Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ X₀ < X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁-X₀-5, 2⋅X₁, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ X₀ < X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁-X₀-5, 2⋅X₁, X₂, X₃, X₄) :|: 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ X₀ < X₂ of depth 2:

new bound:

16⋅X₂+16⋅X₃+8⋅X₄+41 {O(n)}

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁-X₀-5, 2⋅X₁, X₂, X₃, X₄) :|: 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 2:

new bound:

16⋅X₃+24⋅X₂+8⋅X₄+33 {O(n)}

All Bounds

Timebounds

Overall timebound:16⋅X₄+32⋅X₃+40⋅X₂+79 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 16⋅X₂+16⋅X₃+8⋅X₄+41 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 16⋅X₃+24⋅X₂+8⋅X₄+33 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 16⋅X₄+32⋅X₃+40⋅X₂+79 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 16⋅X₂+16⋅X₃+8⋅X₄+41 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 16⋅X₃+24⋅X₂+8⋅X₄+33 {O(n)}
t₆: 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)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: 16⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₃⋅X₄+24⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₂⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅33⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅8⋅X₄⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄+120⋅X₂+40⋅X₄+81⋅X₃+165 {O(EXP)}
t₂, X₁: 2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄ {O(EXP)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 16⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₃⋅X₄+24⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₂⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅33⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅8⋅X₄⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄+120⋅X₂+40⋅X₄+82⋅X₃+165 {O(EXP)}
t₃, X₁: 2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄+X₄ {O(EXP)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: 16⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₃⋅X₄+24⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₂⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅33⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅8⋅X₄⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄+120⋅X₂+40⋅X₄+82⋅X₃+165 {O(EXP)}
t₄, X₁: 2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄+X₄ {O(EXP)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₅, X₀: 16⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₃⋅X₄+24⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₂⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅33⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅8⋅X₄⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄+120⋅X₂+40⋅X₄+81⋅X₃+165 {O(EXP)}
t₅, X₁: 2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄ {O(EXP)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: 16⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄⋅X₄+2⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅32⋅X₃⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅48⋅X₂⋅X₄+2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅66⋅X₄+164⋅X₃+240⋅X₂+80⋅X₄+330 {O(EXP)}
t₆, X₁: 2⋅2^(16⋅X₃+24⋅X₂+8⋅X₄+33)⋅X₄+2⋅X₄ {O(EXP)}
t₆, X₂: 4⋅X₂ {O(n)}
t₆, X₃: 4⋅X₃ {O(n)}
t₆, X₄: 4⋅X₄ {O(n)}