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)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₀, X₄, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ X₃ ≤ 5
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ 0 < X₃
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, -2⋅X₁, 3⋅X₂-2⋅(X₃)³, X₃, X₄) :|: (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, -2⋅X₁, 3⋅X₂-2⋅(X₃)³, X₃, X₄) :|: (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁-1, X₂, X₃, X₄) :|: 0 < X₁

Preprocessing

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 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
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₀, X₄, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ X₃ ≤ 5
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ 0 < X₃
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, -2⋅X₁, 3⋅X₂-2⋅(X₃)³, X₃, X₄) :|: (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0 ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, -2⋅X₁, 3⋅X₂-2⋅(X₃)³, X₃, X₄) :|: (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁-1, X₂, X₃, X₄) :|: 0 < X₁

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ 0 < X₃ of depth 1:

new bound:

X₀ {O(n)}

l2 [X₀ ]
l3 [X₀-1 ]
l1 [X₀ ]

MPRF for transition t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

l2 [X₁ ]
l3 [X₀-1 ]
l1 [X₀ ]

MPRF for transition t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

l2 [X₁ ]
l3 [X₀ ]
l1 [X₀ ]

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant X₃ ≤ 5 ∧ X₃ ≤ 4+X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ for location l3

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₄ 96⋅X₀⋅X₄+27042⋅X₀ {O(n^2)}

TWN-Loops:

Termination: true
Formula:

relevant size-bounds w.r.t. t₃:
X₂: 3⋅X₄ {O(n)}
X₃: 5 {O(1)}
Runtime-bound of t₃: X₀ {O(n)}
Results in: 48⋅X₀⋅X₄+27021⋅X₀ {O(n^2)}

Termination: true
Formula:

relevant size-bounds w.r.t. t₁:
X₂: 3⋅X₄ {O(n)}
Runtime-bound of t₁: X₀ {O(n)}
Results in: 48⋅X₀⋅X₄+21⋅X₀ {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₅ 96⋅X₀⋅X₄+27042⋅X₀ {O(n^2)}

relevant size-bounds w.r.t. t₃:
X₂: 3⋅X₄ {O(n)}
X₃: 5 {O(1)}
Runtime-bound of t₃: X₀ {O(n)}
Results in: 48⋅X₀⋅X₄+27021⋅X₀ {O(n^2)}

relevant size-bounds w.r.t. t₁:
X₂: 3⋅X₄ {O(n)}
Runtime-bound of t₁: X₀ {O(n)}
Results in: 48⋅X₀⋅X₄+21⋅X₀ {O(n^2)}

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₀, X₄, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ X₃ ≤ 5

Analysing control-flow refined program

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant 0 ≤ 5+X₃ ∧ X₁ ≤ 3+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l3___2

Found invariant 0 ≤ 5+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

knowledge_propagation leads to new time bound 2⋅X₀ {O(n)} for transition t₁₄₄: l3(X₀, X₁, X₂, X₃, X₄) → n_l3___2(Arg0_P, -2⋅X₁, NoDet0, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 < X₁ ∧ 0 ≤ 5+X₃ ∧ 0 < X₁ ∧ 1 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₅₁: n_l3___1(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

l2 [X₁ ]
l3 [X₀ ]
n_l3___1 [X₀ ]
n_l3___2 [X₀ ]
l1 [X₀ ]

MPRF for transition t₁₅₂: n_l3___2(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ 3+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

l2 [X₀ ]
l3 [X₁ ]
n_l3___1 [X₀ ]
n_l3___2 [X₀ ]
l1 [X₀ ]

CFR did not improve the program. Rolling back

MPRF for transition t₈: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁-1, X₂, X₃, X₄) :|: 0 < X₁ of depth 1:

new bound:

10⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅X₀+5⋅X₀+X₁ {O(EXP)}

l4 [X₁ ]

Analysing control-flow refined program

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₄₀₄: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁-1, X₂, X₃, X₄) :|: 0 < X₁ of depth 1:

new bound:

10⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅X₀+5⋅X₀+X₁ {O(EXP)}

l4 [X₁ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:10⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅X₀+192⋅X₀⋅X₄+54093⋅X₀+X₁+3 {O(EXP)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀+1 {O(n)}
t₇: 1 {O(1)}
t₃: X₀ {O(n)}
t₄: 96⋅X₀⋅X₄+27042⋅X₀ {O(n^2)}
t₅: 96⋅X₀⋅X₄+27042⋅X₀ {O(n^2)}
t₆: X₀ {O(n)}
t₈: 10⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅X₀+5⋅X₀+X₁ {O(EXP)}

Costbounds

Overall costbound: 10⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅X₀+192⋅X₀⋅X₄+54093⋅X₀+X₁+3 {O(EXP)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀+1 {O(n)}
t₇: 1 {O(1)}
t₃: X₀ {O(n)}
t₄: 96⋅X₀⋅X₄+27042⋅X₀ {O(n^2)}
t₅: 96⋅X₀⋅X₄+27042⋅X₀ {O(n^2)}
t₆: X₀ {O(n)}
t₈: 10⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅X₀+5⋅X₀+X₁ {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⋅X₀ {O(n)}
t₁, X₁: 3⋅X₀ {O(n)}
t₁, X₂: 3⋅X₄ {O(n)}
t₁, X₃: X₃+10 {O(n)}
t₁, X₄: 2⋅X₄ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 3⋅X₀ {O(n)}
t₂, X₂: 3⋅X₄ {O(n)}
t₂, X₃: 5 {O(1)}
t₂, X₄: 2⋅X₄ {O(n)}
t₇, X₀: 3⋅X₀ {O(n)}
t₇, X₁: 10⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅X₀+5⋅X₀+X₁ {O(EXP)}
t₇, X₃: 2⋅X₃+10 {O(n)}
t₇, X₄: 3⋅X₄ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₀ {O(n)}
t₃, X₂: 3⋅X₄ {O(n)}
t₃, X₃: 5 {O(1)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: 2⋅X₀ {O(n)}
t₄, X₁: 2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅5⋅X₀ {O(EXP)}
t₄, X₃: X₃+10 {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅5⋅X₀ {O(EXP)}
t₅, X₃: X₃+10 {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₆, X₀: 2⋅X₀ {O(n)}
t₆, X₁: 10⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅X₀+5⋅X₀ {O(EXP)}
t₆, X₃: X₃+10 {O(n)}
t₆, X₄: 2⋅X₄ {O(n)}
t₈, X₀: 3⋅X₀ {O(n)}
t₈, X₁: 10⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅2^(96⋅X₀⋅X₄+27042⋅X₀)⋅X₀+5⋅X₀+X₁ {O(EXP)}
t₈, X₃: 2⋅X₃+10 {O(n)}
t₈, X₄: 3⋅X₄ {O(n)}