)}
t₁₀, X₃: 0 {O(1)}
t₈, X₀: 3⋅X₀ {O(n)}
t₈, X₁: 1 {O(1)}
t₈, X₂: 3⋅X₀ {O(n)}
t₈, X₃: 6⋅X₀+X₃+8 {O(n)}
t₉, X₀: 3⋅X₀ {O(n)}
t₉, X₁: 2⋅X₀+2 {O(n)}
t₉, X₂: 3⋅X₀ {O(n)}
t₉, X₃: 2⋅X₀+2 {O(n)}
t₁₃, X₀: 13⋅X₀ {O(n)}
t₁₃, X₁: 6⋅X₀+X₁+7 {O(n)}
t₁₃, X₂: X₂+1 {O(n)}
t₁₃, X₃: 6⋅X₀+X₃+8 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 0 {O(1)}
t₁, X₂: X₀ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}