Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 0 < X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₅, X₃, X₄, X₅) :|: X₂ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 3⋅X₁-4⋅X₂, 4⋅X₁-3⋅X₂, 5⋅X₃, 5⋅X₄-(X₀)², X₅) :|: 1 < (X₁)² ∧ 0 < X₀*X₂+2⋅X₀
Preprocessing
Found invariant X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₅, X₃, X₄, X₅) :|: X₂ ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, 3⋅X₁-4⋅X₂, 4⋅X₁-3⋅X₂, 5⋅X₃, 5⋅X₄-(X₀)², X₅) :|: 1 < (X₁)² ∧ 0 < X₀*X₂+2⋅X₀
MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅ of depth 1:
new bound:
X₅ {O(n)}
MPRF:
l2 [X₅ ]
l1 [X₅ ]
MPRF for transition t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 0 < X₂ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:
new bound:
4⋅X₅⋅X₅+X₅ {O(n^2)}
MPRF:
l1 [X₂ ]
MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₅, X₃, X₄, X₅) :|: X₂ ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:
new bound:
X₅+1 {O(n)}
MPRF:
l1 [1 ]
l2 [0 ]
Analysing control-flow refined program
Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l2
Found invariant X₅ ≤ X₂ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1
Found invariant 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location n_l1___1
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₅, X₃, X₄, X₅) :|: X₂ ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₅ ≤ X₂ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₅₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀+X₂, X₁, X₂-1, X₃, X₁, X₅) :|: X₃ ≤ X₀ ∧ X₂ ≤ 1+X₅ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₅ ∧ 0 < X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₂ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
MPRF for transition t₅₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀+X₂, X₁, X₂-1, X₃, X₁, X₅) :|: 0 < X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ 1+X₅ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₅ ∧ 0 < X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₅ ≤ X₂ ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ of depth 1:
new bound:
X₅+1 {O(n)}
MPRF:
n_l1___1 [X₅ ]
l2 [X₂ ]
n_l2___1 [X₅ ]
l1 [X₅+1 ]
MPRF for transition t₅₆: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₅, X₃, X₄, X₅) :|: X₂ ≤ 0 ∧ X₂ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ of depth 1:
new bound:
X₅+1 {O(n)}
MPRF:
n_l1___1 [X₅+1 ]
l2 [X₂ ]
n_l2___1 [X₅ ]
l1 [X₅+1 ]
MPRF for transition t₆₉: n_l2___1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅ of depth 1:
new bound:
X₅ {O(n)}
MPRF:
n_l1___1 [X₅ ]
l2 [X₂ ]
n_l2___1 [X₅ ]
l1 [X₅ ]
knowledge_propagation leads to new time bound X₅+2 {O(n)} for transition t₆₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l2___1(X₀, Arg1_P, Arg2_P, 5⋅X₃, NoDet0, X₅) :|: X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 4⋅X₁ ≤ 3⋅X₂+Arg2_P ∧ 3⋅X₂+Arg2_P ≤ 4⋅X₁ ∧ 7⋅X₁+3⋅Arg1_P ≤ 4⋅Arg2_P ∧ 4⋅Arg2_P ≤ 7⋅X₁+3⋅Arg1_P ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
MPRF for transition t₅₁: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l1___1(X₀+X₂, X₁, X₂-1, X₃, X₁, X₅) :|: X₃ ≤ X₀ ∧ X₂ ≤ 1+X₅ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₂ ≤ 1+X₅ ∧ 0 < X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ of depth 1:
new bound:
18⋅X₅⋅X₅+20⋅X₅ {O(n^2)}
MPRF:
l2 [2⋅X₂ ]
n_l1___1 [X₂+X₅+1 ]
n_l2___1 [2⋅X₅ ]
l1 [2⋅X₂ ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 4⋅X₅⋅X₅+X₅ {O(n^2)}
t₂: X₅+1 {O(n)}
t₃: inf {Infinity}
t₄: X₅ {O(n)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 4⋅X₅⋅X₅+X₅ {O(n^2)}
t₂: X₅+1 {O(n)}
t₃: inf {Infinity}
t₄: X₅ {O(n)}
Sizebounds
t₀, X₀: X₃ {O(n)}
t₀, X₁: X₄ {O(n)}
t₀, X₂: X₅ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₂: 5⋅X₅ {O(n)}
t₁, X₅: 2⋅X₅ {O(n)}
t₂, X₂: 3⋅X₅ {O(n)}
t₂, X₅: 2⋅X₅ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₂: 4⋅X₅ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}