Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(1, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 100 < X₁
t₅: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 100
t₈: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₆: l5(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁-10, X₂, X₃)
t₇: l6(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+11, X₂, X₃)
Preprocessing
Eliminate variables {X₂} that do not contribute to the problem
Found invariant X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀ for location l6
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l7
Found invariant 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l5
Found invariant 0 ≤ X₀ for location l1
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₈: l0(X₀, X₁, X₃) → l2(X₀, X₁, X₃)
t₁₉: l1(X₀, X₁, X₃) → l3(X₀, X₁, X₃) :|: 0 < X₀ ∧ 0 ≤ X₀
t₂₀: l1(X₀, X₁, X₃) → l4(X₀, X₁, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₁: l2(X₀, X₁, X₃) → l1(1, X₃, X₃)
t₂₂: l3(X₀, X₁, X₃) → l5(X₀, X₁, X₃) :|: 100 < X₁ ∧ 1 ≤ X₀
t₂₃: l3(X₀, X₁, X₃) → l6(X₀, X₁, X₃) :|: X₁ ≤ 100 ∧ 1 ≤ X₀
t₂₄: l4(X₀, X₁, X₃) → l7(X₀, X₁, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₅: l5(X₀, X₁, X₃) → l1(X₀-1, X₁-10, X₃) :|: 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₆: l6(X₀, X₁, X₃) → l1(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀
MPRF for transition t₂₃: l3(X₀, X₁, X₃) → l6(X₀, X₁, X₃) :|: X₁ ≤ 100 ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+101 {O(n)}
MPRF:
l3 [10⋅X₀+91-X₁ ]
l5 [10⋅X₀+91-X₁ ]
l6 [10⋅X₀+90-X₁ ]
l1 [10⋅X₀+91-X₁ ]
MPRF for transition t₂₆: l6(X₀, X₁, X₃) → l1(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+101 {O(n)}
MPRF:
l3 [10⋅X₀+91-X₁ ]
l5 [10⋅X₀+91-X₁ ]
l6 [10⋅X₀+91-X₁ ]
l1 [10⋅X₀+91-X₁ ]
MPRF for transition t₁₉: l1(X₀, X₁, X₃) → l3(X₀, X₁, X₃) :|: 0 < X₀ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃+204⋅X₃+10405 {O(n^2)}
MPRF:
l3 [X₀ ]
l6 [X₀ ]
l5 [X₀ ]
l1 [X₀+1 ]
MPRF for transition t₂₂: l3(X₀, X₁, X₃) → l5(X₀, X₁, X₃) :|: 100 < X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃+203⋅X₃+10303 {O(n^2)}
MPRF:
l3 [X₀ ]
l6 [X₀ ]
l5 [X₀-1 ]
l1 [X₀ ]
MPRF for transition t₂₅: l5(X₀, X₁, X₃) → l1(X₀-1, X₁-10, X₃) :|: 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃⋅X₃+203⋅X₃+10303 {O(n^2)}
MPRF:
l3 [X₀ ]
l6 [X₀ ]
l5 [X₀ ]
l1 [X₀ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₂₀: l1→l4
Cut unsatisfiable transition t₉₉: n_l1___4→l4
Cut unsatisfiable transition t₁₀₀: n_l1___6→l4
Cut unsatisfiable transition t₁₀₁: n_l1___9→l4
Found invariant X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___6
Found invariant X₃ ≤ 89 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 189 ∧ X₃ ≤ 87+X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 98+X₀ ∧ 2 ≤ X₀ for location n_l6___1
Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___9
Found invariant 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l5___11
Found invariant X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ for location n_l1___4
Found invariant X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___10
Found invariant X₃ ≤ 100 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 200 ∧ X₃ ≤ 99+X₀ ∧ X₀+X₃ ≤ 101 ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ X₀+X₁ ≤ 101 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l6___14
Found invariant X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ for location n_l3___3
Found invariant X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___5
Found invariant 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location n_l1___13
Found invariant X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l5___2
Found invariant 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l3___12
Found invariant 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l7
Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___8
Found invariant X₃ ≤ X₁ ∧ 101 ≤ X₃ ∧ 202 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 102 ≤ X₀+X₃ ∧ 100+X₀ ≤ X₃ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l5___15
Found invariant X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l5___7
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l1
Found invariant 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___16
MPRF for transition t₇₁: n_l1___4(X₀, X₁, X₃) → n_l3___3(X₀, X₁, X₃) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ 0 < X₀ ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₃+123 {O(n)}
MPRF:
n_l3___3 [101-X₁ ]
n_l6___1 [101-X₁ ]
n_l1___4 [112-X₁ ]
MPRF for transition t₇₉: n_l3___3(X₀, X₁, X₃) → n_l6___1(X₀, X₁, X₃) :|: X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₃+223 {O(n)}
MPRF:
n_l3___3 [212-X₁-X₃ ]
n_l6___1 [201-X₁-X₃ ]
n_l1___4 [212-X₁-X₃ ]
MPRF for transition t₈₇: n_l6___1(X₀, X₁, X₃) → n_l1___4(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ 89 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 189 ∧ X₃ ≤ 87+X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 98+X₀ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₃+112 {O(n)}
MPRF:
n_l3___3 [101-X₁ ]
n_l6___1 [101-X₁ ]
n_l1___4 [101-X₁ ]
MPRF for transition t₆₉: n_l1___13(X₀, X₁, X₃) → n_l3___12(X₀, X₁, X₃) :|: 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 0 < X₀ ∧ 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₃+114 {O(n)}
MPRF:
n_l3___12 [X₀ ]
n_l3___5 [X₀ ]
n_l3___8 [X₀-1 ]
n_l5___11 [X₀ ]
n_l1___13 [X₀+1 ]
n_l5___7 [X₀-1 ]
n_l1___6 [X₀ ]
n_l6___10 [X₀ ]
n_l1___9 [X₀-1 ]
MPRF for transition t₇₂: n_l1___6(X₀, X₁, X₃) → n_l3___5(X₀, X₁, X₃) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 0 < X₀ ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
910⋅X₃+122213 {O(n)}
MPRF:
n_l3___12 [910⋅X₀+10⋅X₁ ]
n_l3___5 [910⋅X₀+9191-91⋅X₁ ]
n_l3___8 [910⋅X₀+9282-91⋅X₁ ]
n_l5___11 [910⋅X₀+10⋅X₁-1010 ]
n_l1___13 [910⋅X₀+10⋅X₁ ]
n_l5___7 [910⋅X₀+9282-91⋅X₁ ]
n_l1___6 [910⋅X₀+9282-91⋅X₁ ]
n_l6___10 [910⋅X₀+9191-91⋅X₁ ]
n_l1___9 [910⋅X₀+9282-91⋅X₁ ]
MPRF for transition t₇₃: n_l1___9(X₀, X₁, X₃) → n_l3___8(X₀, X₁, X₃) :|: 101 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ 0 < X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
10⋅X₃+1352 {O(n)}
MPRF:
n_l3___12 [10⋅X₀+20 ]
n_l3___5 [10⋅X₀+111-X₁ ]
n_l3___8 [10⋅X₀+111-X₁ ]
n_l5___11 [10⋅X₀+10 ]
n_l1___13 [10⋅X₀+20 ]
n_l5___7 [10⋅X₀+111-X₁ ]
n_l1___6 [10⋅X₀+111-X₁ ]
n_l6___10 [10⋅X₀+111-X₁ ]
n_l1___9 [10⋅X₀+112-X₁ ]
MPRF for transition t₇₄: n_l3___12(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+115 {O(n)}
MPRF:
n_l3___12 [X₀+1 ]
n_l3___5 [X₀+1 ]
n_l3___8 [X₀ ]
n_l5___11 [X₀ ]
n_l1___13 [X₀+1 ]
n_l5___7 [X₀ ]
n_l1___6 [X₀+1 ]
n_l6___10 [X₀+1 ]
n_l1___9 [X₀ ]
MPRF for transition t₇₅: n_l3___12(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+115 {O(n)}
MPRF:
n_l3___12 [X₀ ]
n_l3___5 [X₀-1 ]
n_l3___8 [X₀-2 ]
n_l5___11 [X₀-1 ]
n_l1___13 [X₀ ]
n_l5___7 [X₀-2 ]
n_l1___6 [X₀-1 ]
n_l6___10 [X₀-1 ]
n_l1___9 [X₀-2 ]
MPRF for transition t₈₀: n_l3___5(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+115 {O(n)}
MPRF:
n_l3___12 [X₀+1 ]
n_l3___5 [X₀+1 ]
n_l3___8 [X₀ ]
n_l5___11 [X₀ ]
n_l1___13 [X₀+1 ]
n_l5___7 [X₀ ]
n_l1___6 [X₀+1 ]
n_l6___10 [X₀+1 ]
n_l1___9 [X₀ ]
MPRF for transition t₈₁: n_l3___5(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
9⋅X₃+1219 {O(n)}
MPRF:
n_l3___12 [9⋅X₀ ]
n_l3___5 [9⋅X₀+92-X₁ ]
n_l3___8 [9⋅X₀+93-X₁ ]
n_l5___11 [9⋅X₀-9 ]
n_l1___13 [9⋅X₀ ]
n_l5___7 [9⋅X₀+93-X₁ ]
n_l1___6 [9⋅X₀+92-X₁ ]
n_l6___10 [9⋅X₀+91-X₁ ]
n_l1___9 [9⋅X₀+93-X₁ ]
MPRF for transition t₈₂: n_l3___8(X₀, X₁, X₃) → n_l5___7(X₀, X₁, X₃) :|: X₁ ≤ 111 ∧ 101 ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
101⋅X₃+11615 {O(n)}
MPRF:
n_l3___12 [101⋅X₀-91 ]
n_l3___5 [101⋅X₀-X₁ ]
n_l3___8 [101⋅X₀-X₁-90 ]
n_l5___11 [101⋅X₀-101 ]
n_l1___13 [101⋅X₀ ]
n_l5___7 [101⋅X₀-X₁-91 ]
n_l1___6 [101⋅X₀-X₁ ]
n_l6___10 [101⋅X₀-X₁ ]
n_l1___9 [101⋅X₀-X₁-90 ]
MPRF for transition t₈₃: n_l5___11(X₀, X₁, X₃) → n_l1___13(X₀-1, X₁-10, X₃) :|: 100 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+114 {O(n)}
MPRF:
n_l3___12 [X₀ ]
n_l3___5 [X₀ ]
n_l3___8 [X₀-1 ]
n_l5___11 [X₀ ]
n_l1___13 [X₀ ]
n_l5___7 [X₀-1 ]
n_l1___6 [X₀ ]
n_l6___10 [X₀ ]
n_l1___9 [X₀-1 ]
MPRF for transition t₈₆: n_l5___7(X₀, X₁, X₃) → n_l1___6(X₀-1, X₁-10, X₃) :|: X₁ ≤ 111 ∧ 101 ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
101⋅X₃+11615 {O(n)}
MPRF:
n_l3___12 [101⋅X₀ ]
n_l3___5 [101⋅X₀-X₁ ]
n_l3___8 [101⋅X₀-X₁-90 ]
n_l5___11 [101⋅X₀-101 ]
n_l1___13 [101⋅X₀ ]
n_l5___7 [101⋅X₀-X₁-90 ]
n_l1___6 [101⋅X₀-X₁ ]
n_l6___10 [101⋅X₀-X₁ ]
n_l1___9 [101⋅X₀-X₁-90 ]
MPRF for transition t₈₈: n_l6___10(X₀, X₁, X₃) → n_l1___9(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
10⋅X₃+1332 {O(n)}
MPRF:
n_l3___12 [10⋅X₀ ]
n_l3___5 [10⋅X₀+91-X₁ ]
n_l3___8 [10⋅X₀+91-X₁ ]
n_l5___11 [10⋅X₀-10 ]
n_l1___13 [10⋅X₀ ]
n_l5___7 [10⋅X₀+91-X₁ ]
n_l1___6 [10⋅X₀+91-X₁ ]
n_l6___10 [10⋅X₀+91-X₁ ]
n_l1___9 [10⋅X₀+91-X₁ ]
CFR: Improvement to new bound with the following program:
new bound:
1150⋅X₃+150377 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₃
Temp_Vars:
Locations: l0, l1, l2, l4, l7, n_l1___13, n_l1___4, n_l1___6, n_l1___9, n_l3___12, n_l3___16, n_l3___3, n_l3___5, n_l3___8, n_l5___11, n_l5___15, n_l5___2, n_l5___7, n_l6___1, n_l6___10, n_l6___14
Transitions:
t₁₈: l0(X₀, X₁, X₃) → l2(X₀, X₁, X₃)
t₇₀: l1(X₀, X₁, X₃) → n_l3___16(X₀, X₁, X₃) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 < X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₁: l2(X₀, X₁, X₃) → l1(1, X₃, X₃)
t₂₄: l4(X₀, X₁, X₃) → l7(X₀, X₁, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₉₈: n_l1___13(X₀, X₁, X₃) → l4(X₀, X₁, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆₉: n_l1___13(X₀, X₁, X₃) → n_l3___12(X₀, X₁, X₃) :|: 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 0 < X₀ ∧ 91 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₇₁: n_l1___4(X₀, X₁, X₃) → n_l3___3(X₀, X₁, X₃) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ 0 < X₀ ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀
t₇₂: n_l1___6(X₀, X₁, X₃) → n_l3___5(X₀, X₁, X₃) :|: 0 < X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 0 < X₀ ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇₃: n_l1___9(X₀, X₁, X₃) → n_l3___8(X₀, X₁, X₃) :|: 101 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₀ ∧ 91 ≤ X₁ ∧ 2 ≤ X₀ ∧ X₁ ≤ 111 ∧ 0 < X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₇₄: n_l3___12(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇₅: n_l3___12(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 0 < X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₇₆: n_l3___16(X₀, X₁, X₃) → n_l5___15(X₀, X₁, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₇₇: n_l3___16(X₀, X₁, X₃) → n_l6___14(X₀, X₁, X₃) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₇₈: n_l3___3(X₀, X₁, X₃) → n_l5___2(X₀, X₁, X₃) :|: X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀
t₇₉: n_l3___3(X₀, X₁, X₃) → n_l6___1(X₀, X₁, X₃) :|: X₁ ≤ 111 ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 2 ≤ X₀
t₈₀: n_l3___5(X₀, X₁, X₃) → n_l5___11(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₁: n_l3___5(X₀, X₁, X₃) → n_l6___10(X₀, X₁, X₃) :|: 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 101 ∧ X₁ ≤ 100+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₂: n_l3___8(X₀, X₁, X₃) → n_l5___7(X₀, X₁, X₃) :|: X₁ ≤ 111 ∧ 101 ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 100 < X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₈₃: n_l5___11(X₀, X₁, X₃) → n_l1___13(X₀-1, X₁-10, X₃) :|: 100 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₄: n_l5___15(X₀, X₁, X₃) → n_l1___13(X₀-1, X₁-10, X₃) :|: 100 < X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ X₃ ≤ X₁ ∧ 101 ≤ X₃ ∧ 202 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 102 ≤ X₀+X₃ ∧ 100+X₀ ≤ X₃ ∧ 101 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 100+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₈₅: n_l5___2(X₀, X₁, X₃) → n_l1___6(X₀-1, X₁-10, X₃) :|: X₁ ≤ 111 ∧ 100 < X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ X₃ ≤ 100 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 211 ∧ X₃ ≤ 98+X₀ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 101 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₈₆: n_l5___7(X₀, X₁, X₃) → n_l1___6(X₀-1, X₁-10, X₃) :|: X₁ ≤ 111 ∧ 101 ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 101 ≤ X₁ ∧ X₁ ≤ 111 ∧ X₁ ≤ 109+X₀ ∧ 102 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₈₇: n_l6___1(X₀, X₁, X₃) → n_l1___4(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ 89 ∧ 11+X₃ ≤ X₁ ∧ X₁+X₃ ≤ 189 ∧ X₃ ≤ 87+X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 98+X₀ ∧ 2 ≤ X₀
t₈₈: n_l6___10(X₀, X₁, X₃) → n_l1___9(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ 91 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ 91 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₈₉: n_l6___14(X₀, X₁, X₃) → n_l1___4(X₀+1, X₁+11, X₃) :|: X₁ ≤ 100 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₁ ≤ 100 ∧ X₃ ≤ 100 ∧ X₃ ≤ X₁ ∧ X₁+X₃ ≤ 200 ∧ X₃ ≤ 99+X₀ ∧ X₀+X₃ ≤ 101 ∧ X₁ ≤ X₃ ∧ X₁ ≤ 100 ∧ X₁ ≤ 99+X₀ ∧ X₀+X₁ ≤ 101 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:1150⋅X₃+150388 {O(n)}
t₁₈: 1 {O(1)}
t₇₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₆₉: X₃+114 {O(n)}
t₉₈: 1 {O(1)}
t₇₁: X₃+123 {O(n)}
t₇₂: 910⋅X₃+122213 {O(n)}
t₇₃: 10⋅X₃+1352 {O(n)}
t₇₄: X₃+115 {O(n)}
t₇₅: X₃+115 {O(n)}
t₇₆: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₇₉: 2⋅X₃+223 {O(n)}
t₈₀: X₃+115 {O(n)}
t₈₁: 9⋅X₃+1219 {O(n)}
t₈₂: 101⋅X₃+11615 {O(n)}
t₈₃: X₃+114 {O(n)}
t₈₄: 1 {O(1)}
t₈₅: 1 {O(1)}
t₈₆: 101⋅X₃+11615 {O(n)}
t₈₇: X₃+112 {O(n)}
t₈₈: 10⋅X₃+1332 {O(n)}
t₈₉: 1 {O(1)}
Costbounds
Overall costbound: 1150⋅X₃+150388 {O(n)}
t₁₈: 1 {O(1)}
t₇₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₄: 1 {O(1)}
t₆₉: X₃+114 {O(n)}
t₉₈: 1 {O(1)}
t₇₁: X₃+123 {O(n)}
t₇₂: 910⋅X₃+122213 {O(n)}
t₇₃: 10⋅X₃+1352 {O(n)}
t₇₄: X₃+115 {O(n)}
t₇₅: X₃+115 {O(n)}
t₇₆: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₇₉: 2⋅X₃+223 {O(n)}
t₈₀: X₃+115 {O(n)}
t₈₁: 9⋅X₃+1219 {O(n)}
t₈₂: 101⋅X₃+11615 {O(n)}
t₈₃: X₃+114 {O(n)}
t₈₄: 1 {O(1)}
t₈₅: 1 {O(1)}
t₈₆: 101⋅X₃+11615 {O(n)}
t₈₇: X₃+112 {O(n)}
t₈₈: 10⋅X₃+1332 {O(n)}
t₈₉: 1 {O(1)}
Sizebounds
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₇₀, X₀: 1 {O(1)}
t₇₀, X₁: X₃ {O(n)}
t₇₀, X₃: X₃ {O(n)}
t₂₁, X₀: 1 {O(1)}
t₂₁, X₁: X₃ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₄, X₀: 0 {O(1)}
t₂₄, X₁: X₃+101 {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₆₉, X₀: 11⋅X₃+1446 {O(n)}
t₆₉, X₁: 101 {O(1)}
t₆₉, X₃: X₃ {O(n)}
t₉₈, X₀: 0 {O(1)}
t₉₈, X₁: X₃+101 {O(n)}
t₉₈, X₃: 2⋅X₃ {O(n)}
t₇₁, X₀: X₃+114 {O(n)}
t₇₁, X₁: 12⋅X₃+1243 {O(n)}
t₇₁, X₃: X₃ {O(n)}
t₇₂, X₀: 11⋅X₃+1446 {O(n)}
t₇₂, X₁: 101 {O(1)}
t₇₂, X₃: X₃ {O(n)}
t₇₃, X₀: 11⋅X₃+1446 {O(n)}
t₇₃, X₁: 111 {O(1)}
t₇₃, X₃: X₃ {O(n)}
t₇₄, X₀: 11⋅X₃+1446 {O(n)}
t₇₄, X₁: 101 {O(1)}
t₇₄, X₃: X₃ {O(n)}
t₇₅, X₀: 11⋅X₃+1446 {O(n)}
t₇₅, X₁: 100 {O(1)}
t₇₅, X₃: X₃ {O(n)}
t₇₆, X₀: 1 {O(1)}
t₇₆, X₁: X₃ {O(n)}
t₇₆, X₃: X₃ {O(n)}
t₇₇, X₀: 1 {O(1)}
t₇₇, X₁: X₃ {O(n)}
t₇₇, X₃: X₃ {O(n)}
t₇₈, X₀: X₃+114 {O(n)}
t₇₈, X₁: 111 {O(1)}
t₇₈, X₃: X₃ {O(n)}
t₇₉, X₀: X₃+114 {O(n)}
t₇₉, X₁: 12⋅X₃+1243 {O(n)}
t₇₉, X₃: X₃ {O(n)}
t₈₀, X₀: 11⋅X₃+1446 {O(n)}
t₈₀, X₁: 101 {O(1)}
t₈₀, X₃: X₃ {O(n)}
t₈₁, X₀: 11⋅X₃+1446 {O(n)}
t₈₁, X₁: 100 {O(1)}
t₈₁, X₃: X₃ {O(n)}
t₈₂, X₀: 11⋅X₃+1446 {O(n)}
t₈₂, X₁: 111 {O(1)}
t₈₂, X₃: X₃ {O(n)}
t₈₃, X₀: 11⋅X₃+1446 {O(n)}
t₈₃, X₁: 101 {O(1)}
t₈₃, X₃: X₃ {O(n)}
t₈₄, X₀: 0 {O(1)}
t₈₄, X₁: X₃ {O(n)}
t₈₄, X₃: X₃ {O(n)}
t₈₅, X₀: X₃+114 {O(n)}
t₈₅, X₁: 101 {O(1)}
t₈₅, X₃: X₃ {O(n)}
t₈₆, X₀: 11⋅X₃+1446 {O(n)}
t₈₆, X₁: 101 {O(1)}
t₈₆, X₃: X₃ {O(n)}
t₈₇, X₀: X₃+114 {O(n)}
t₈₇, X₁: 12⋅X₃+1243 {O(n)}
t₈₇, X₃: X₃ {O(n)}
t₈₈, X₀: 11⋅X₃+1446 {O(n)}
t₈₈, X₁: 111 {O(1)}
t₈₈, X₃: X₃ {O(n)}
t₈₉, X₀: 2 {O(1)}
t₈₉, X₁: X₃+11 {O(n)}
t₈₉, X₃: X₃ {O(n)}