Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₆: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂
t₅: l1(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₂ ≤ 0
t₇: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₈: l2(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: D+1 ≤ X₁
t₉: l2(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₁+1 ≤ D
t₁₀: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1)
t₂: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 1 ≤ X₀
t₃: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 0
t₄: l5(X₀, X₁, X₂) → l1(X₀, D, X₀)
t₁₁: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₁: l7(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
Preprocessing
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l2
Found invariant X₀ ≤ 0 for location l6
Found invariant 1 ≤ X₀ for location l5
Found invariant X₀ ≤ 0 for location l8
Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l1
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₆: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₅: l1(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₇: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₈: l2(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: D+1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₉: l2(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₁+1 ≤ D ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₁₀: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₂: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 1 ≤ X₀
t₃: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ ≤ 0
t₄: l5(X₀, X₁, X₂) → l1(X₀, D, X₀) :|: 1 ≤ X₀
t₁₁: l6(X₀, X₁, X₂) → l8(X₀, X₁, X₂) :|: X₀ ≤ 0
t₁: l7(X₀, X₁, X₂) → l4(X₀, X₁, X₂)
MPRF for transition t₅: l1(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₇: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₁₀: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
Chain transitions t₄: l5→l1 and t₅: l1→l4 to t₈₅: l5→l4
Chain transitions t₁₀: l3→l1 and t₅: l1→l4 to t₈₆: l3→l4
Chain transitions t₁₀: l3→l1 and t₆: l1→l2 to t₈₇: l3→l2
Chain transitions t₄: l5→l1 and t₆: l1→l2 to t₈₈: l5→l2
Chain transitions t₈₈: l5→l2 and t₉: l2→l4 to t₈₉: l5→l4
Chain transitions t₈₇: l3→l2 and t₉: l2→l4 to t₉₀: l3→l4
Chain transitions t₈₇: l3→l2 and t₈: l2→l4 to t₉₁: l3→l4
Chain transitions t₈₈: l5→l2 and t₈: l2→l4 to t₉₂: l5→l4
Chain transitions t₈₇: l3→l2 and t₇: l2→l3 to t₉₃: l3→l3
Chain transitions t₈₈: l5→l2 and t₇: l2→l3 to t₉₄: l5→l3
Chain transitions t₁: l7→l4 and t₃: l4→l6 to t₉₅: l7→l6
Chain transitions t₉₂: l5→l4 and t₃: l4→l6 to t₉₆: l5→l6
Chain transitions t₉₂: l5→l4 and t₂: l4→l5 to t₉₇: l5→l5
Chain transitions t₁: l7→l4 and t₂: l4→l5 to t₉₈: l7→l5
Chain transitions t₈₉: l5→l4 and t₂: l4→l5 to t₉₉: l5→l5
Chain transitions t₈₉: l5→l4 and t₃: l4→l6 to t₁₀₀: l5→l6
Chain transitions t₈₅: l5→l4 and t₂: l4→l5 to t₁₀₁: l5→l5
Chain transitions t₈₅: l5→l4 and t₃: l4→l6 to t₁₀₂: l5→l6
Chain transitions t₉₁: l3→l4 and t₂: l4→l5 to t₁₀₃: l3→l5
Chain transitions t₉₁: l3→l4 and t₃: l4→l6 to t₁₀₄: l3→l6
Chain transitions t₉₀: l3→l4 and t₂: l4→l5 to t₁₀₅: l3→l5
Chain transitions t₉₀: l3→l4 and t₃: l4→l6 to t₁₀₆: l3→l6
Chain transitions t₈₆: l3→l4 and t₂: l4→l5 to t₁₀₇: l3→l5
Chain transitions t₈₆: l3→l4 and t₃: l4→l6 to t₁₀₈: l3→l6
Analysing control-flow refined program
Cut unsatisfiable transition t₈₅: l5→l4
Cut unsatisfiable transition t₉₆: l5→l6
Cut unsatisfiable transition t₁₀₀: l5→l6
Cut unsatisfiable transition t₁₀₁: l5→l5
Cut unsatisfiable transition t₁₀₂: l5→l6
Cut unsatisfiable transition t₁₀₄: l3→l6
Cut unsatisfiable transition t₁₀₆: l3→l6
Cut unsatisfiable transition t₁₀₇: l3→l5
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l2
Found invariant X₀ ≤ 0 for location l6
Found invariant 1 ≤ X₀ for location l5
Found invariant X₀ ≤ 0 for location l8
Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l1
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₉₃: l3(X₀, X₁, X₂) -{3}> l3(X₀, X₁, X₂-1) :|: 2 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀+1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀+1 ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₉₄: l5(X₀, X₁, X₂) -{3}> l3(X₀, D, X₀) :|: 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ 2⋅X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₀ ∧ 2 ≤ 2⋅X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₁₀₃: l3(X₀, X₁, X₂) -{4}> l5(X₂-1, X₁, X₂-1) :|: 2 ≤ X₂ ∧ Temp_Int₂₃₇+1 ≤ X₁ ∧ 2 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀+1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀+1 ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₁₀₅: l3(X₀, X₁, X₂) -{4}> l5(X₂-1, X₁, X₂-1) :|: 2 ≤ X₂ ∧ X₁+1 ≤ Temp_Int₂₃₃ ∧ 2 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀+1 ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀+1 ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {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 t₃₂₉: n_l4___5→l6
Eliminate variables {NoDet0,X₁} that do not contribute to the problem
Found invariant 1 ≤ X₀ for location n_l5___1
Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___7
Found invariant X₀ ≤ 0 for location l6
Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___6
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___2
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___5
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l5___4
Found invariant X₀ ≤ 0 for location l8
Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₃₅₄: l1(X₀, X₁) → n_l2___7(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₃₅₆: l3(X₀, X₁) → l1(X₀, X₁-1) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀+1 {O(n)}
MPRF for transition t₃₆₂: n_l2___2(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₃₆₅: n_l2___7(X₀, X₁) → l3(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF for transition t₃₆₆: n_l2___7(X₀, X₁) → n_l4___5(Arg0_P, Arg2_P) :|: 1+X₁ ≤ X₀ ∧ Arg2_P ≤ X₀ ∧ 1 ≤ Arg2_P ∧ X₁ ≤ Arg2_P ∧ Arg2_P ≤ X₁ ∧ Arg0_P ≤ Arg2_P ∧ Arg2_P ≤ Arg0_P ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+1 {O(n)}
MPRF for transition t₃₆₇: n_l2___7(X₀, X₁) → n_l4___5(Arg0_P, Arg2_P) :|: 1+X₁ ≤ X₀ ∧ Arg2_P ≤ X₀ ∧ 1 ≤ Arg2_P ∧ Arg0_P ≤ Arg2_P ∧ Arg2_P ≤ Arg0_P ∧ X₁ ≤ Arg2_P ∧ Arg2_P ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: X₀+1 {O(n)}
t₆: inf {Infinity}
t₇: X₀ {O(n)}
t₈: inf {Infinity}
t₉: inf {Infinity}
t₁₀: X₀ {O(n)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: X₀+1 {O(n)}
t₆: inf {Infinity}
t₇: X₀ {O(n)}
t₈: inf {Infinity}
t₉: inf {Infinity}
t₁₀: X₀ {O(n)}
t₁₁: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₂: 2⋅X₀+X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₂: X₀ {O(n)}
t₅, X₀: 0 {O(1)}
t₅, X₂: 0 {O(1)}
t₆, X₀: X₀ {O(n)}
t₆, X₂: X₀ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₂: X₀ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₂: X₀ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₂: X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₂: X₀ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₂: X₂ {O(n)}