Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀, X₁) → l1(1, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁
t₀: l1(X₀, X₁) → l2(X₀-1, X₁) :|: 1 ≤ X₀
t₄: l2(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁
t₁: l2(X₀, X₁) → l2(X₀-1, X₁+1) :|: 1 ≤ X₀
Preprocessing
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀, X₁) → l1(1, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₀: l1(X₀, X₁) → l2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l2(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁: l2(X₀, X₁) → l2(X₀-1, X₁+1) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
MPRF for transition t₀: l1(X₀, X₁) → l2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l2 [X₀+X₁ ]
l1 [X₀+X₁ ]
MPRF for transition t₄: l2(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
l2 [X₀+X₁+1 ]
l1 [X₀+X₁ ]
Found invariant 1 ≤ 0 for location l2
Found invariant 1 ≤ 0 for location l1
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Analysing control-flow refined program
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___1
Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___1
MPRF for transition t₆₁: l1(X₀, X₁) → n_l1___1(X₀+1, X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l1___1 [X₀+X₁-1 ]
l2 [X₀+X₁ ]
n_l2___1 [X₀+X₁ ]
l1 [X₀+X₁ ]
MPRF for transition t₆₂: l1(X₀, X₁) → n_l1___1(X₀+1, X₁-1) :|: 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l1___1 [X₀+X₁-1 ]
l2 [X₀+X₁ ]
n_l2___1 [X₀+X₁ ]
l1 [X₀+X₁ ]
MPRF for transition t₇₅: l2(X₀, X₁) → n_l2___1(X₀-1, X₁+1) :|: 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁+2 {O(n)}
MPRF:
n_l1___1 [X₀+X₁-1 ]
l2 [X₀+X₁ ]
n_l2___1 [X₀+X₁-1 ]
l1 [X₀+X₁-1 ]
MPRF for transition t₆₅: n_l1___1(X₀, X₁) → l2(X₀-1, X₁) :|: 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l1___1 [X₀+X₁ ]
l2 [X₀+X₁ ]
n_l2___1 [X₀+X₁ ]
l1 [X₀+X₁ ]
MPRF for transition t₇₈: n_l2___1(X₀, X₁) → l1(X₀+1, X₁-1) :|: 1 ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₁+1 {O(n)}
MPRF:
n_l1___1 [X₀+X₁ ]
l2 [X₀+X₁+1 ]
n_l2___1 [X₀+X₁+1 ]
l1 [X₀+X₁ ]
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___1
Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___1
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___1
Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___1
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___1
Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___1
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₂: 1 {O(1)}
t₀: X₁+1 {O(n)}
t₃: inf {Infinity}
t₁: inf {Infinity}
t₄: X₁+1 {O(n)}
Costbounds
Overall costbound: inf {Infinity}
t₂: 1 {O(1)}
t₀: X₁+1 {O(n)}
t₃: inf {Infinity}
t₁: inf {Infinity}
t₄: X₁+1 {O(n)}
Sizebounds
t₂, X₀: 1 {O(1)}
t₂, X₁: X₁ {O(n)}