Initial Problem
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: 1 ≤ X₁ ∧ X₁ ≤ 254
t₃: l1(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
t₄: l1(X₀, X₁) → l5(X₀, X₁) :|: 255 ≤ X₁
t₅: l2(X₀, X₁) → l3(X₀, X₁) :|: X₀+1 ≤ 0
t₆: l2(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ X₀
t₇: l2(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₈: l3(X₀, X₁) → l1(X₀, X₁+1)
t₉: l4(X₀, X₁) → l1(X₀, X₁-1)
t₁₀: l5(X₀, X₁) → l7(X₀, X₁)
t₁: l6(X₀, X₁) → l1(X₁, X₀)
Preprocessing
Found invariant X₁ ≤ 254 ∧ 1 ≤ X₁ for location l2
Found invariant X₁ ≤ 254 ∧ X₁ ≤ 254+X₀ ∧ X₀+X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₁ ≤ 254 ∧ 1 ≤ X₁ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: 1 ≤ X₁ ∧ X₁ ≤ 254
t₃: l1(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
t₄: l1(X₀, X₁) → l5(X₀, X₁) :|: 255 ≤ X₁
t₅: l2(X₀, X₁) → l3(X₀, X₁) :|: X₀+1 ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁
t₆: l2(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁
t₇: l2(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁
t₈: l3(X₀, X₁) → l1(X₀, X₁+1) :|: X₁ ≤ 254 ∧ 1 ≤ X₁
t₉: l4(X₀, X₁) → l1(X₀, X₁-1) :|: X₁ ≤ 254 ∧ X₁ ≤ 254+X₀ ∧ X₀+X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₀: l5(X₀, X₁) → l7(X₀, X₁)
t₁: l6(X₀, X₁) → l1(X₁, X₀)
Chain transitions t₁: l6→l1 and t₄: l1→l5 to t₁₀₃: l6→l5
Chain transitions t₉: l4→l1 and t₄: l1→l5 to t₁₀₄: l4→l5
Chain transitions t₉: l4→l1 and t₃: l1→l5 to t₁₀₅: l4→l5
Chain transitions t₁: l6→l1 and t₃: l1→l5 to t₁₀₆: l6→l5
Chain transitions t₈: l3→l1 and t₃: l1→l5 to t₁₀₇: l3→l5
Chain transitions t₈: l3→l1 and t₄: l1→l5 to t₁₀₈: l3→l5
Chain transitions t₈: l3→l1 and t₂: l1→l2 to t₁₀₉: l3→l2
Chain transitions t₉: l4→l1 and t₂: l1→l2 to t₁₁₀: l4→l2
Chain transitions t₁: l6→l1 and t₂: l1→l2 to t₁₁₁: l6→l2
Chain transitions t₁₁₁: l6→l2 and t₇: l2→l4 to t₁₁₂: l6→l4
Chain transitions t₁₁₀: l4→l2 and t₇: l2→l4 to t₁₁₃: l4→l4
Chain transitions t₁₁₀: l4→l2 and t₆: l2→l3 to t₁₁₄: l4→l3
Chain transitions t₁₁₁: l6→l2 and t₆: l2→l3 to t₁₁₅: l6→l3
Chain transitions t₁₀₉: l3→l2 and t₆: l2→l3 to t₁₁₆: l3→l3
Chain transitions t₁₀₉: l3→l2 and t₇: l2→l4 to t₁₁₇: l3→l4
Chain transitions t₁₀₉: l3→l2 and t₅: l2→l3 to t₁₁₈: l3→l3
Chain transitions t₁₁₀: l4→l2 and t₅: l2→l3 to t₁₁₉: l4→l3
Chain transitions t₁₁₁: l6→l2 and t₅: l2→l3 to t₁₂₀: l6→l3
Analysing control-flow refined program
Cut unsatisfiable transition t₁₀₄: l4→l5
Cut unsatisfiable transition t₁₀₇: l3→l5
Cut unsatisfiable transition t₁₁₄: l4→l3
Cut unsatisfiable transition t₁₁₇: l3→l4
Cut unsatisfiable transition t₁₁₉: l4→l3
Found invariant X₁ ≤ 254 ∧ 1 ≤ X₁ for location l2
Found invariant X₁ ≤ 254 ∧ X₁ ≤ 254+X₀ ∧ X₀+X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₁ ≤ 254 ∧ 1 ≤ X₁ for location l3
MPRF for transition t₁₁₆: l3(X₀, X₁) -{3}> l3(X₀, 1+X₁) :|: 0 ≤ X₁ ∧ X₁ ≤ 253 ∧ 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 253 ∧ 0 ≤ X₁ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ of depth 1:
new bound:
1018 {O(1)}
MPRF for transition t₁₁₈: l3(X₀, X₁) -{3}> l3(X₀, 1+X₁) :|: 0 ≤ X₁ ∧ X₁ ≤ 253 ∧ X₀+1 ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 253 ∧ 0 ≤ X₁ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ of depth 1:
new bound:
1018 {O(1)}
MPRF for transition t₁₁₃: l4(X₀, X₁) -{3}> l4(X₀, X₁-1) :|: 2 ≤ X₁ ∧ X₁ ≤ 255 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254+X₀ ∧ X₀+X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 255 ∧ 2 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254+X₀ ∧ X₀+X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:
new bound:
254 {O(1)}
Analysing control-flow refined program
Cut unsatisfiable transition t₂₇₂: n_l1___6→l5
Cut unsatisfiable transition t₂₇₃: n_l1___9→l5
Cut unsatisfiable transition t₂₇₄: n_l1___3→l5
Found invariant X₁ ≤ 255 ∧ X₁ ≤ 254+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___4
Found invariant X₁ ≤ 255 ∧ X₀+X₁ ≤ 254 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l1___9
Found invariant X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___5
Found invariant X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___3
Found invariant X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l2___2
Found invariant X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___12
Found invariant X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___11
Found invariant X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___1
Found invariant X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l2___8
Found invariant X₁ ≤ 254 ∧ 1 ≤ X₁ for location n_l2___13
Found invariant X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___7
Found invariant X₁ ≤ 254 ∧ X₁ ≤ 254+X₀ ∧ X₀+X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___10
MPRF for transition t₂₄₅: n_l1___6(X₀, X₁) → n_l2___5(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ X₁ ≤ 255 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 255 ∧ X₁ ≤ 254+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
510 {O(1)}
MPRF for transition t₂₅₁: n_l2___5(X₀, X₁) → n_l3___4(X₀, X₁) :|: 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
510 {O(1)}
MPRF for transition t₂₅₅: n_l3___4(X₀, X₁) → n_l1___6(X₀, X₁+1) :|: 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
510 {O(1)}
MPRF for transition t₂₄₆: n_l1___9(X₀, X₁) → n_l2___8(X₀, X₁) :|: 1 ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 2 ≤ X₁ ∧ X₁ ≤ 255 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 255 ∧ X₀+X₁ ≤ 254 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:
new bound:
511 {O(1)}
MPRF for transition t₂₅₂: n_l2___8(X₀, X₁) → n_l3___7(X₀, X₁) :|: 2 ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:
new bound:
510 {O(1)}
MPRF for transition t₂₅₆: n_l3___7(X₀, X₁) → n_l1___9(X₀, X₁+1) :|: 2 ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 of depth 1:
new bound:
510 {O(1)}
MPRF for transition t₂₄₄: n_l1___3(X₀, X₁) → n_l2___2(X₀, X₁) :|: X₁ ≤ 254 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:
new bound:
254 {O(1)}
MPRF for transition t₂₅₀: n_l2___2(X₀, X₁) → n_l4___1(0, X₁) :|: X₁ ≤ 253 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:
new bound:
253 {O(1)}
MPRF for transition t₂₅₇: n_l4___1(X₀, X₁) → n_l1___3(0, X₁-1) :|: X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ of depth 1:
new bound:
253 {O(1)}
CFR: Improvement to new bound with the following program:
new bound:
Infinite
cfr-program:
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l5, l6, l7, n_l1___3, n_l1___6, n_l1___9, n_l2___13, n_l2___2, n_l2___5, n_l2___8, n_l3___11, n_l3___12, n_l3___4, n_l3___7, n_l4___1, n_l4___10
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₃: l1(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
t₄: l1(X₀, X₁) → l5(X₀, X₁) :|: 255 ≤ X₁
t₂₄₃: l1(X₀, X₁) → n_l2___13(X₀, X₁) :|: 1 ≤ X₁ ∧ X₁ ≤ 254
t₁₀: l5(X₀, X₁) → l7(X₀, X₁)
t₁: l6(X₀, X₁) → l1(X₁, X₀)
t₂₇₁: n_l1___3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0 ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₄₄: n_l1___3(X₀, X₁) → n_l2___2(X₀, X₁) :|: X₁ ≤ 254 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₇₅: n_l1___6(X₀, X₁) → l5(X₀, X₁) :|: 255 ≤ X₁ ∧ X₁ ≤ 255 ∧ X₁ ≤ 254+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₄₅: n_l1___6(X₀, X₁) → n_l2___5(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ X₁ ≤ 255 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 255 ∧ X₁ ≤ 254+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₇₆: n_l1___9(X₀, X₁) → l5(X₀, X₁) :|: 255 ≤ X₁ ∧ X₁ ≤ 255 ∧ X₀+X₁ ≤ 254 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₄₆: n_l1___9(X₀, X₁) → n_l2___8(X₀, X₁) :|: 1 ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 2 ≤ X₁ ∧ X₁ ≤ 255 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 255 ∧ X₀+X₁ ≤ 254 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₄₇: n_l2___13(X₀, X₁) → n_l3___11(X₀, X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁
t₂₄₈: n_l2___13(X₀, X₁) → n_l3___12(X₀, X₁) :|: 1+X₀ ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁
t₂₄₉: n_l2___13(X₀, X₁) → n_l4___10(0, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁
t₂₅₀: n_l2___2(X₀, X₁) → n_l4___1(0, X₁) :|: X₁ ≤ 253 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₅₁: n_l2___5(X₀, X₁) → n_l3___4(X₀, X₁) :|: 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₅₂: n_l2___8(X₀, X₁) → n_l3___7(X₀, X₁) :|: 2 ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₅₃: n_l3___11(X₀, X₁) → n_l1___6(X₀, X₁+1) :|: 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₅₄: n_l3___12(X₀, X₁) → n_l1___9(X₀, X₁+1) :|: 1+X₀ ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₅₅: n_l3___4(X₀, X₁) → n_l1___6(X₀, X₁+1) :|: 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₅₆: n_l3___7(X₀, X₁) → n_l1___9(X₀, X₁+1) :|: 2 ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₅₇: n_l4___1(X₀, X₁) → n_l1___3(0, X₁-1) :|: X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₅₈: n_l4___10(X₀, X₁) → n_l1___3(0, X₁-1) :|: X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254+X₀ ∧ X₀+X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
CFR: Improvement to new bound with the following program:
new bound:
3821 {O(1)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l5, l6, l7, n_l1___3, n_l1___6, n_l1___9, n_l2___13, n_l2___2, n_l2___5, n_l2___8, n_l3___11, n_l3___12, n_l3___4, n_l3___7, n_l4___1, n_l4___10
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₃: l1(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0
t₄: l1(X₀, X₁) → l5(X₀, X₁) :|: 255 ≤ X₁
t₂₄₃: l1(X₀, X₁) → n_l2___13(X₀, X₁) :|: 1 ≤ X₁ ∧ X₁ ≤ 254
t₁₀: l5(X₀, X₁) → l7(X₀, X₁)
t₁: l6(X₀, X₁) → l1(X₁, X₀)
t₂₇₁: n_l1___3(X₀, X₁) → l5(X₀, X₁) :|: X₁ ≤ 0 ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₄₄: n_l1___3(X₀, X₁) → n_l2___2(X₀, X₁) :|: X₁ ≤ 254 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₇₅: n_l1___6(X₀, X₁) → l5(X₀, X₁) :|: 255 ≤ X₁ ∧ X₁ ≤ 255 ∧ X₁ ≤ 254+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₄₅: n_l1___6(X₀, X₁) → n_l2___5(X₀, X₁) :|: 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ X₁ ≤ 255 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 255 ∧ X₁ ≤ 254+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₇₆: n_l1___9(X₀, X₁) → l5(X₀, X₁) :|: 255 ≤ X₁ ∧ X₁ ≤ 255 ∧ X₀+X₁ ≤ 254 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₄₆: n_l1___9(X₀, X₁) → n_l2___8(X₀, X₁) :|: 1 ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 2 ≤ X₁ ∧ X₁ ≤ 255 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 255 ∧ X₀+X₁ ≤ 254 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₄₇: n_l2___13(X₀, X₁) → n_l3___11(X₀, X₁) :|: 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁
t₂₄₈: n_l2___13(X₀, X₁) → n_l3___12(X₀, X₁) :|: 1+X₀ ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁
t₂₄₉: n_l2___13(X₀, X₁) → n_l4___10(0, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁
t₂₅₀: n_l2___2(X₀, X₁) → n_l4___1(0, X₁) :|: X₁ ≤ 253 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₅₁: n_l2___5(X₀, X₁) → n_l3___4(X₀, X₁) :|: 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₅₂: n_l2___8(X₀, X₁) → n_l3___7(X₀, X₁) :|: 2 ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₅₃: n_l3___11(X₀, X₁) → n_l1___6(X₀, X₁+1) :|: 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₅₄: n_l3___12(X₀, X₁) → n_l1___9(X₀, X₁+1) :|: 1+X₀ ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₅₅: n_l3___4(X₀, X₁) → n_l1___6(X₀, X₁+1) :|: 2 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₁ ≤ 253+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₅₆: n_l3___7(X₀, X₁) → n_l1___9(X₀, X₁+1) :|: 2 ≤ X₁ ∧ 1+X₀ ≤ 0 ∧ X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254 ∧ X₀+X₁ ≤ 253 ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
t₂₅₇: n_l4___1(X₀, X₁) → n_l1___3(0, X₁-1) :|: X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 253 ∧ X₁ ≤ 253+X₀ ∧ X₀+X₁ ≤ 253 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₅₈: n_l4___10(X₀, X₁) → n_l1___3(0, X₁-1) :|: X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 254 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 254 ∧ X₁ ≤ 254+X₀ ∧ X₀+X₁ ≤ 254 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
All Bounds
Timebounds
Overall timebound:3836 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁₀: 1 {O(1)}
t₂₄₃: 1 {O(1)}
t₂₄₄: 254 {O(1)}
t₂₄₅: 510 {O(1)}
t₂₄₆: 511 {O(1)}
t₂₄₇: 1 {O(1)}
t₂₄₈: 1 {O(1)}
t₂₄₉: 1 {O(1)}
t₂₅₀: 253 {O(1)}
t₂₅₁: 510 {O(1)}
t₂₅₂: 510 {O(1)}
t₂₅₃: 1 {O(1)}
t₂₅₄: 1 {O(1)}
t₂₅₅: 510 {O(1)}
t₂₅₆: 510 {O(1)}
t₂₅₇: 253 {O(1)}
t₂₅₈: 1 {O(1)}
t₂₇₁: 1 {O(1)}
t₂₇₅: 1 {O(1)}
t₂₇₆: 1 {O(1)}
Costbounds
Overall costbound: 3836 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁₀: 1 {O(1)}
t₂₄₃: 1 {O(1)}
t₂₄₄: 254 {O(1)}
t₂₄₅: 510 {O(1)}
t₂₄₆: 511 {O(1)}
t₂₄₇: 1 {O(1)}
t₂₄₈: 1 {O(1)}
t₂₄₉: 1 {O(1)}
t₂₅₀: 253 {O(1)}
t₂₅₁: 510 {O(1)}
t₂₅₂: 510 {O(1)}
t₂₅₃: 1 {O(1)}
t₂₅₄: 1 {O(1)}
t₂₅₅: 510 {O(1)}
t₂₅₆: 510 {O(1)}
t₂₅₇: 253 {O(1)}
t₂₅₈: 1 {O(1)}
t₂₇₁: 1 {O(1)}
t₂₇₅: 1 {O(1)}
t₂₇₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₃, X₀: X₁ {O(n)}
t₃, X₁: X₀ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₀ {O(n)}
t₁₀, X₀: 6⋅X₁ {O(n)}
t₁₀, X₁: 2⋅X₀+510 {O(n)}
t₂₄₃, X₀: X₁ {O(n)}
t₂₄₃, X₁: 254 {O(1)}
t₂₄₄, X₀: 0 {O(1)}
t₂₄₄, X₁: 253 {O(1)}
t₂₄₅, X₀: X₁ {O(n)}
t₂₄₅, X₁: 254 {O(1)}
t₂₄₆, X₀: X₁ {O(n)}
t₂₄₆, X₁: 254 {O(1)}
t₂₄₇, X₀: X₁ {O(n)}
t₂₄₇, X₁: 254 {O(1)}
t₂₄₈, X₀: X₁ {O(n)}
t₂₄₈, X₁: 254 {O(1)}
t₂₄₉, X₀: 0 {O(1)}
t₂₄₉, X₁: 254 {O(1)}
t₂₅₀, X₀: 0 {O(1)}
t₂₅₀, X₁: 253 {O(1)}
t₂₅₁, X₀: X₁ {O(n)}
t₂₅₁, X₁: 254 {O(1)}
t₂₅₂, X₀: X₁ {O(n)}
t₂₅₂, X₁: 254 {O(1)}
t₂₅₃, X₀: X₁ {O(n)}
t₂₅₃, X₁: 255 {O(1)}
t₂₅₄, X₀: X₁ {O(n)}
t₂₅₄, X₁: 255 {O(1)}
t₂₅₅, X₀: X₁ {O(n)}
t₂₅₅, X₁: 255 {O(1)}
t₂₅₆, X₀: X₁ {O(n)}
t₂₅₆, X₁: 255 {O(1)}
t₂₅₇, X₀: 0 {O(1)}
t₂₅₇, X₁: 252 {O(1)}
t₂₅₈, X₀: 0 {O(1)}
t₂₅₈, X₁: 253 {O(1)}
t₂₇₁, X₀: 0 {O(1)}
t₂₇₁, X₁: 0 {O(1)}
t₂₇₅, X₀: 2⋅X₁ {O(n)}
t₂₇₅, X₁: 255 {O(1)}
t₂₇₆, X₀: 2⋅X₁ {O(n)}
t₂₇₆, X₁: 255 {O(1)}