Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(1, 1, 0, 1, 1, X₅)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 29
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, 1, X₃, X₄, 1) :|: 30 ≤ X₃
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃+10, X₄, X₅) :|: X₄ ≤ 12 ∧ 10 ≤ X₄
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃+1, X₄, X₅) :|: 13 ≤ X₄
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃+1, X₄, X₅) :|: X₄ ≤ 9
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃+2, X₄-10, X₅) :|: X₃ ≤ X₄
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, G, X₅) :|: X₄+1 ≤ X₃ ∧ 6 ≤ X₄
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄+2, X₅) :|: X₄+1 ≤ X₃ ∧ X₄ ≤ 5
Preprocessing
Eliminate variables {X₀,X₁,X₂,X₅} that do not contribute to the problem
Found invariant 1 ≤ X₀ for location l2
Found invariant 0 ≤ 9+X₁ ∧ 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 18 ≤ X₁ ∧ 48 ≤ X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ 30 ≤ X₀ for location l4
Found invariant 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: G
Locations: l0, l1, l2, l3, l4
Transitions:
t₁₉: l0(X₀, X₁) → l1(1, 1)
t₂₀: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 29 ∧ 0 ≤ 9+X₁ ∧ 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ 1 ≤ X₀
t₂₁: l1(X₀, X₁) → l4(X₀, X₁) :|: 30 ≤ X₀ ∧ 0 ≤ 9+X₁ ∧ 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ 1 ≤ X₀
t₂₂: l2(X₀, X₁) → l3(X₀+10, X₁) :|: X₁ ≤ 12 ∧ 10 ≤ X₁ ∧ 1 ≤ X₀
t₂₃: l2(X₀, X₁) → l3(X₀+1, X₁) :|: 13 ≤ X₁ ∧ 1 ≤ X₀
t₂₄: l2(X₀, X₁) → l3(X₀+1, X₁) :|: X₁ ≤ 9 ∧ 1 ≤ X₀
t₂₅: l3(X₀, X₁) → l1(X₀+2, X₁-10) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₆: l3(X₀, X₁) → l2(X₀, G) :|: X₁+1 ≤ X₀ ∧ 6 ≤ X₁ ∧ 1 ≤ X₀
t₂₇: l3(X₀, X₁) → l2(X₀, X₁+2) :|: X₁+1 ≤ X₀ ∧ X₁ ≤ 5 ∧ 1 ≤ X₀
MPRF for transition t₂₀: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 29 ∧ 0 ≤ 9+X₁ ∧ 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
31 {O(1)}
MPRF for transition t₂₅: l3(X₀, X₁) → l1(X₀+2, X₁-10) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
31 {O(1)}
Chain transitions t₂₅: l3→l1 and t₂₁: l1→l4 to t₁₃₈: l3→l4
Chain transitions t₁₉: l0→l1 and t₂₁: l1→l4 to t₁₃₉: l0→l4
Chain transitions t₁₉: l0→l1 and t₂₀: l1→l3 to t₁₄₀: l0→l3
Chain transitions t₂₅: l3→l1 and t₂₀: l1→l3 to t₁₄₁: l3→l3
Chain transitions t₂₇: l3→l2 and t₂₄: l2→l3 to t₁₄₂: l3→l3
Chain transitions t₂₆: l3→l2 and t₂₄: l2→l3 to t₁₄₃: l3→l3
Chain transitions t₂₆: l3→l2 and t₂₃: l2→l3 to t₁₄₄: l3→l3
Chain transitions t₂₇: l3→l2 and t₂₃: l2→l3 to t₁₄₅: l3→l3
Chain transitions t₂₆: l3→l2 and t₂₂: l2→l3 to t₁₄₆: l3→l3
Chain transitions t₂₇: l3→l2 and t₂₂: l2→l3 to t₁₄₇: l3→l3
Analysing control-flow refined program
Cut unsatisfiable transition t₁₃₉: l0→l4
Cut unsatisfiable transition t₁₄₅: l3→l3
Cut unsatisfiable transition t₁₄₇: l3→l3
Found invariant 1 ≤ X₀ for location l2
Found invariant 0 ≤ 9+X₁ ∧ 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 18 ≤ X₁ ∧ 48 ≤ X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ 30 ≤ X₀ for location l4
Found invariant 1 ≤ X₀ for location l3
MPRF for transition t₁₄₁: l3(X₀, X₁) -{2}> l3(2+X₀, X₁-10) :|: X₀ ≤ X₁ ∧ X₀ ≤ 27 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ 1+X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
225 {O(1)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₃₇₄: n_l3___13→l1
Cut unsatisfiable transition t₃₇₇: n_l3___9→l1
Found invariant X₀ ≤ 29 ∧ 7 ≤ X₀ for location n_l2___15
Found invariant 14 ≤ X₀ for location n_l2___6
Found invariant X₁ ≤ 7 ∧ 1+X₁ ≤ X₀ ∧ 8 ≤ X₀ for location n_l2___7
Found invariant X₁ ≤ 7 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 24 ∧ 0 ≤ 7+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 17 ∧ 1 ≤ X₀ for location n_l2___14
Found invariant X₁ ≤ 7 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 25 ∧ 0 ≤ 7+X₁ ∧ 0 ≤ 3+X₀+X₁ ∧ X₀ ≤ 11+X₁ ∧ X₀ ≤ 18 ∧ 2 ≤ X₀ for location n_l3___5
Found invariant X₀ ≤ 19 ∧ 14 ≤ X₀ for location n_l2___1
Found invariant X₁ ≤ 7 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 23 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 9+X₁ ∧ X₀ ≤ 16 ∧ 2 ≤ X₀ for location n_l2___3
Found invariant 13 ≤ X₁ ∧ 21 ≤ X₀+X₁ ∧ 8 ≤ X₀ for location n_l3___12
Found invariant X₁ ≤ 9 ∧ X₁ ≤ 1+X₀ ∧ 8 ≤ X₀ for location n_l3___11
Found invariant X₁ ≤ 12 ∧ 5+X₁ ≤ X₀ ∧ 10 ≤ X₁ ∧ 27 ≤ X₀+X₁ ∧ 17 ≤ X₀ for location n_l3___13
Found invariant 13 ≤ X₁ ∧ 21 ≤ X₀+X₁ ∧ X₀ ≤ 6+X₁ ∧ X₀ ≤ 19 ∧ 8 ≤ X₀ for location n_l3___2
Found invariant X₁ ≤ 9 ∧ 6+X₁ ≤ X₀ ∧ 15 ≤ X₀ for location n_l3___9
Found invariant 0 ≤ 9+X₁ ∧ 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant 18 ≤ X₁ ∧ 48 ≤ X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ 30 ≤ X₀ for location l4
Found invariant 17 ≤ X₀ for location n_l2___10
Found invariant 8 ≤ X₀ for location n_l2___8
Found invariant 0 ≤ 9+X₁ ∧ 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ X₀ ≤ 29 ∧ 1 ≤ X₀ for location l3
Found invariant X₀ ≤ 18 ∧ 7 ≤ X₀ for location n_l2___4
knowledge_propagation leads to new time bound 31 {O(1)} for transition t₃₅₀: l3(X₀, X₁) → n_l2___14(X₀, X₁+2) :|: 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ X₀ ≤ 29 ∧ 1+X₁ ≤ X₀ ∧ X₁ ≤ 5 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ 9+X₁ ∧ 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ X₀ ≤ 29 ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound 31 {O(1)} for transition t₃₅₁: l3(X₀, X₁) → n_l2___15(X₀, NoDet0) :|: 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ X₀ ≤ 29 ∧ 1+X₁ ≤ X₀ ∧ 6 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ 9+X₁ ∧ 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ X₀ ≤ 29 ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound 31 {O(1)} for transition t₃₃₁: n_l2___14(X₀, X₁) → n_l3___5(X₀+1, X₁) :|: 0 ≤ 4+X₀+X₁ ∧ X₁ ≤ 1+X₀ ∧ X₁ ≤ 7 ∧ X₀ ≤ 10+X₁ ∧ X₁ ≤ 9 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 7 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 24 ∧ 0 ≤ 7+X₁ ∧ 0 ≤ 4+X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 17 ∧ 1 ≤ X₀
knowledge_propagation leads to new time bound 31 {O(1)} for transition t₃₃₂: n_l2___15(X₀, X₁) → n_l3___11(X₀+1, X₁) :|: X₀ ≤ 29 ∧ 7 ≤ X₀ ∧ X₁ ≤ 9 ∧ 1 ≤ X₀ ∧ X₀ ≤ 29 ∧ 7 ≤ X₀
knowledge_propagation leads to new time bound 31 {O(1)} for transition t₃₃₃: n_l2___15(X₀, X₁) → n_l3___12(X₀+1, X₁) :|: X₀ ≤ 29 ∧ 7 ≤ X₀ ∧ 13 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 29 ∧ 7 ≤ X₀
knowledge_propagation leads to new time bound 31 {O(1)} for transition t₃₃₄: n_l2___15(X₀, X₁) → n_l3___13(X₀+10, X₁) :|: X₀ ≤ 29 ∧ 7 ≤ X₀ ∧ 10 ≤ X₁ ∧ X₁ ≤ 12 ∧ 1 ≤ X₀ ∧ X₀ ≤ 29 ∧ 7 ≤ X₀
MPRF for transition t₃₂₅: n_l2___1(X₀, X₁) → n_l3___12(X₀+1, X₁) :|: X₀ ≤ 29 ∧ 14 ≤ X₀ ∧ 13 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 19 ∧ 14 ≤ X₀ of depth 1:
new bound:
1490 {O(1)}
MPRF for transition t₃₂₆: n_l2___1(X₀, X₁) → n_l3___13(X₀+10, X₁) :|: X₀ ≤ 29 ∧ 14 ≤ X₀ ∧ 10 ≤ X₁ ∧ X₁ ≤ 12 ∧ 1 ≤ X₀ ∧ X₀ ≤ 19 ∧ 14 ≤ X₀ of depth 1:
new bound:
5287 {O(1)}
MPRF for transition t₃₂₇: n_l2___1(X₀, X₁) → n_l3___9(X₀+1, X₁) :|: X₀ ≤ 29 ∧ 14 ≤ X₀ ∧ X₁ ≤ 9 ∧ 1 ≤ X₀ ∧ X₀ ≤ 19 ∧ 14 ≤ X₀ of depth 1:
new bound:
705 {O(1)}
MPRF for transition t₃₃₅: n_l2___3(X₀, X₁) → n_l3___5(X₀+1, X₁) :|: 0 ≤ 4+X₀+X₁ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 7 ∧ X₀ ≤ 10+X₁ ∧ X₁ ≤ 9 ∧ 1 ≤ X₀ ∧ X₁ ≤ 7 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 23 ∧ 0 ≤ 5+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ X₀ ≤ 9+X₁ ∧ X₀ ≤ 16 ∧ 2 ≤ X₀ of depth 1:
new bound:
9101 {O(1)}
MPRF for transition t₃₃₆: n_l2___4(X₀, X₁) → n_l3___11(X₀+1, X₁) :|: X₀ ≤ 21 ∧ 7 ≤ X₀ ∧ X₁ ≤ 9 ∧ 1 ≤ X₀ ∧ X₀ ≤ 18 ∧ 7 ≤ X₀ of depth 1:
new bound:
25 {O(1)}
MPRF for transition t₃₃₇: n_l2___4(X₀, X₁) → n_l3___13(X₀+10, X₁) :|: X₀ ≤ 21 ∧ 7 ≤ X₀ ∧ 10 ≤ X₁ ∧ X₁ ≤ 12 ∧ 1 ≤ X₀ ∧ X₀ ≤ 18 ∧ 7 ≤ X₀ of depth 1:
new bound:
551 {O(1)}
MPRF for transition t₃₃₈: n_l2___4(X₀, X₁) → n_l3___2(X₀+1, X₁) :|: X₀ ≤ 21 ∧ 7 ≤ X₀ ∧ 13 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 18 ∧ 7 ≤ X₀ of depth 1:
new bound:
1072 {O(1)}
MPRF for transition t₃₅₂: n_l3___2(X₀, X₁) → n_l2___1(X₀, NoDet0) :|: 6 ≤ X₁ ∧ 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ X₀ ≤ 29 ∧ 2 ≤ X₀ ∧ 13 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ 6 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 13 ≤ X₁ ∧ 21 ≤ X₀+X₁ ∧ X₀ ≤ 6+X₁ ∧ X₀ ≤ 19 ∧ 8 ≤ X₀ of depth 1:
new bound:
16479 {O(1)}
MPRF for transition t₃₅₃: n_l3___5(X₀, X₁) → n_l2___3(X₀, X₁+2) :|: 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ X₀ ≤ 29 ∧ 2 ≤ X₀ ∧ X₁ ≤ 9 ∧ 1+X₁ ≤ X₀ ∧ X₁ ≤ 5 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 7 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 25 ∧ 0 ≤ 7+X₁ ∧ 0 ≤ 3+X₀+X₁ ∧ X₀ ≤ 11+X₁ ∧ X₀ ≤ 18 ∧ 2 ≤ X₀ of depth 1:
new bound:
2575 {O(1)}
MPRF for transition t₃₅₄: n_l3___5(X₀, X₁) → n_l2___4(X₀, NoDet0) :|: 0 ≤ 6+X₀+X₁ ∧ X₀ ≤ 12+X₁ ∧ X₀ ≤ 29 ∧ 2 ≤ X₀ ∧ X₁ ≤ 9 ∧ 1+X₁ ≤ X₀ ∧ 6 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 7 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 25 ∧ 0 ≤ 7+X₁ ∧ 0 ≤ 3+X₀+X₁ ∧ X₀ ≤ 11+X₁ ∧ X₀ ≤ 18 ∧ 2 ≤ X₀ of depth 1:
new bound:
55454 {O(1)}
MPRF for transition t₃₇₂: n_l3___11(X₀, X₁) → l1(X₀+2, X₁-10) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ 1+X₀ ∧ 8 ≤ X₀ of depth 1:
new bound:
16941 {O(1)}
MPRF for transition t₃₇₃: n_l3___12(X₀, X₁) → l1(X₀+2, X₁-10) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 13 ≤ X₁ ∧ 21 ≤ X₀+X₁ ∧ 8 ≤ X₀ of depth 1:
new bound:
2418 {O(1)}
MPRF for transition t₃₇₅: n_l3___2(X₀, X₁) → l1(X₀+2, X₁-10) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 13 ≤ X₁ ∧ 21 ≤ X₀+X₁ ∧ X₀ ≤ 6+X₁ ∧ X₀ ≤ 19 ∧ 8 ≤ X₀ of depth 1:
new bound:
691878 {O(1)}
MPRF for transition t₃₇₆: n_l3___5(X₀, X₁) → l1(X₀+2, X₁-10) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ 7 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 25 ∧ 0 ≤ 7+X₁ ∧ 0 ≤ 3+X₀+X₁ ∧ X₀ ≤ 11+X₁ ∧ X₀ ≤ 18 ∧ 2 ≤ X₀ of depth 1:
new bound:
280 {O(1)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: 31 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: 31 {O(1)}
t₂₆: inf {Infinity}
t₂₇: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: 31 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₃: inf {Infinity}
t₂₄: inf {Infinity}
t₂₅: 31 {O(1)}
t₂₆: inf {Infinity}
t₂₇: inf {Infinity}
Sizebounds
t₁₉, X₀: 1 {O(1)}
t₁₉, X₁: 1 {O(1)}
t₂₀, X₀: 29 {O(1)}
t₂₂, X₁: 12 {O(1)}