Initial Problem

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

Preprocessing

Found invariant 0 ≤ X₄ for location l2

Found invariant 0 ≤ X₄ for location l4

Found invariant X₄ ≤ 0 for location l3

Problem after Preprocessing

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

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄-1) :|: 0 < X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF for transition t₂: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₀+X₁, X₁, X₄) :|: 0 ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF for transition t₃: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₁, X₀+X₁, X₄) :|: 0 ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF for transition t₄: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₂+X₃, X₁, X₂, X₃, X₄) :|: 0 ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀ ∧ X₄ ≤ 0 of depth 1:

new bound:

2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₀+1 {O(EXP)}

Analysing control-flow refined program

Found invariant 0 ≤ X₄ for location l2

Found invariant 0 ≤ X₄ for location l4

Found invariant X₄ ≤ 0 ∧ X₄ ≤ 1+X₀ ∧ 0 ≤ 1+X₀ for location n_l3___1

Found invariant X₄ ≤ 0 for location l3

MPRF for transition t₄₃: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l3___1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 1+X₀ ∧ 0 ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ 0 ∧ X₄ ≤ 0 ∧ X₄ ≤ 0 ∧ X₄ ≤ 0 ∧ X₄ ≤ 1+X₀ ∧ 0 ≤ 1+X₀ of depth 1:

new bound:

2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₀+2 {O(EXP)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+4⋅X₄+X₀+3 {O(EXP)}
t₀: 1 {O(1)}
t₁: X₄ {O(n)}
t₂: X₄ {O(n)}
t₃: X₄ {O(n)}
t₄: X₄ {O(n)}
t₅: 1 {O(1)}
t₆: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₀+1 {O(EXP)}

Costbounds

Overall costbound: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+4⋅X₄+X₀+3 {O(EXP)}
t₀: 1 {O(1)}
t₁: X₄ {O(n)}
t₂: X₄ {O(n)}
t₃: X₄ {O(n)}
t₄: X₄ {O(n)}
t₅: 1 {O(1)}
t₆: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₀+1 {O(EXP)}

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: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀ {O(EXP)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₁+X₂ {O(EXP)}
t₁, X₃: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₁+X₃ {O(EXP)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀ {O(EXP)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀ {O(EXP)}
t₂, X₃: X₁ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀ {O(EXP)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₁ {O(n)}
t₃, X₃: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀ {O(EXP)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀ {O(EXP)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₁ {O(EXP)}
t₄, X₃: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₁ {O(EXP)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₀ {O(EXP)}
t₅, X₁: 2⋅X₁ {O(n)}
t₅, X₂: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₁+X₂ {O(EXP)}
t₅, X₃: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₁+X₃ {O(EXP)}
t₅, X₄: 2⋅X₄ {O(n)}
t₆, X₀: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₀+1 {O(EXP)}
t₆, X₁: 2⋅X₁ {O(n)}
t₆, X₂: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₁+X₂ {O(EXP)}
t₆, X₃: 2⋅2^(X₄)⋅X₁⋅X₄+2^(X₄)⋅3⋅X₁+2^(X₄)⋅X₀+X₁+X₃ {O(EXP)}
t₆, X₄: 2⋅X₄ {O(n)}