Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
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_bb6_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₃, X₁, X₂, X₃, X₄)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₀
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb6_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ 0
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb3_in(X₀, 1, 1+X₀, X₃, X₄)
t₅: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₂
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₂ ≤ X₁
t₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb3_in(X₀, 1+X₁, X₂, X₃, X₄)
t₈: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(X₂-2, X₁, X₂, X₃, X₄)
t₉: eval_foo_bb6_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Eliminate variables [X₄] that do not contribute to the problem

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb5_in

Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location eval_foo_stop

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb3_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location eval_foo_bb2_in

Found invariant X₀ ≤ X₃ for location eval_foo_bb1_in

Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location eval_foo_bb6_in

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb4_in

Problem after Preprocessing

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_bb6_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₉: eval_foo_bb0_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₃, X₁, X₂, X₃)
t₂₀: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₃
t₂₁: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb6_in(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₀ ≤ X₃
t₂₂: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, 1, 1+X₀, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃
t₂₃: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_bb4_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ X₁ ≤ 2+X₃ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1+X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃
t₂₄: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_bb5_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₀ ∧ X₁ ≤ 2+X₃ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1+X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃
t₂₅: eval_foo_bb4_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, 1+X₁, X₂, X₃) :|: X₁ ≤ 1+X₀ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃
t₂₆: eval_foo_bb5_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂-2, X₁, X₂, X₃) :|: X₁ ≤ 2+X₀ ∧ X₁ ≤ 2+X₃ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1+X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃
t₂₇: eval_foo_bb6_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₀ ≤ X₃
t₂₈: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₂₀: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [X₀]
• eval_foo_bb3_in: [X₀]
• eval_foo_bb4_in: [X₀]
• eval_foo_bb5_in: [X₀]

MPRF for transition t₂₂: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, 1, 1+X₀, X₃) :|: 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [1+X₀]
• eval_foo_bb3_in: [X₂-1]
• eval_foo_bb4_in: [X₀]
• eval_foo_bb5_in: [X₀]

MPRF for transition t₂₄: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_bb5_in(X₀, X₁, X₂, X₃) :|: 1+X₂ ≤ X₁ ∧ X₁ ≤ 2+X₀ ∧ X₁ ≤ 2+X₃ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1+X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [1+X₀]
• eval_foo_bb3_in: [1+X₀]
• eval_foo_bb4_in: [X₂]
• eval_foo_bb5_in: [X₁-2]

MPRF for transition t₂₆: eval_foo_bb5_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(X₂-2, X₁, X₂, X₃) :|: X₁ ≤ 2+X₀ ∧ X₁ ≤ 2+X₃ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ 1+X₂ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

• eval_foo_bb1_in: [1+X₀]
• eval_foo_bb2_in: [1+X₀]
• eval_foo_bb3_in: [X₂]
• eval_foo_bb4_in: [X₂]
• eval_foo_bb5_in: [1+X₀]

TWN: t₂₅: eval_foo_bb4_in→eval_foo_bb3_in

Show Graph

Termination: true
Formula:

TWN - Lifting for [23: eval_foo_bb3_in->eval_foo_bb4_in; 25: eval_foo_bb4_in->eval_foo_bb3_in] of 12⋅X₁+4⋅X₀+4⋅X₂+4⋅X₃+40 {O(n)}

Cut unsatisfiable transition [t₂₄: eval_foo_bb3_in→eval_foo_bb5_in; t₅₀: eval_foo_bb3_in→eval_foo_bb5_in]

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location eval_foo_bb5_in

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_foo_bb4_in_v2

Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location eval_foo_stop

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb3_in

Found invariant 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location eval_foo_bb2_in

Found invariant X₀ ≤ X₃ for location eval_foo_bb1_in

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 1 ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb4_in_v1

Found invariant X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location eval_foo_bb6_in

Found invariant 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ 2+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ X₁ ≤ 1+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ X₁ ≤ 2+X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb3_in_v1

All Bounds

Timebounds

Overall timebound:24⋅X₃⋅X₃+156⋅X₃+136 {O(n^2)}
t₁₉: 1 {O(1)}
t₂₀: X₃+1 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: X₃+1 {O(n)}
t₂₃: 12⋅X₃⋅X₃+76⋅X₃+64 {O(n^2)}
t₂₄: X₃+1 {O(n)}
t₂₅: 12⋅X₃⋅X₃+76⋅X₃+64 {O(n^2)}
t₂₆: X₃+1 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}

Costbounds

Overall costbound: 24⋅X₃⋅X₃+156⋅X₃+136 {O(n^2)}
t₁₉: 1 {O(1)}
t₂₀: X₃+1 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: X₃+1 {O(n)}
t₂₃: 12⋅X₃⋅X₃+76⋅X₃+64 {O(n^2)}
t₂₄: X₃+1 {O(n)}
t₂₅: 12⋅X₃⋅X₃+76⋅X₃+64 {O(n^2)}
t₂₆: X₃+1 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}

Sizebounds

t₁₉, X₀: X₃ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₀: X₃+1 {O(n)}
t₂₀, X₁: X₁+X₃+6 {O(n)}
t₂₀, X₂: X₂+X₃+2 {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₁, X₀: 2⋅X₃+1 {O(n)}
t₂₁, X₁: X₁+X₃+6 {O(n)}
t₂₁, X₂: X₂+X₃+2 {O(n)}
t₂₁, X₃: 2⋅X₃ {O(n)}
t₂₂, X₀: X₃+1 {O(n)}
t₂₂, X₁: 1 {O(1)}
t₂₂, X₂: X₃+2 {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₃, X₀: X₃+1 {O(n)}
t₂₃, X₁: X₃+6 {O(n)}
t₂₃, X₂: X₃+2 {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₄, X₀: X₃+1 {O(n)}
t₂₄, X₁: X₃+6 {O(n)}
t₂₄, X₂: X₃+2 {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₅, X₀: X₃+1 {O(n)}
t₂₅, X₁: X₃+6 {O(n)}
t₂₅, X₂: X₃+2 {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₆, X₀: X₃+1 {O(n)}
t₂₆, X₁: X₃+6 {O(n)}
t₂₆, X₂: X₃+2 {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₇, X₀: 2⋅X₃+1 {O(n)}
t₂₇, X₁: X₁+X₃+6 {O(n)}
t₂₇, X₂: X₂+X₃+2 {O(n)}
t₂₇, X₃: 2⋅X₃ {O(n)}
t₂₈, X₀: X₀ {O(n)}
t₂₈, X₁: X₁ {O(n)}
t₂₈, X₂: X₂ {O(n)}
t₂₈, X₃: X₃ {O(n)}