Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3
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
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
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
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
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
TWN. Size Bound: t₄: l3→l3 for X₂
cycle: [t₄: l3→l3; t₅: l3→l3]
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0 ∨ (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁,(X₀,X₁,X₂,X₃,X₄) -> (X₀,-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃,X₄)
order: [X₀; X₁; X₃; X₂; X₄]
closed-form:
X₀: X₀
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³
X₄: X₄
Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0 ∨ (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁,(X₂,X₃) -> (3⋅X₂-2⋅(X₃)³,X₃)
closed-form: X₂ * 3^n + [[n != 0]] * -(X₃)³ * 3^n + [[n != 0]] * (X₃)³
runtime bound: 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}
TWN Size Bound - Lifting for t₄: l3→l3 and X₂: 125⋅3^(32⋅X₄+27021)+125⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)+15⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₃⋅X₃+2⋅3^(32⋅X₄+27021)⋅X₄+2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₄+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅75⋅X₃+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₃⋅X₃⋅X₃+X₃⋅X₃⋅X₃+15⋅X₃⋅X₃+75⋅X₃+250 {O(EXP)}
TWN. Size Bound: t₅: l3→l3 for X₂
cycle: [t₄: l3→l3; t₅: l3→l3]
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0 ∨ (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁,(X₀,X₁,X₂,X₃,X₄) -> (X₀,-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃,X₄)
order: [X₀; X₁; X₃; X₂; X₄]
closed-form:
X₀: X₀
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³
X₄: X₄
Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0 ∨ (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁,(X₂,X₃) -> (3⋅X₂-2⋅(X₃)³,X₃)
closed-form: X₂ * 3^n + [[n != 0]] * -(X₃)³ * 3^n + [[n != 0]] * (X₃)³
runtime bound: 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}
TWN Size Bound - Lifting for t₅: l3→l3 and X₂: 125⋅3^(32⋅X₄+27021)+125⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)+15⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₃⋅X₃+2⋅3^(32⋅X₄+27021)⋅X₄+2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₄+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅75⋅X₃+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₃⋅X₃⋅X₃+X₃⋅X₃⋅X₃+15⋅X₃⋅X₃+75⋅X₃+250 {O(EXP)}
Solv. Size Bound: t₆: l3→l1 for X₁
Solv. Size Bound: t₆: l3→l1 for X₂
cycle: [t₆: l3→l1; t₂: l1→l2; t₃: l2→l3]
loop: (0 ≤ 5+X₃ ∧ X₃ ≤ 5 ∧ 1 < X₀,(X₂,X₄) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₀+1 {O(n)}
Solv. Size Bound - Lifting for t₆: l3→l1 and X₂: 8⋅X₄ {O(n)}
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)}
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)}
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)}
TWN: t₄: l3→l3
cycle: [t₄: l3→l3; t₅: l3→l3]
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0 ∨ (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁,(X₁,X₂,X₃) -> (-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃)
order: [X₁; X₃; X₂]
closed-form:
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³
Termination: true
Formula:
0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0 ∨ (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁,(X₁,X₂,X₃) -> (-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃)
order: [X₁; X₃; X₂]
closed-form:
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³
Termination: true
Formula:
0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}
TWN - Lifting for t₄: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₃:
X₂: 2⋅X₄ {O(n)}
X₃: 5 {O(1)}
Runtime-bound of t₃: X₀ {O(n)}
Results in: 32⋅X₀⋅X₄+27021⋅X₀ {O(n^2)}
TWN - Lifting for t₄: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₁:
X₂: 2⋅X₄ {O(n)}
X₃: X₃+5 {O(n)}
Runtime-bound of t₁: X₀ {O(n)}
Results in: 8⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₀⋅X₃⋅X₃⋅X₃+10240⋅X₀⋅X₃⋅X₃+26200⋅X₀⋅X₃+32⋅X₀⋅X₄+27021⋅X₀ {O(n^6)}
TWN: t₅: l3→l3
TWN - Lifting for t₅: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₃:
X₂: 2⋅X₄ {O(n)}
X₃: 5 {O(1)}
Runtime-bound of t₃: X₀ {O(n)}
Results in: 32⋅X₀⋅X₄+27021⋅X₀ {O(n^2)}
TWN - Lifting for t₅: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₁:
X₂: 2⋅X₄ {O(n)}
X₃: X₃+5 {O(n)}
Runtime-bound of t₁: X₀ {O(n)}
Results in: 8⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₀⋅X₃⋅X₃⋅X₃+10240⋅X₀⋅X₃⋅X₃+26200⋅X₀⋅X₃+32⋅X₀⋅X₄+27021⋅X₀ {O(n^6)}
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
TWN Size Bound - Lifting for t₄: l3→l3 and X₂: 125⋅3^(32⋅X₄+27021)+125⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)+15⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₃⋅X₃+2⋅3^(32⋅X₄+27021)⋅X₄+2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₄+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅75⋅X₃+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₃⋅X₃⋅X₃+X₃⋅X₃⋅X₃+15⋅X₃⋅X₃+75⋅X₃+250 {O(EXP)}
TWN Size Bound - Lifting for t₅: l3→l3 and X₂: 125⋅3^(32⋅X₄+27021)+125⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)+15⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₃⋅X₃+2⋅3^(32⋅X₄+27021)⋅X₄+2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₄+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅75⋅X₃+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₃⋅X₃⋅X₃+10240⋅X₃⋅X₃+26200⋅X₃+32⋅X₄+27021)⋅X₃⋅X₃⋅X₃+X₃⋅X₃⋅X₃+15⋅X₃⋅X₃+75⋅X₃+250 {O(EXP)}
Chain transitions t₆: l3→l1 and t₁: l1→l3 to t₁₃₄: l3→l3
Chain transitions t₀: l0→l1 and t₁: l1→l3 to t₁₃₅: l0→l3
Chain transitions t₀: l0→l1 and t₂: l1→l2 to t₁₃₆: l0→l2
Chain transitions t₆: l3→l1 and t₂: l1→l2 to t₁₃₇: l3→l2
Chain transitions t₁₃₇: l3→l2 and t₃: l2→l3 to t₁₃₈: l3→l3
Chain transitions t₁₃₆: l0→l2 and t₃: l2→l3 to t₁₃₉: l0→l3
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
TWN Size Bound - Lifting for t₄: l3→l3 and X₂: 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{O(1)}
TWN Size Bound - Lifting for t₅: l3→l3 and X₂: 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{O(1)}
MPRF for transition t₁₃₄: l3(X₀, X₁, X₂, X₃, X₄) -{2}> l3(X₀-1, X₀-1, X₄, X₃, X₄) :|: 1 < X₀ ∧ 0 < X₃ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀ {O(n)}
MPRF for transition t₁₃₈: l3(X₀, X₁, X₂, X₃, X₄) -{3}> l3(X₀-1, X₀-1, X₄, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ X₃ ≤ 5 ∧ 1 < X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀ {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
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 t₂₃₀: l3(X₀, X₁, X₂, X₃, X₄) → n_l3___2(Arg0_P, -2⋅X₁, NoDet0, X₃, X₄) :|: 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 5+X₃ ∧ 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 t₂₃₇: 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)}
MPRF for transition t₂₃₈: 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)}
TWN: t₂₂₈: n_l3___1→n_l3___2
cycle: [t₂₂₉: n_l3___2→n_l3___1; t₂₂₈: n_l3___1→n_l3___2]
loop: (X₁ < 0 ∧ X₁ < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅X₁ < 0,(X₁) -> (4⋅X₁)
order: [X₁]
closed-form:
X₁: X₁ * 4^n
Termination: true
Formula:
2⋅X₁ < 0 ∧ X₁ < 0
TWN - Lifting for t₂₂₈: n_l3___1→n_l3___2 of 4 {O(1)}
relevant size-bounds w.r.t. t₂₃₀:
Runtime-bound of t₂₃₀: 2⋅X₀ {O(n)}
Results in: 8⋅X₀ {O(n)}
TWN: t₂₂₉: n_l3___2→n_l3___1
TWN - Lifting for t₂₂₉: n_l3___2→n_l3___1 of 4 {O(1)}
relevant size-bounds w.r.t. t₂₃₀:
Runtime-bound of t₂₃₀: 2⋅X₀ {O(n)}
Results in: 8⋅X₀ {O(n)}
CFR did not improve the program. Rolling back
CFR: Improvement to new bound with the following program:
new bound:
24⋅X₀+1 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: Arg0_P, Arg3_P, NoDet0
Locations: l0, l1, l2, l3, n_l3___1, n_l3___2
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
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 ∧ 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 ∧ 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
t₂₃₀: l3(X₀, X₁, X₂, X₃, X₄) → n_l3___2(Arg0_P, -2⋅X₁, NoDet0, X₃, X₄) :|: 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 5+X₃ ∧ 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
t₂₃₇: 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
t₂₂₈: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l3___2(Arg0_P, -2⋅X₁, NoDet0, X₃, X₄) :|: 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₃₈: 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
t₂₂₉: n_l3___2(X₀, X₁, X₂, X₃, X₄) → n_l3___1(Arg0_P, -2⋅X₁, NoDet0, Arg3_P, X₄) :|: X₁ < 0 ∧ X₁ < 0 ∧ 0 ≤ 5+Arg3_P ∧ 1 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 0 ≤ 5+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
All Bounds
Timebounds
Overall timebound:24⋅X₀+2 {O(n)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀+1 {O(n)}
t₃: X₀ {O(n)}
t₆: X₀ {O(n)}
t₂₂₈: 8⋅X₀ {O(n)}
t₂₂₉: 8⋅X₀ {O(n)}
t₂₃₀: 2⋅X₀ {O(n)}
t₂₃₇: X₀ {O(n)}
t₂₃₈: X₀ {O(n)}
Costbounds
Overall costbound: 24⋅X₀+2 {O(n)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀+1 {O(n)}
t₃: X₀ {O(n)}
t₆: X₀ {O(n)}
t₂₂₈: 8⋅X₀ {O(n)}
t₂₂₉: 8⋅X₀ {O(n)}
t₂₃₀: 2⋅X₀ {O(n)}
t₂₃₇: X₀ {O(n)}
t₂₃₈: X₀ {O(n)}
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: X₀ {O(n)}
t₁, X₁: 4⋅X₀ {O(n)}
t₁, X₂: 4⋅X₄ {O(n)}
t₁, X₃: X₃+5 {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: 4⋅X₀ {O(n)}
t₂, X₂: 4⋅X₄ {O(n)}
t₂, X₃: 5 {O(1)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀ {O(n)}
t₃, X₂: 4⋅X₄ {O(n)}
t₃, X₃: 5 {O(1)}
t₃, X₄: X₄ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 5⋅X₀ {O(n)}
t₆, X₂: 8⋅X₄ {O(n)}
t₆, X₃: X₃+5 {O(n)}
t₆, X₄: X₄ {O(n)}
t₂₂₈, X₀: X₀ {O(n)}
t₂₂₈, X₁: 10⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀ {O(EXP)}
t₂₂₈, X₃: X₃+5 {O(n)}
t₂₂₈, X₄: X₄ {O(n)}
t₂₂₉, X₀: X₀ {O(n)}
t₂₂₉, X₁: 10⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀ {O(EXP)}
t₂₂₉, X₃: X₃+5 {O(n)}
t₂₂₉, X₄: X₄ {O(n)}
t₂₃₀, X₀: X₀ {O(n)}
t₂₃₀, X₁: 10⋅X₀ {O(n)}
t₂₃₀, X₃: X₃+5 {O(n)}
t₂₃₀, X₄: X₄ {O(n)}
t₂₃₇, X₀: X₀ {O(n)}
t₂₃₇, X₁: 10⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀ {O(EXP)}
t₂₃₇, X₃: X₃+5 {O(n)}
t₂₃₇, X₄: X₄ {O(n)}
t₂₃₈, X₀: X₀ {O(n)}
t₂₃₈, X₁: 10⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀+10⋅X₀ {O(EXP)}
t₂₃₈, X₃: X₃+5 {O(n)}
t₂₃₈, X₄: X₄ {O(n)}