Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₃, 1, X₂, X₃)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb5_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: 101 ≤ X₀
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb4_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 100
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₀-10, X₁-1, X₂, X₃)
t₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(11+X₀, 1+X₁, X₂, X₃)
t₈: eval_foo_bb5_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃)
t₀: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Eliminate variables [X₂] that do not contribute to the problem

Found invariant X₁ ≤ 0 ∧ 0 ≤ X₁ for location eval_foo_bb5_in

Found invariant 1 ≤ X₁ for location eval_foo_bb2_in

Found invariant 0 ≤ X₁ for location eval_foo_bb1_in

Found invariant X₁ ≤ 0 ∧ 0 ≤ X₁ for location eval_foo_stop

Found invariant 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ for location eval_foo_bb3_in

Found invariant 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₇: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₂, 1, X₂)
t₁₈: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 0 ≤ X₁
t₁₉: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb5_in(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₂₀: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ 1 ≤ X₁
t₂₁: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ 1 ≤ X₁
t₂₂: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₀-10, X₁-1, X₂) :|: 1 ≤ X₁ ∧ 101 ≤ X₀ ∧ 102 ≤ X₀+X₁
t₂₃: eval_foo_bb4_in(X₀, X₁, X₂) → eval_foo_bb1_in(11+X₀, 1+X₁, X₂) :|: X₀ ≤ 100 ∧ X₀ ≤ 99+X₁ ∧ 1 ≤ X₁
t₂₄: eval_foo_bb5_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂) :|: 0 ≤ X₁ ∧ X₁ ≤ 0
t₂₅: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

MPRF for transition t₂₁: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ 1 ≤ X₁ of depth 1:

new bound:

X₂+101 {O(n)}

• eval_foo_bb1_in: [91+10⋅X₁-X₀]
• eval_foo_bb2_in: [91+10⋅X₁-X₀]
• eval_foo_bb3_in: [91+10⋅X₁-X₀]
• eval_foo_bb4_in: [90+10⋅X₁-X₀]

MPRF for transition t₂₃: eval_foo_bb4_in(X₀, X₁, X₂) → eval_foo_bb1_in(11+X₀, 1+X₁, X₂) :|: X₀ ≤ 100 ∧ X₀ ≤ 99+X₁ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₂+101 {O(n)}

• eval_foo_bb1_in: [91+10⋅X₁-X₀]
• eval_foo_bb2_in: [91+10⋅X₁-X₀]
• eval_foo_bb3_in: [91+10⋅X₁-X₀]
• eval_foo_bb4_in: [91+10⋅X₁-X₀]

MPRF for transition t₁₈: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂⋅X₂+204⋅X₂+10405 {O(n^2)}

• eval_foo_bb1_in: [1+X₁]
• eval_foo_bb2_in: [X₁]
• eval_foo_bb3_in: [X₁]
• eval_foo_bb4_in: [X₁]

MPRF for transition t₂₀: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₂⋅X₂+294⋅X₂+19585 {O(n^2)}

• eval_foo_bb1_in: [91+X₁]
• eval_foo_bb2_in: [91+X₁]
• eval_foo_bb3_in: [90+X₁]
• eval_foo_bb4_in: [91+X₁]

MPRF for transition t₂₂: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₀-10, X₁-1, X₂) :|: 1 ≤ X₁ ∧ 101 ≤ X₀ ∧ 102 ≤ X₀+X₁ of depth 1:

new bound:

12⋅X₂⋅X₂+2415⋅X₂+121493 {O(n^2)}

• eval_foo_bb1_in: [X₀-91]
• eval_foo_bb2_in: [X₀-100]
• eval_foo_bb3_in: [X₀-100]
• eval_foo_bb4_in: [X₀-100]

Cut unsatisfiable transition [t₁₉: eval_foo_bb1_in→eval_foo_bb5_in; t₄₆: eval_foo_bb1_in→eval_foo_bb5_in]

Found invariant X₁ ≤ 0 ∧ 91+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀ for location eval_foo_bb5_in

Found invariant 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 ∧ 91 ≤ X₀ for location eval_foo_bb4_in_v2

Found invariant X₂ ≤ 10+X₀ ∧ 101 ≤ X₂ ∧ 101 ≤ X₁+X₂ ∧ 101+X₁ ≤ X₂ ∧ 192 ≤ X₀+X₂ ∧ 10+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 91+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀ for location eval_foo_bb1_in_v1

Found invariant 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ for location eval_foo_bb1_in_v3

Found invariant X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 for location eval_foo_bb2_in_v5

Found invariant 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀ for location eval_foo_bb1_in_v2

Found invariant X₁ ≤ 0 ∧ 91+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ 91 ≤ X₀ for location eval_foo_stop

Found invariant 1 ≤ 0 for location eval_foo_bb2_in_v2

Found invariant 0 ≤ X₁ ∧ 91 ≤ X₀+X₁ ∧ X₀ ≤ 91+X₁ ∧ X₀ ≤ 91 ∧ 91 ≤ X₀ for location eval_foo_bb1_in_v4

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ for location eval_foo_bb1_in

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ for location eval_foo_bb2_in_v1

Found invariant 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 101 ≤ X₀ for location eval_foo_bb3_in_v3

Found invariant X₂ ≤ 100 ∧ X₂ ≤ 99+X₁ ∧ X₁+X₂ ≤ 101 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 200 ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₀+X₁ ≤ 101 ∧ 1 ≤ X₁ ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 100 for location eval_foo_bb4_in_v1

Found invariant 2 ≤ X₁ ∧ 104 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 102 ≤ X₀ for location eval_foo_bb2_in_v3

Found invariant 2 ≤ X₁ ∧ 103 ≤ X₀+X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 ∧ 101 ≤ X₀ for location eval_foo_bb3_in_v2

Found invariant X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 211 ∧ 2 ≤ X₁ ∧ X₀ ≤ 109+X₁ ∧ X₀ ≤ 111 for location eval_foo_bb1_in_v5

Found invariant 1 ≤ X₁ ∧ 92 ≤ X₀+X₁ ∧ X₀ ≤ 100+X₁ ∧ X₀ ≤ 101 ∧ 91 ≤ X₀ for location eval_foo_bb2_in_v4

Found invariant X₂ ≤ 89 ∧ X₂ ≤ 87+X₁ ∧ 11+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 189 ∧ 2 ≤ X₁ ∧ X₀ ≤ 98+X₁ ∧ X₀ ≤ 100 for location eval_foo_bb4_in_v3

Found invariant X₂ ≤ X₀ ∧ 101 ≤ X₂ ∧ 102 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 202 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ 100+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 102 ≤ X₀+X₁ ∧ 101 ≤ X₀ for location eval_foo_bb3_in_v1

Cut unsatisfiable transition [t₅₂: eval_foo_bb1_in_v1→eval_foo_bb2_in_v2; t₅₃: eval_foo_bb2_in_v2→eval_foo_bb4_in_v2; t₅₄: eval_foo_bb2_in_v2→eval_foo_bb3_in_v1]

Cut unreachable locations [eval_foo_bb2_in_v2] from the program graph

Analysing control-flow refined program

MPRF for transition t₆₆: eval_foo_bb1_in_v5(X₀, X₁, X₂) → eval_foo_bb2_in_v5(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀+X₂ ≤ 211 ∧ X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 2 ≤ X₁ ∧ 11+X₂ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂+123 {O(n)}

• eval_foo_bb1_in_v5: [112-X₀]
• eval_foo_bb2_in_v5: [101-X₀]
• eval_foo_bb4_in_v3: [101-X₀]

MPRF for transition t₆₇: eval_foo_bb2_in_v5(X₀, X₁, X₂) → eval_foo_bb4_in_v3(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ X₀+X₂ ≤ 211 ∧ X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 11+X₂ ≤ X₀ of depth 1:

new bound:

X₂+122 {O(n)}

• eval_foo_bb1_in_v5: [91+10⋅X₁-X₀]
• eval_foo_bb2_in_v5: [91+10⋅X₁-X₀]
• eval_foo_bb4_in_v3: [90+10⋅X₁-X₀]

MPRF for transition t₆₉: eval_foo_bb4_in_v3(X₀, X₁, X₂) → eval_foo_bb1_in_v5(11+X₀, 1+X₁, X₂) :|: X₀+X₂ ≤ 189 ∧ X₀ ≤ 100 ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 98+X₁ ∧ X₂ ≤ 89 ∧ X₂ ≤ 87+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 11+X₂ ≤ X₀ of depth 1:

new bound:

X₂+122 {O(n)}

• eval_foo_bb1_in_v5: [91+10⋅X₁-X₀]
• eval_foo_bb2_in_v5: [91+10⋅X₁-X₀]
• eval_foo_bb4_in_v3: [91+10⋅X₁-X₀]

MPRF for transition t₅₅: eval_foo_bb4_in_v2(X₀, X₁, X₂) → eval_foo_bb1_in_v2(11+X₀, 1+X₁, X₂) :|: X₀ ≤ 100 ∧ X₀ ≤ 99+X₁ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 92 ≤ X₀+X₁ of depth 1:

new bound:

10⋅X₂+1480 {O(n)}

• eval_foo_bb1_in_v2: [109+10⋅X₁-X₀]
• eval_foo_bb1_in_v3: [109+10⋅X₁-X₀]
• eval_foo_bb1_in_v4: [18+10⋅X₁]
• eval_foo_bb2_in_v3: [109+10⋅X₁-X₀]
• eval_foo_bb2_in_v4: [109+10⋅X₁-X₀]
• eval_foo_bb3_in_v2: [109+10⋅X₁-X₀]
• eval_foo_bb3_in_v3: [109+10⋅X₁-X₀]
• eval_foo_bb4_in_v2: [109+10⋅X₁-X₀]

MPRF for transition t₅₆: eval_foo_bb1_in_v2(X₀, X₁, X₂) → eval_foo_bb2_in_v3(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ 2 ≤ X₁ ∧ 91 ≤ X₀ ∧ 101 ≤ X₀ ∧ 102 ≤ X₀ ∧ 104 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

10⋅X₂+1482 {O(n)}

• eval_foo_bb1_in_v2: [112+10⋅X₁-X₀]
• eval_foo_bb1_in_v3: [111+10⋅X₁-X₀]
• eval_foo_bb1_in_v4: [20+10⋅X₁]
• eval_foo_bb2_in_v3: [111+10⋅X₁-X₀]
• eval_foo_bb2_in_v4: [111+10⋅X₁-X₀]
• eval_foo_bb3_in_v2: [111+10⋅X₁-X₀]
• eval_foo_bb3_in_v3: [111+10⋅X₁-X₀]
• eval_foo_bb4_in_v2: [111+10⋅X₁-X₀]

MPRF for transition t₅₇: eval_foo_bb2_in_v3(X₀, X₁, X₂) → eval_foo_bb3_in_v2(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 102 ≤ X₀ ∧ 104 ≤ X₀+X₁ of depth 1:

new bound:

10⋅X₂+1552 {O(n)}

• eval_foo_bb1_in_v2: [182+10⋅X₁-X₀]
• eval_foo_bb1_in_v3: [181+10⋅X₁-X₀]
• eval_foo_bb1_in_v4: [90+10⋅X₁]
• eval_foo_bb2_in_v3: [182+10⋅X₁-X₀]
• eval_foo_bb2_in_v4: [181+10⋅X₁-X₀]
• eval_foo_bb3_in_v2: [181+10⋅X₁-X₀]
• eval_foo_bb3_in_v3: [181+10⋅X₁-X₀]
• eval_foo_bb4_in_v2: [181+10⋅X₁-X₀]

MPRF for transition t₅₈: eval_foo_bb3_in_v2(X₀, X₁, X₂) → eval_foo_bb1_in_v3(X₀-10, X₁-1, X₂) :|: X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 101 ≤ X₀ ∧ 102 ≤ X₀+X₁ ∧ 103 ≤ X₀+X₁ of depth 1:

new bound:

10⋅X₂+1473 {O(n)}

• eval_foo_bb1_in_v2: [102+10⋅X₁-X₀]
• eval_foo_bb1_in_v3: [101+10⋅X₁-X₀]
• eval_foo_bb1_in_v4: [101+10⋅X₁-X₀]
• eval_foo_bb2_in_v3: [102+10⋅X₁-X₀]
• eval_foo_bb2_in_v4: [101+10⋅X₁-X₀]
• eval_foo_bb3_in_v2: [102+10⋅X₁-X₀]
• eval_foo_bb3_in_v3: [101+10⋅X₁-X₀]
• eval_foo_bb4_in_v2: [101+10⋅X₁-X₀]

MPRF for transition t₅₉: eval_foo_bb1_in_v3(X₀, X₁, X₂) → eval_foo_bb2_in_v4(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 111 ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 91 ≤ X₀ ∧ 92 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

10⋅X₂+1493 {O(n)}

• eval_foo_bb1_in_v2: [122+10⋅X₁-X₀]
• eval_foo_bb1_in_v3: [122+10⋅X₁-X₀]
• eval_foo_bb1_in_v4: [30+10⋅X₁]
• eval_foo_bb2_in_v3: [122+10⋅X₁-X₀]
• eval_foo_bb2_in_v4: [121+10⋅X₁-X₀]
• eval_foo_bb3_in_v2: [122+10⋅X₁-X₀]
• eval_foo_bb3_in_v3: [121+10⋅X₁-X₀]
• eval_foo_bb4_in_v2: [121+10⋅X₁-X₀]

MPRF for transition t₆₀: eval_foo_bb2_in_v4(X₀, X₁, X₂) → eval_foo_bb4_in_v2(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ X₀ ≤ 111 ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 92 ≤ X₀+X₁ of depth 1:

new bound:

10⋅X₂+1552 {O(n)}

• eval_foo_bb1_in_v2: [181+10⋅X₁-X₀]
• eval_foo_bb1_in_v3: [181+10⋅X₁-X₀]
• eval_foo_bb1_in_v4: [90+10⋅X₁]
• eval_foo_bb2_in_v3: [181+10⋅X₁-X₀]
• eval_foo_bb2_in_v4: [181+10⋅X₁-X₀]
• eval_foo_bb3_in_v2: [181+10⋅X₁-X₀]
• eval_foo_bb3_in_v3: [181+10⋅X₁-X₀]
• eval_foo_bb4_in_v2: [180+10⋅X₁-X₀]

MPRF for transition t₆₁: eval_foo_bb2_in_v4(X₀, X₁, X₂) → eval_foo_bb3_in_v3(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ X₀ ≤ 111 ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 92 ≤ X₀+X₁ of depth 1:

new bound:

X₂+135 {O(n)}

• eval_foo_bb1_in_v2: [9+X₁]
• eval_foo_bb1_in_v3: [10+X₁]
• eval_foo_bb1_in_v4: [10+X₁]
• eval_foo_bb2_in_v3: [9+X₁]
• eval_foo_bb2_in_v4: [10+X₁]
• eval_foo_bb3_in_v2: [9+X₁]
• eval_foo_bb3_in_v3: [9+X₁]
• eval_foo_bb4_in_v2: [10+X₁]

MPRF for transition t₆₂: eval_foo_bb3_in_v3(X₀, X₁, X₂) → eval_foo_bb1_in_v4(X₀-10, X₁-1, X₂) :|: X₀ ≤ 111 ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 1 ≤ X₁ ∧ 101 ≤ X₀ ∧ 102 ≤ X₀+X₁ of depth 1:

new bound:

X₂+126 {O(n)}

• eval_foo_bb1_in_v2: [X₁]
• eval_foo_bb1_in_v3: [1+X₁]
• eval_foo_bb1_in_v4: [1+X₁]
• eval_foo_bb2_in_v3: [X₁]
• eval_foo_bb2_in_v4: [1+X₁]
• eval_foo_bb3_in_v2: [X₁]
• eval_foo_bb3_in_v3: [1+X₁]
• eval_foo_bb4_in_v2: [1+X₁]

MPRF for transition t₆₄: eval_foo_bb1_in_v4(X₀, X₁, X₂) → eval_foo_bb2_in_v4(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 111 ∧ X₀ ≤ 91 ∧ X₀ ≤ 91+X₁ ∧ 91 ≤ X₀ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂+145 {O(n)}

• eval_foo_bb1_in_v2: [19+X₁]
• eval_foo_bb1_in_v3: [20+X₁]
• eval_foo_bb1_in_v4: [21+X₁]
• eval_foo_bb2_in_v3: [19+X₁]
• eval_foo_bb2_in_v4: [20+X₁]
• eval_foo_bb3_in_v2: [19+X₁]
• eval_foo_bb3_in_v3: [20+X₁]
• eval_foo_bb4_in_v2: [20+X₁]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb1_in_v1, eval_foo_bb1_in_v2, eval_foo_bb1_in_v3, eval_foo_bb1_in_v4, eval_foo_bb1_in_v5, eval_foo_bb2_in_v1, eval_foo_bb2_in_v3, eval_foo_bb2_in_v4, eval_foo_bb2_in_v5, eval_foo_bb3_in_v1, eval_foo_bb3_in_v2, eval_foo_bb3_in_v3, eval_foo_bb4_in_v1, eval_foo_bb4_in_v2, eval_foo_bb4_in_v3, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₇: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₂, 1, X₂)
t₄₇: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in_v1(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁
t₅₁: eval_foo_bb1_in_v1(X₀, X₁, X₂) → eval_foo_bb5_in(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₂ ≤ 10+X₀ ∧ 10+X₀ ≤ X₂ ∧ 91 ≤ X₀ ∧ 91 ≤ X₀+X₁ ∧ 91+X₁ ≤ X₀ ∧ 101 ≤ X₁+X₂ ∧ 101+X₁ ≤ X₂ ∧ 101 ≤ X₂ ∧ 192 ≤ X₀+X₂ ∧ 0 ≤ X₁
t₅₆: eval_foo_bb1_in_v2(X₀, X₁, X₂) → eval_foo_bb2_in_v3(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ 2 ≤ X₁ ∧ 91 ≤ X₀ ∧ 101 ≤ X₀ ∧ 102 ≤ X₀ ∧ 104 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₅₉: eval_foo_bb1_in_v3(X₀, X₁, X₂) → eval_foo_bb2_in_v4(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 111 ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 91 ≤ X₀ ∧ 92 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₆₄: eval_foo_bb1_in_v4(X₀, X₁, X₂) → eval_foo_bb2_in_v4(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 111 ∧ X₀ ≤ 91 ∧ X₀ ≤ 91+X₁ ∧ 91 ≤ X₀ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₆₃: eval_foo_bb1_in_v4(X₀, X₁, X₂) → eval_foo_bb5_in(X₀, X₁, X₂) :|: X₁ ≤ 0 ∧ X₀ ≤ 111 ∧ X₀ ≤ 91 ∧ X₀ ≤ 91+X₁ ∧ 91 ≤ X₀ ∧ 91 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₆₆: eval_foo_bb1_in_v5(X₀, X₁, X₂) → eval_foo_bb2_in_v5(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀+X₂ ≤ 211 ∧ X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 2 ≤ X₁ ∧ 11+X₂ ≤ X₀ ∧ 0 ≤ X₁
t₄₉: eval_foo_bb2_in_v1(X₀, X₁, X₂) → eval_foo_bb3_in_v1(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₄₈: eval_foo_bb2_in_v1(X₀, X₁, X₂) → eval_foo_bb4_in_v1(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅₇: eval_foo_bb2_in_v3(X₀, X₁, X₂) → eval_foo_bb3_in_v2(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 102 ≤ X₀ ∧ 104 ≤ X₀+X₁
t₆₁: eval_foo_bb2_in_v4(X₀, X₁, X₂) → eval_foo_bb3_in_v3(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ X₀ ≤ 111 ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 92 ≤ X₀+X₁
t₆₀: eval_foo_bb2_in_v4(X₀, X₁, X₂) → eval_foo_bb4_in_v2(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ X₀ ≤ 111 ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 92 ≤ X₀+X₁
t₆₈: eval_foo_bb2_in_v5(X₀, X₁, X₂) → eval_foo_bb3_in_v2(X₀, X₁, X₂) :|: 101 ≤ X₀ ∧ X₀+X₂ ≤ 211 ∧ X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 11+X₂ ≤ X₀
t₆₇: eval_foo_bb2_in_v5(X₀, X₁, X₂) → eval_foo_bb4_in_v3(X₀, X₁, X₂) :|: X₀ ≤ 100 ∧ X₀+X₂ ≤ 211 ∧ X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ X₂ ≤ 100 ∧ X₂ ≤ 98+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 11+X₂ ≤ X₀
t₅₀: eval_foo_bb3_in_v1(X₀, X₁, X₂) → eval_foo_bb1_in_v1(X₀-10, X₁-1, X₂) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 100+X₁ ≤ X₀ ∧ 100+X₁ ≤ X₂ ∧ 101 ≤ X₀ ∧ 101 ≤ X₂ ∧ 102 ≤ X₀+X₁ ∧ 102 ≤ X₁+X₂ ∧ 202 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅₈: eval_foo_bb3_in_v2(X₀, X₁, X₂) → eval_foo_bb1_in_v3(X₀-10, X₁-1, X₂) :|: X₀ ≤ 111 ∧ X₀ ≤ 109+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 101 ≤ X₀ ∧ 102 ≤ X₀+X₁ ∧ 103 ≤ X₀+X₁
t₆₂: eval_foo_bb3_in_v3(X₀, X₁, X₂) → eval_foo_bb1_in_v4(X₀-10, X₁-1, X₂) :|: X₀ ≤ 111 ∧ X₀ ≤ 101 ∧ X₀ ≤ 100+X₁ ∧ 1 ≤ X₁ ∧ 101 ≤ X₀ ∧ 102 ≤ X₀+X₁
t₆₅: eval_foo_bb4_in_v1(X₀, X₁, X₂) → eval_foo_bb1_in_v5(11+X₀, 1+X₁, X₂) :|: X₀+X₂ ≤ 200 ∧ X₀+X₁ ≤ 101 ∧ X₁+X₂ ≤ 101 ∧ X₀ ≤ 100 ∧ X₂ ≤ 100 ∧ X₀ ≤ 99+X₁ ∧ X₂ ≤ 99+X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₅₅: eval_foo_bb4_in_v2(X₀, X₁, X₂) → eval_foo_bb1_in_v2(11+X₀, 1+X₁, X₂) :|: X₀ ≤ 100 ∧ X₀ ≤ 99+X₁ ∧ 1 ≤ X₁ ∧ 91 ≤ X₀ ∧ 92 ≤ X₀+X₁
t₆₉: eval_foo_bb4_in_v3(X₀, X₁, X₂) → eval_foo_bb1_in_v5(11+X₀, 1+X₁, X₂) :|: X₀+X₂ ≤ 189 ∧ X₀ ≤ 100 ∧ X₀ ≤ 99+X₁ ∧ X₀ ≤ 98+X₁ ∧ X₂ ≤ 89 ∧ X₂ ≤ 87+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₁ ∧ 11+X₂ ≤ X₀
t₂₄: eval_foo_bb5_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂) :|: 91 ≤ X₀ ∧ 91 ≤ X₀+X₁ ∧ 91+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₂₅: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

All Bounds

Timebounds

Overall timebound:66⋅X₂+9816 {O(n)}
t₁₇: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₉: 1 {O(1)}
t₅₀: 1 {O(1)}
t₅₁: 1 {O(1)}
t₅₅: 10⋅X₂+1480 {O(n)}
t₅₆: 10⋅X₂+1482 {O(n)}
t₅₇: 10⋅X₂+1552 {O(n)}
t₅₈: 10⋅X₂+1473 {O(n)}
t₅₉: 10⋅X₂+1493 {O(n)}
t₆₀: 10⋅X₂+1552 {O(n)}
t₆₁: X₂+135 {O(n)}
t₆₂: X₂+126 {O(n)}
t₆₃: 1 {O(1)}
t₆₄: X₂+145 {O(n)}
t₆₅: 1 {O(1)}
t₆₆: X₂+123 {O(n)}
t₆₇: X₂+122 {O(n)}
t₆₈: 1 {O(1)}
t₆₉: X₂+122 {O(n)}

Costbounds

Overall costbound: 66⋅X₂+9816 {O(n)}
t₁₇: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₄₇: 1 {O(1)}
t₄₈: 1 {O(1)}
t₄₉: 1 {O(1)}
t₅₀: 1 {O(1)}
t₅₁: 1 {O(1)}
t₅₅: 10⋅X₂+1480 {O(n)}
t₅₆: 10⋅X₂+1482 {O(n)}
t₅₇: 10⋅X₂+1552 {O(n)}
t₅₈: 10⋅X₂+1473 {O(n)}
t₅₉: 10⋅X₂+1493 {O(n)}
t₆₀: 10⋅X₂+1552 {O(n)}
t₆₁: X₂+135 {O(n)}
t₆₂: X₂+126 {O(n)}
t₆₃: 1 {O(1)}
t₆₄: X₂+145 {O(n)}
t₆₅: 1 {O(1)}
t₆₆: X₂+123 {O(n)}
t₆₇: X₂+122 {O(n)}
t₆₈: 1 {O(1)}
t₆₉: X₂+122 {O(n)}

Sizebounds

t₁₇, X₀: X₂ {O(n)}
t₁₇, X₁: 1 {O(1)}
t₁₇, X₂: X₂ {O(n)}
t₂₄, X₀: X₂+91 {O(n)}
t₂₄, X₁: 0 {O(1)}
t₂₄, X₂: 2⋅X₂ {O(n)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₄₇, X₀: X₂ {O(n)}
t₄₇, X₁: 1 {O(1)}
t₄₇, X₂: X₂ {O(n)}
t₄₈, X₀: X₂ {O(n)}
t₄₈, X₁: 1 {O(1)}
t₄₈, X₂: X₂ {O(n)}
t₄₉, X₀: X₂ {O(n)}
t₄₉, X₁: 1 {O(1)}
t₄₉, X₂: X₂ {O(n)}
t₅₀, X₀: X₂ {O(n)}
t₅₀, X₁: 0 {O(1)}
t₅₀, X₂: X₂ {O(n)}
t₅₁, X₀: X₂ {O(n)}
t₅₁, X₁: 0 {O(1)}
t₅₁, X₂: X₂ {O(n)}
t₅₅, X₀: 111 {O(1)}
t₅₅, X₁: 11⋅X₂+1606 {O(n)}
t₅₅, X₂: X₂ {O(n)}
t₅₆, X₀: 111 {O(1)}
t₅₆, X₁: 11⋅X₂+1606 {O(n)}
t₅₆, X₂: X₂ {O(n)}
t₅₇, X₀: 111 {O(1)}
t₅₇, X₁: 11⋅X₂+1606 {O(n)}
t₅₇, X₂: X₂ {O(n)}
t₅₈, X₀: 101 {O(1)}
t₅₈, X₁: 11⋅X₂+1606 {O(n)}
t₅₈, X₂: X₂ {O(n)}
t₅₉, X₀: 101 {O(1)}
t₅₉, X₁: 11⋅X₂+1606 {O(n)}
t₅₉, X₂: X₂ {O(n)}
t₆₀, X₀: 100 {O(1)}
t₆₀, X₁: 11⋅X₂+1606 {O(n)}
t₆₀, X₂: X₂ {O(n)}
t₆₁, X₀: 101 {O(1)}
t₆₁, X₁: 11⋅X₂+1606 {O(n)}
t₆₁, X₂: X₂ {O(n)}
t₆₂, X₀: 91 {O(1)}
t₆₂, X₁: 11⋅X₂+1606 {O(n)}
t₆₂, X₂: X₂ {O(n)}
t₆₃, X₀: 91 {O(1)}
t₆₃, X₁: 0 {O(1)}
t₆₃, X₂: X₂ {O(n)}
t₆₄, X₀: 91 {O(1)}
t₆₄, X₁: 11⋅X₂+1606 {O(n)}
t₆₄, X₂: X₂ {O(n)}
t₆₅, X₀: X₂+11 {O(n)}
t₆₅, X₁: 2 {O(1)}
t₆₅, X₂: X₂ {O(n)}
t₆₆, X₀: 12⋅X₂+1375 {O(n)}
t₆₆, X₁: X₂+126 {O(n)}
t₆₆, X₂: X₂ {O(n)}
t₆₇, X₀: 12⋅X₂+1364 {O(n)}
t₆₇, X₁: X₂+115 {O(n)}
t₆₇, X₂: X₂ {O(n)}
t₆₈, X₀: 111 {O(1)}
t₆₈, X₁: X₂+126 {O(n)}
t₆₈, X₂: X₂ {O(n)}
t₆₉, X₀: 12⋅X₂+1364 {O(n)}
t₆₉, X₁: X₂+125 {O(n)}
t₆₉, X₂: X₂ {O(n)}