Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀-1, 3⋅X₁+X₂, -6⋅X₁-2⋅X₂, X₃+2⋅(X₀)²) :|: 0 < X₀
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁-1, X₂, X₃-1) :|: 0 < X₁+X₃

Preprocessing

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀-1, 3⋅X₁+X₂, -6⋅X₁-2⋅X₂, X₃+2⋅(X₀)²) :|: 0 < X₀
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃) → l2(X₀, X₁-1, X₂, X₃-1) :|: 0 < X₁+X₃ ∧ X₀ ≤ 0

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀-1, 3⋅X₁+X₂, -6⋅X₁-2⋅X₂, X₃+2⋅Temp_Int₉₀) :|: 0 < X₀ ∧ 0 < Temp_Int₉₀ ∧ X₀ ≤ Temp_Int₉₀ of depth 1:

new bound:

X₀ {O(n)}

Analysing control-flow refined program

Found invariant X₀ ≤ 0 for location l2

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: 1 {O(1)}
t₃: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 12^(X₀)⋅X₁+12^(X₀)⋅X₂ {O(EXP)}
t₁, X₂: 12^(X₀)⋅X₁+12^(X₀)⋅X₂ {O(EXP)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 12^(X₀)⋅X₁+12^(X₀)⋅X₂+X₁ {O(EXP)}
t₂, X₂: 12^(X₀)⋅X₁+12^(X₀)⋅X₂+X₂ {O(EXP)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₂: 12^(X₀)⋅X₁+12^(X₀)⋅X₂+X₂ {O(EXP)}