Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₁: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, 0, X₄) :|: X₄ ≤ X₂+1
t₁₂: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₂+1, X₄) :|: X₂+1 < X₄
t₁₃: l11(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, 0, X₄) :|: X₂+X₄ ≤ 1
t₁₄: l11(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₂-1, X₄) :|: 1 < X₄+X₂
t₁₅: l12(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁-1, X₃, X₃, X₄) :|: 1 < X₁
t₁₆: l12(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 1
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₄, 0, X₃, X₄) :|: 1 ≤ X₄
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 1
t₇: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₁₇: l7(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄)
t₉: l8(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀
t₁₀: l8(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₈: l9(X₀, X₁, X₂, X₃, X₄) → l8(nondef_0, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l11

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ for location l6

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ for location l12

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

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l10

Found invariant 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₁: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, 0, X₄) :|: X₄ ≤ X₂+1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₂: l10(X₀, X₁, X₂, X₃, X₄) → l12(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 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₃: l11(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, 0, X₄) :|: X₂+X₄ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₄: l11(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₂-1, X₄) :|: 1 < X₄+X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0
t₁₅: l12(X₀, X₁, X₂, X₃, X₄) → l6(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 ∧ 1 ≤ X₁
t₁₆: l12(X₀, X₁, X₂, X₃, X₄) → l7(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 ∧ 1 ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₄, 0, X₃, X₄) :|: 1 ≤ X₄
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₄ < 1
t₇: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁
t₁₇: l7(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄)
t₉: l8(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁
t₁₀: l8(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁
t₈: l9(X₀, X₁, X₂, X₃, X₄) → l8(nondef_0, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁

MPRF for transition t₁₁: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, 0, X₄) :|: X₄ ≤ X₂+1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l12 [X₁-1 ]
l6 [X₁ ]
l10 [X₁ ]
l11 [X₁ ]
l9 [X₁ ]
l8 [X₁ ]

MPRF for transition t₁₂: l10(X₀, X₁, X₂, X₃, X₄) → l12(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 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l12 [X₁-1 ]
l6 [X₁ ]
l10 [X₁ ]
l11 [X₁ ]
l9 [X₁ ]
l8 [X₁ ]

MPRF for transition t₁₃: l11(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, 0, X₄) :|: X₂+X₄ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

2⋅X₄+1 {O(n)}

MPRF:

l12 [X₁+X₄-2 ]
l6 [X₁+X₄-1 ]
l10 [X₁+X₄-1 ]
l11 [X₁+X₄-1 ]
l9 [X₁+X₄-1 ]
l8 [X₁+X₄-1 ]

MPRF for transition t₁₄: l11(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₂-1, X₄) :|: 1 < X₄+X₂ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l12 [X₁-1 ]
l6 [X₁ ]
l10 [X₁ ]
l11 [X₁ ]
l9 [X₁ ]
l8 [X₁ ]

MPRF for transition t₁₅: l12(X₀, X₁, X₂, X₃, X₄) → l6(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 ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l12 [X₁ ]
l6 [X₁ ]
l10 [X₁ ]
l11 [X₁ ]
l9 [X₁ ]
l8 [X₁ ]

MPRF for transition t₇: l6(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₄+2 {O(n)}

MPRF:

l12 [X₁+X₄+1 ]
l6 [X₁+X₄+2 ]
l10 [X₁+X₄+1 ]
l11 [X₁+X₄+1 ]
l9 [X₁+X₄+1 ]
l8 [X₁+X₄+1 ]

MPRF for transition t₉: l8(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l12 [X₁ ]
l6 [X₁+1 ]
l10 [X₁ ]
l11 [X₁ ]
l9 [X₁+1 ]
l8 [X₁+1 ]

MPRF for transition t₁₀: l8(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l12 [X₁ ]
l6 [X₁+1 ]
l10 [X₁ ]
l11 [X₁ ]
l9 [X₁+1 ]
l8 [X₁+1 ]

MPRF for transition t₈: l9(X₀, X₁, X₂, X₃, X₄) → l8(nondef_0, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄+2 {O(n)}

MPRF:

l12 [X₁+1 ]
l6 [X₁+2 ]
l10 [X₁+1 ]
l11 [X₁+1 ]
l9 [X₁+2 ]
l8 [X₁+1 ]

All Bounds

Timebounds

Overall timebound:11⋅X₄+16 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: X₄ {O(n)}
t₁₂: X₄ {O(n)}
t₁₃: 2⋅X₄+1 {O(n)}
t₁₄: X₄ {O(n)}
t₁₅: X₄ {O(n)}
t₁₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 2⋅X₄+2 {O(n)}
t₁₇: 1 {O(1)}
t₉: X₄+1 {O(n)}
t₁₀: X₄+1 {O(n)}
t₈: X₄+2 {O(n)}

Costbounds

Overall costbound: 11⋅X₄+16 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: X₄ {O(n)}
t₁₂: X₄ {O(n)}
t₁₃: 2⋅X₄+1 {O(n)}
t₁₄: X₄ {O(n)}
t₁₅: X₄ {O(n)}
t₁₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 2⋅X₄+2 {O(n)}
t₁₇: 1 {O(1)}
t₉: X₄+1 {O(n)}
t₁₀: X₄+1 {O(n)}
t₈: X₄+2 {O(n)}

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)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₁₁, X₁: X₄ {O(n)}
t₁₁, X₂: 2⋅X₄ {O(n)}
t₁₁, X₃: 0 {O(1)}
t₁₁, X₄: X₄ {O(n)}
t₁₂, X₁: X₄ {O(n)}
t₁₂, X₂: 2⋅X₄ {O(n)}
t₁₂, X₃: 2⋅X₄ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₃, X₁: X₄ {O(n)}
t₁₃, X₂: 2⋅X₄ {O(n)}
t₁₃, X₃: 0 {O(1)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₁: X₄ {O(n)}
t₁₄, X₂: 2⋅X₄ {O(n)}
t₁₄, X₃: 2⋅X₄ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₁: X₄ {O(n)}
t₁₅, X₂: 2⋅X₄ {O(n)}
t₁₅, X₃: 4⋅X₄ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₆, X₁: 1 {O(1)}
t₁₆, X₂: 8⋅X₄ {O(n)}
t₁₆, X₃: 4⋅X₄ {O(n)}
t₁₆, X₄: 4⋅X₄ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
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)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₄ {O(n)}
t₅, X₂: 0 {O(1)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₁: X₄ {O(n)}
t₇, X₂: 2⋅X₄ {O(n)}
t₇, X₃: 4⋅X₄+X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₁₇, X₁: X₁+1 {O(n)}
t₁₇, X₂: 8⋅X₄+X₂ {O(n)}
t₁₇, X₃: 4⋅X₄+X₃ {O(n)}
t₁₇, X₄: 5⋅X₄ {O(n)}
t₉, X₁: X₄ {O(n)}
t₉, X₂: 2⋅X₄ {O(n)}
t₉, X₃: 4⋅X₄+X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₁: X₄ {O(n)}
t₁₀, X₂: 2⋅X₄ {O(n)}
t₁₀, X₃: 4⋅X₄+X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₈, X₁: X₄ {O(n)}
t₈, X₂: 2⋅X₄ {O(n)}
t₈, X₃: 4⋅X₄+X₃ {O(n)}
t₈, X₄: X₄ {O(n)}