Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(nondef.0, X₁, X₂, X₃, X₄)
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₄ ≤ X₂+1
t₉: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂+1, X₄) :|: X₂+1 < X₄
t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₂ ≤ 1
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂-1, X₄) :|: 1 < X₂
t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₄, 0, X₃, X₄) :|: 1 ≤ X₄
t₂: l7(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 1
t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁-1, X₃, X₃, X₄) :|: 1 < X₁
t₁₃: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1

Preprocessing

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l2

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l5

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l8

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l1

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(nondef.0, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₄ ≤ X₂+1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂+1, X₄) :|: X₂+1 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂-1, X₄) :|: 1 < X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₄, 0, X₃, X₄) :|: 1 ≤ X₄
t₂: l7(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 1
t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁-1, X₃, X₃, X₄) :|: 1 < X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₃: l8(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁

MPRF for transition t₆: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l4 [X₁-1 ]
l5 [X₁ ]
l8 [X₁-1 ]
l2 [X₁ ]

MPRF for transition t₇: l1(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l3 [X₁+1 ]
l1 [X₁+1 ]
l4 [X₁ ]
l5 [X₁ ]
l8 [X₁ ]
l2 [X₁+1 ]

MPRF for transition t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l4 [X₁ ]
l5 [X₁ ]
l8 [X₁ ]
l2 [X₁+1 ]

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(nondef.0, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁-1 ]
l4 [X₁-1 ]
l5 [X₁-1 ]
l8 [X₁-1 ]
l2 [X₁ ]

MPRF for transition t₈: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₄ ≤ X₂+1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₄ {O(n)}

MPRF:

l3 [X₁+X₄ ]
l1 [X₁+X₄ ]
l4 [X₁+X₄ ]
l5 [X₁+X₄ ]
l8 [X₁+X₄-1 ]
l2 [X₁+X₄ ]

MPRF for transition t₉: l4(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂+1, X₄) :|: X₂+1 < X₄ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l4 [X₁ ]
l5 [X₁-1 ]
l8 [X₁-1 ]
l2 [X₁ ]

MPRF for transition t₁₀: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, 0, X₄) :|: X₂ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l4 [X₁-1 ]
l5 [X₁ ]
l8 [X₁-1 ]
l2 [X₁ ]

MPRF for transition t₁₁: l5(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₂-1, X₄) :|: 1 < X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l4 [X₁ ]
l5 [X₁ ]
l8 [X₁-1 ]
l2 [X₁ ]

MPRF for transition t₁₂: l8(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁-1, X₃, X₃, X₄) :|: 1 < X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]
l4 [X₁ ]
l5 [X₁ ]
l8 [X₁ ]
l2 [X₁ ]

All Bounds

Timebounds

Overall timebound:10⋅X₄+7 {O(n)}
t₀: 1 {O(1)}
t₆: X₄ {O(n)}
t₇: X₄+1 {O(n)}
t₃: X₄+1 {O(n)}
t₅: X₄ {O(n)}
t₈: 2⋅X₄ {O(n)}
t₉: X₄ {O(n)}
t₁₀: X₄ {O(n)}
t₁₁: X₄ {O(n)}
t₁₄: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₁₂: X₄ {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 10⋅X₄+7 {O(n)}
t₀: 1 {O(1)}
t₆: X₄ {O(n)}
t₇: X₄+1 {O(n)}
t₃: X₄+1 {O(n)}
t₅: X₄ {O(n)}
t₈: 2⋅X₄ {O(n)}
t₉: X₄ {O(n)}
t₁₀: X₄ {O(n)}
t₁₁: X₄ {O(n)}
t₁₄: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₁₂: X₄ {O(n)}
t₁₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₆, X₁: X₄ {O(n)}
t₆, X₂: X₄+1 {O(n)}
t₆, X₃: 2⋅X₄+X₃+3 {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₁: X₄ {O(n)}
t₇, X₂: X₄+1 {O(n)}
t₇, X₃: 2⋅X₄+X₃+3 {O(n)}
t₇, X₄: X₄ {O(n)}
t₃, X₁: X₄ {O(n)}
t₃, X₂: X₄+1 {O(n)}
t₃, X₃: 2⋅X₄+X₃+3 {O(n)}
t₃, X₄: X₄ {O(n)}
t₅, X₁: X₄ {O(n)}
t₅, X₂: X₄+1 {O(n)}
t₅, X₃: 2⋅X₄+X₃+3 {O(n)}
t₅, X₄: X₄ {O(n)}
t₈, X₁: X₄ {O(n)}
t₈, X₂: X₄+1 {O(n)}
t₈, X₃: 0 {O(1)}
t₈, X₄: X₄ {O(n)}
t₉, X₁: X₄ {O(n)}
t₉, X₂: X₄+1 {O(n)}
t₉, X₃: X₄+2 {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₁: X₄ {O(n)}
t₁₀, X₂: 1 {O(1)}
t₁₀, X₃: 0 {O(1)}
t₁₀, X₄: X₄ {O(n)}
t₁₁, X₁: X₄ {O(n)}
t₁₁, X₂: X₄+1 {O(n)}
t₁₁, X₃: X₄+1 {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₄, X₁: X₁+1 {O(n)}
t₁₄, X₂: 3⋅X₄+X₂+4 {O(n)}
t₁₄, X₃: 2⋅X₄+X₃+3 {O(n)}
t₁₄, X₄: 5⋅X₄ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: 0 {O(1)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₁₂, X₁: X₄ {O(n)}
t₁₂, X₂: X₄+1 {O(n)}
t₁₂, X₃: 2⋅X₄+3 {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₃, X₁: 1 {O(1)}
t₁₃, X₂: 3⋅X₄+4 {O(n)}
t₁₃, X₃: 2⋅X₄+3 {O(n)}
t₁₃, X₄: 4⋅X₄ {O(n)}