Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂ < X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 0, 0)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃+1) :|: X₃ < X₀ ∧ X₃ < X₀
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃+1) :|: X₃ < X₀ ∧ X₀ ≤ X₃
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, 0) :|: X₀ ≤ X₃ ∧ X₃ < X₀
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, 0) :|: X₀ ≤ X₃ ∧ X₀ ≤ X₃
t₈: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Preprocessing
Cut unsatisfiable transition t₅: l3→l1
Cut unsatisfiable transition t₆: l3→l1
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l5
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location l1
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l4
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 0, 0)
t₄: l3(X₀, X₁, X₂, X₃) → l1(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
t₇: l3(X₀, X₁, X₂, X₃) → l1(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
t₈: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂
MPRF for transition t₇: l3(X₀, X₁, X₂, X₃) → l1(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: t₂: l1→l3
cycle: [t₂: l1→l3; t₄: l3→l1]
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 t₂: l1→l3 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₇:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₇: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+5⋅X₁ {O(n^2)}
TWN - Lifting for t₂: l1→l3 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₀+5 {O(n)}
TWN: t₄: l3→l1
TWN - Lifting for t₄: l3→l1 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₇:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₇: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+5⋅X₁ {O(n^2)}
TWN - Lifting for t₄: l3→l1 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₀+5 {O(n)}
Chain transitions t₇: l3→l1 and t₃: l1→l4 to t₅₃: l3→l4
Chain transitions t₄: l3→l1 and t₃: l1→l4 to t₅₄: l3→l4
Chain transitions t₄: l3→l1 and t₂: l1→l3 to t₅₅: l3→l3
Chain transitions t₇: l3→l1 and t₂: l1→l3 to t₅₆: l3→l3
Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₅₇: l2→l3
Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₅₈: l2→l4
Analysing control-flow refined program
Cut unsatisfiable transition t₅₄: l3→l4
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l5
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location l1
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l4
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l3
MPRF for transition t₅₆: l3(X₀, X₁, X₂, X₃) -{2}> l3(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: t₅₅: l3→l3
cycle: [t₅₅: l3→l3]
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 t₅₅: l3→l3 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₅₆:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₅₆: X₁ {O(n)}
Results in: 2⋅X₀⋅X₁+5⋅X₁ {O(n^2)}
TWN - Lifting for t₅₅: l3→l3 of 2⋅X₀+2⋅X₃+5 {O(n)}
relevant size-bounds w.r.t. t₅₇:
X₀: X₀ {O(n)}
X₃: 0 {O(1)}
Runtime-bound of t₅₇: 1 {O(1)}
Results in: 2⋅X₀+5 {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₁₄₁: n_l1___6→l4
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_l1___6
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_l3___4
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_l1___3
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l5
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_l1___5
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_l3___2
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ for location l1
Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l4
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_l3___1
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_l3___7
Cut unsatisfiable transition t₁₂₇: n_l3___2→n_l1___5
MPRF for transition t₁₂₃: n_l1___5(X₀, X₁, X₂, X₃) → n_l3___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 t₁₂₆: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___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 t₁₂₂: n_l1___3(X₀, X₁, X₂, X₃) → n_l3___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 t₁₂₈: n_l3___2(X₀, X₁, X₂, X₃) → n_l1___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 t₁₂₉: n_l3___4(X₀, X₁, X₂, X₃) → n_l1___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: t₁₂₄: n_l1___6→n_l3___4
cycle: [t₁₃₀: n_l3___4→n_l1___6; t₁₂₄: n_l1___6→n_l3___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 t₁₂₄: n_l1___6→n_l3___4 of 2⋅X₀+2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₁₃₂:
X₀: X₀ {O(n)}
X₃: 1 {O(1)}
Runtime-bound of t₁₃₂: 1 {O(1)}
Results in: 2⋅X₀+8 {O(n)}
TWN - Lifting for t₁₂₄: n_l1___6→n_l3___4 of 2⋅X₀+2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₁₂₈:
X₀: X₀ {O(n)}
X₃: 1 {O(1)}
Runtime-bound of t₁₂₈: X₁+1 {O(n)}
Results in: 2⋅X₀⋅X₁+2⋅X₀+8⋅X₁+8 {O(n^2)}
TWN: t₁₃₀: n_l3___4→n_l1___6
TWN - Lifting for t₁₃₀: n_l3___4→n_l1___6 of 2⋅X₀+2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₁₃₂:
X₀: X₀ {O(n)}
X₃: 1 {O(1)}
Runtime-bound of t₁₃₂: 1 {O(1)}
Results in: 2⋅X₀+8 {O(n)}
TWN - Lifting for t₁₃₀: n_l3___4→n_l1___6 of 2⋅X₀+2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₁₂₈:
X₀: X₀ {O(n)}
X₃: 1 {O(1)}
Runtime-bound of t₁₂₈: 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+14 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₃: 1 {O(1)}
t₄: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₇: X₁ {O(n)}
t₈: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₀⋅X₁+11⋅X₁+4⋅X₀+14 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₃: 1 {O(1)}
t₄: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₇: X₁ {O(n)}
t₈: 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: 0 {O(1)}
t₁, X₃: 0 {O(1)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₁ {O(n)}
t₂, X₃: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: X₁ {O(n)}
t₃, X₃: 0 {O(1)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁ {O(n)}
t₄, X₃: 2⋅X₀⋅X₁+2⋅X₀+5⋅X₁+5 {O(n^2)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁ {O(n)}
t₇, X₃: 0 {O(1)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: X₁ {O(n)}
t₈, X₃: 0 {O(1)}