Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁-5, -2⋅X₁, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant X₀ ≤ 0 for location l5

Found invariant X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁-5, -2⋅X₁, X₂, X₃) :|: 1 ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ of depth 2:

new bound:

32⋅X₂+8⋅X₃+57 {O(n)}

MPRF:

l3 [3⋅X₀+X₁-22 ; X₀+X₁-5 ]
l1 [3⋅X₀+X₁-7 ; X₀ ]

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁-5, -2⋅X₁, X₂, X₃) :|: 1 ≤ X₀ of depth 2:

new bound:

32⋅X₂+8⋅X₃+65 {O(n)}

MPRF:

l3 [3⋅X₀+X₁-7 ; 0 ]
l1 [3⋅X₀+X₁-7 ; X₀-1 ]

All Bounds

Timebounds

Overall timebound:16⋅X₃+64⋅X₂+126 {O(n)}
t₀: 1 {O(1)}
t₂: 32⋅X₂+8⋅X₃+57 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 32⋅X₂+8⋅X₃+65 {O(n)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 16⋅X₃+64⋅X₂+126 {O(n)}
t₀: 1 {O(1)}
t₂: 32⋅X₂+8⋅X₃+57 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 32⋅X₂+8⋅X₃+65 {O(n)}
t₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: 2^(32⋅X₂+8⋅X₃+65)⋅32⋅X₂⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅65⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅8⋅X₃⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅X₃+24⋅X₃+97⋅X₂+195 {O(EXP)}
t₂, X₁: 2^(32⋅X₂+8⋅X₃+65)⋅X₃ {O(EXP)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 2^(32⋅X₂+8⋅X₃+65)⋅32⋅X₂⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅65⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅8⋅X₃⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅X₃+24⋅X₃+98⋅X₂+195 {O(EXP)}
t₃, X₁: 2^(32⋅X₂+8⋅X₃+65)⋅X₃+X₃ {O(EXP)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₄, X₀: 2^(32⋅X₂+8⋅X₃+65)⋅32⋅X₂⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅65⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅8⋅X₃⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅X₃+24⋅X₃+97⋅X₂+195 {O(EXP)}
t₄, X₁: 2^(32⋅X₂+8⋅X₃+65)⋅X₃ {O(EXP)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: 2^(32⋅X₂+8⋅X₃+65)⋅32⋅X₂⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅65⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅8⋅X₃⋅X₃+2^(32⋅X₂+8⋅X₃+65)⋅X₃+24⋅X₃+98⋅X₂+195 {O(EXP)}
t₅, X₁: 2^(32⋅X₂+8⋅X₃+65)⋅X₃+X₃ {O(EXP)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}