Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ < 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₆, X₃, X₅, X₃, X₄, X₅, X₆)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀-X₁, X₂+1, X₁+1, X₃, X₄, X₅, X₆)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Eliminate variables {X₄} that do not contribute to the problem

Found invariant 1+X₀ ≤ 0 for location l5

Found invariant 1+X₀ ≤ 0 for location l4

Found invariant 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₂: l0(X₀, X₁, X₂, X₃, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₅, X₆)
t₁₃: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 ≤ X₀
t₁₄: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₅, X₆) :|: X₀ < 0
t₁₅: l2(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₆, X₃, X₅, X₃, X₅, X₆)
t₁₆: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₀-X₁, X₂+1, X₁+1, X₃, X₅, X₆) :|: 0 ≤ X₀
t₁₇: l4(X₀, X₁, X₂, X₃, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₅, X₆) :|: 1+X₀ ≤ 0

MPRF for transition t₁₃: l1(X₀, X₁, X₂, X₃, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₅, X₆) :|: 0 ≤ X₀ of depth 3:

new bound:

27⋅X₅+54⋅X₃+81⋅X₆+28 {O(n)}

MPRF:

l3 [-X₁-X₂-2 ; 2⋅X₀-2⋅X₁-X₂ ; X₀-X₁ ]
l1 [-X₁-X₂ ; 2⋅X₀+1-X₁ ; X₀ ]

MPRF for transition t₁₆: l3(X₀, X₁, X₂, X₃, X₅, X₆) → l1(X₀-X₁, X₂+1, X₁+1, X₃, X₅, X₆) :|: 0 ≤ X₀ of depth 3:

new bound:

27⋅X₅+54⋅X₃+81⋅X₆+28 {O(n)}

MPRF:

l3 [-X₁-X₂ ; 2⋅X₀+1-X₁ ; 0 ]
l1 [-X₁-X₂ ; 2⋅X₀+1-X₁ ; X₀ ]

All Bounds

Timebounds

Overall timebound:108⋅X₃+162⋅X₆+54⋅X₅+60 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 27⋅X₅+54⋅X₃+81⋅X₆+28 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 27⋅X₅+54⋅X₃+81⋅X₆+28 {O(n)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: 108⋅X₃+162⋅X₆+54⋅X₅+60 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 27⋅X₅+54⋅X₃+81⋅X₆+28 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 27⋅X₅+54⋅X₃+81⋅X₆+28 {O(n)}
t₁₇: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₂, X₆: X₆ {O(n)}
t₁₃, X₀: 13122⋅X₆⋅X₆+1485⋅X₅⋅X₅+17577⋅X₃⋅X₆+5886⋅X₃⋅X₃+5913⋅X₃⋅X₅+8829⋅X₅⋅X₆+3107⋅X₅+6185⋅X₃+9235⋅X₆+1624 {O(n^2)}
t₁₃, X₁: 109⋅X₃+162⋅X₆+55⋅X₅+56 {O(n)}
t₁₃, X₂: 109⋅X₃+162⋅X₆+55⋅X₅+56 {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₃, X₆: X₆ {O(n)}
t₁₄, X₀: 13122⋅X₆⋅X₆+1485⋅X₅⋅X₅+17577⋅X₃⋅X₆+5886⋅X₃⋅X₃+5913⋅X₃⋅X₅+8829⋅X₅⋅X₆+3107⋅X₅+6185⋅X₃+9236⋅X₆+1624 {O(n^2)}
t₁₄, X₁: 110⋅X₃+162⋅X₆+55⋅X₅+56 {O(n)}
t₁₄, X₂: 109⋅X₃+162⋅X₆+56⋅X₅+56 {O(n)}
t₁₄, X₃: 2⋅X₃ {O(n)}
t₁₄, X₅: 2⋅X₅ {O(n)}
t₁₄, X₆: 2⋅X₆ {O(n)}
t₁₅, X₀: X₆ {O(n)}
t₁₅, X₁: X₃ {O(n)}
t₁₅, X₂: X₅ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₆: X₆ {O(n)}
t₁₆, X₀: 13122⋅X₆⋅X₆+1485⋅X₅⋅X₅+17577⋅X₃⋅X₆+5886⋅X₃⋅X₃+5913⋅X₃⋅X₅+8829⋅X₅⋅X₆+3107⋅X₅+6185⋅X₃+9235⋅X₆+1624 {O(n^2)}
t₁₆, X₁: 109⋅X₃+162⋅X₆+55⋅X₅+56 {O(n)}
t₁₆, X₂: 109⋅X₃+162⋅X₆+55⋅X₅+56 {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₅: X₅ {O(n)}
t₁₆, X₆: X₆ {O(n)}
t₁₇, X₀: 13122⋅X₆⋅X₆+1485⋅X₅⋅X₅+17577⋅X₃⋅X₆+5886⋅X₃⋅X₃+5913⋅X₃⋅X₅+8829⋅X₅⋅X₆+3107⋅X₅+6185⋅X₃+9236⋅X₆+1624 {O(n^2)}
t₁₇, X₁: 110⋅X₃+162⋅X₆+55⋅X₅+56 {O(n)}
t₁₇, X₂: 109⋅X₃+162⋅X₆+56⋅X₅+56 {O(n)}
t₁₇, X₃: 2⋅X₃ {O(n)}
t₁₇, X₅: 2⋅X₅ {O(n)}
t₁₇, X₆: 2⋅X₆ {O(n)}