Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₀: l10(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₂ < X₁
t₁₁: l10(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂
t₁₂: l11(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃+1) :|: X₃ < X₀ ∧ X₃ < X₀
t₁₃: l11(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂+1, X₃+1) :|: X₃ < X₀ ∧ X₀ ≤ X₃
t₁₄: l11(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, 0) :|: X₀ ≤ X₃ ∧ X₃ < X₀
t₁₅: l11(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂+1, 0) :|: X₀ ≤ X₃ ∧ X₀ ≤ X₃
t₁₆: l12(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, 0, 0)
Preprocessing
Cut unsatisfiable transition t₁₃: l11→l10
Cut unsatisfiable transition t₁₄: l11→l10
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l11
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l12
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l13
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location l10
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₀: l10(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂
t₁₁: l10(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂
t₁₂: l11(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃+1) :|: X₃ < X₀ ∧ X₃ < X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₅: l11(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂+1, 0) :|: X₀ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₆: l12(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, 0, 0)
MPRF for transition t₁₅: l11(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂+1, 0) :|: X₀ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁ {O(n)}
TWN: t₁₀: l10→l11
cycle: [t₁₀: l10→l11; t₁₂: l11→l10]
loop: (X₂ < X₁ ∧ X₃ < X₀ ∧ X₃ < X₀,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,X₃+1)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0 ∧ X₂ < X₁
∨ X₃ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ < X₁
Stabilization-Threshold for: X₃ < X₀
alphas_abs: X₃+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+2 {O(n)}
loop: (X₂ < X₁ ∧ X₃ < X₀ ∧ X₃ < X₀,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,X₃+1)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0 ∧ X₂ < X₁
∨ X₃ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ < X₁
Stabilization-Threshold for: X₃ < X₀
alphas_abs: X₃+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+2 {O(n)}
TWN - Lifting for t₁₀: l10→l11 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₉:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₉: 1 {O(1)}
Results in: 2⋅X₀+5 {O(n)}
TWN - Lifting for t₁₀: l10→l11 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₁₅:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₁₅: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+5⋅X₁ {O(n^2)}
TWN: t₁₂: l11→l10
TWN - Lifting for t₁₂: l11→l10 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₉:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₉: 1 {O(1)}
Results in: 2⋅X₀+5 {O(n)}
TWN - Lifting for t₁₂: l11→l10 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₁₅:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₁₅: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+5⋅X₁ {O(n^2)}
Chain transitions t₉: l9→l10 and t₁₁: l10→l12 to t₉₃: l9→l12
Chain transitions t₁₅: l11→l10 and t₁₁: l10→l12 to t₉₄: l11→l12
Chain transitions t₁₅: l11→l10 and t₁₀: l10→l11 to t₉₅: l11→l11
Chain transitions t₉: l9→l10 and t₁₀: l10→l11 to t₉₆: l9→l11
Chain transitions t₁₂: l11→l10 and t₁₀: l10→l11 to t₉₇: l11→l11
Chain transitions t₁₂: l11→l10 and t₁₁: l10→l12 to t₉₈: l11→l12
Analysing control-flow refined program
Cut unsatisfiable transition t₉₈: l11→l12
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l11
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l12
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l13
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location l10
MPRF for transition t₉₅: l11(X₀, X₁, X₂, X₃) -{2}> l11(X₀, X₁, 1+X₂, 0) :|: X₀ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ < X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ 0 ≤ 0 ∧ 0 ≤ 1+X₂ ∧ 0 ≤ 1+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:
new bound:
X₁ {O(n)}
TWN: t₉₇: l11→l11
cycle: [t₉₇: l11→l11]
loop: (X₃ < X₀ ∧ X₃ < X₀ ∧ X₂ < X₁,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,1+X₃)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃ + [[n != 0]] * n^1
Termination: true
Formula:
X₂ < X₁ ∧ 1 < 0
∨ X₂ < X₁ ∧ X₃ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: X₃ < X₀
alphas_abs: X₃+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+2 {O(n)}
loop: (X₃ < X₀ ∧ X₃ < X₀ ∧ X₂ < X₁,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,1+X₃)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃ + [[n != 0]] * n^1
Termination: true
Formula:
X₂ < X₁ ∧ 1 < 0
∨ X₂ < X₁ ∧ X₃ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: X₃ < X₀
alphas_abs: X₃+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+2 {O(n)}
TWN - Lifting for t₉₇: l11→l11 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₉₆:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₉₆: 1 {O(1)}
Results in: 2⋅X₀+5 {O(n)}
TWN - Lifting for t₉₇: l11→l11 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₉₅:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₉₅: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+5⋅X₁ {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₂₀₂: n_l10___6→l12
Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l10___3
Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l11___4
Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l10___6
Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l11___2
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l12
Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l10___5
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l11___7
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l13
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location l10
Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l11___1
Cut unsatisfiable transition t₁₈₈: n_l11___2→n_l10___5
MPRF for transition t₁₈₄: n_l10___5(X₀, X₁, X₂, X₃) → n_l11___1(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ < X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₁+2 {O(n)}
MPRF for transition t₁₈₇: n_l11___1(X₀, X₁, X₂, X₃) → n_l10___5(X₀, X₁, X₂+1, 0) :|: X₀ ≤ 0 ∧ X₂ < X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ 0 ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ X₀ ≤ 0 of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₁₈₃: n_l10___3(X₀, X₁, X₂, X₃) → n_l11___2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ < X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
MPRF for transition t₁₈₉: n_l11___2(X₀, X₁, X₂, X₃) → n_l10___6(X₀, X₁, X₂, X₃+1) :|: X₂ < X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ 0 ∧ X₃ < X₀ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF for transition t₁₉₀: n_l11___4(X₀, X₁, X₂, X₃) → n_l10___3(X₀, X₁, X₂+1, 0) :|: X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁ {O(n)}
TWN: t₁₈₅: n_l10___6→n_l11___4
cycle: [t₁₉₁: n_l11___4→n_l10___6; t₁₈₅: n_l10___6→n_l11___4]
loop: (1+X₂ ≤ X₁ ∧ X₂ < X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ < X₁ ∧ X₃ < X₀,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,X₃+1)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0 ∧ X₂ < X₁ ∧ 1+X₂ < X₁
∨ 1 < 0 ∧ X₂ < X₁ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂
∨ X₃ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ < X₁ ∧ 1+X₂ < X₁
∨ X₃ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ < X₁ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂
Stabilization-Threshold for: X₃ < X₀
alphas_abs: X₀+X₃
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+2 {O(n)}
loop: (1+X₂ ≤ X₁ ∧ X₂ < X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ < X₁ ∧ X₃ < X₀,(X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,X₃+1)
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃ + [[n != 0]] * n^1
Termination: true
Formula:
1 < 0 ∧ X₂ < X₁ ∧ 1+X₂ < X₁
∨ 1 < 0 ∧ X₂ < X₁ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂
∨ X₃ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ < X₁ ∧ 1+X₂ < X₁
∨ X₃ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ < X₁ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ 1+X₂
Stabilization-Threshold for: X₃ < X₀
alphas_abs: X₀+X₃
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+2 {O(n)}
TWN - Lifting for t₁₈₅: n_l10___6→n_l11___4 of 2⋅X₀+2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₁₉₃:
X₀: X₀ {O(n)}
X₃: 1 {O(1)}
Runtime-bound of t₁₉₃: 1 {O(1)}
Results in: 2⋅X₀+8 {O(n)}
TWN - Lifting for t₁₈₅: n_l10___6→n_l11___4 of 2⋅X₀+2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₁₈₉:
X₀: X₀ {O(n)}
X₃: 1 {O(1)}
Runtime-bound of t₁₈₉: X₁+1 {O(n)}
Results in: 2⋅X₀⋅X₁+2⋅X₀+8⋅X₁+8 {O(n^2)}
TWN: t₁₉₁: n_l11___4→n_l10___6
TWN - Lifting for t₁₉₁: n_l11___4→n_l10___6 of 2⋅X₀+2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₁₉₃:
X₀: X₀ {O(n)}
X₃: 1 {O(1)}
Runtime-bound of t₁₉₃: 1 {O(1)}
Results in: 2⋅X₀+8 {O(n)}
TWN - Lifting for t₁₉₁: n_l11___4→n_l10___6 of 2⋅X₀+2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₁₈₉:
X₀: X₀ {O(n)}
X₃: 1 {O(1)}
Runtime-bound of t₁₈₉: X₁+1 {O(n)}
Results in: 2⋅X₀⋅X₁+2⋅X₀+8⋅X₁+8 {O(n^2)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:4⋅X₀⋅X₁+11⋅X₁+4⋅X₀+22 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₁₅: X₁ {O(n)}
t₁₆: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₀⋅X₁+11⋅X₁+4⋅X₀+22 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₁₁: 1 {O(1)}
t₁₂: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₁₅: X₁ {O(n)}
t₁₆: 1 {O(1)}
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: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 0 {O(1)}
t₉, X₃: 0 {O(1)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁ {O(n)}
t₁₀, X₃: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}
t₁₁, X₂: X₁ {O(n)}
t₁₁, X₃: 0 {O(1)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₁ {O(n)}
t₁₂, X₃: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₁ {O(n)}
t₁₅, X₃: 0 {O(1)}
t₁₆, X₀: 2⋅X₀ {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}
t₁₆, X₂: X₁ {O(n)}
t₁₆, X₃: 0 {O(1)}