YES(?,POLY) * Step 1: UnsatRules WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (?,1) 3. lbl52(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= D && B >= 0 && D >= 1 && A >= D && F = A] (?,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (?,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 8. lbl72(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && 0 >= A && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,4,5},2->{6,7,8},3->{},4->{3,4,5},5->{6,7,8},6->{},7->{3,4,5},8->{6,7,8},9->{0,1,2}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [3,8] * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (?,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (?,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{6,7},4->{4,5},5->{6,7},6->{},7->{4,5},9->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,5)] * Step 3: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] (?,1) 1. start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] (?,1) 2. start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] (?,1) 4. lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] (?,1) 5. lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] (?,1) 6. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] (?,1) 7. lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] (?,1) 9. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{6,7},4->{4,5},5->{6,7},6->{},7->{4},9->{0,1,2}] + Applied Processor: FromIts + Details: () * Step 4: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] lbl52(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] lbl52(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] lbl72(A,B,C,D,E,F) -> lbl52(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl52,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{4,5},2->{6,7},4->{4,5},5->{6,7},6->{},7->{4},9->{0,1,2}] + Applied Processor: Unfold + Details: () * Step 5: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: start.0(A,B,C,D,E,F) -> stop.10(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl52.4(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl52.5(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] start.2(A,B,C,D,E,F) -> lbl72.6(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] start.2(A,B,C,D,E,F) -> lbl72.7(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] lbl52.4(A,B,C,D,E,F) -> lbl52.4(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] lbl52.4(A,B,C,D,E,F) -> lbl52.5(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] lbl52.5(A,B,C,D,E,F) -> lbl72.6(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] lbl52.5(A,B,C,D,E,F) -> lbl72.7(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] lbl72.6(A,B,C,D,E,F) -> stop.10(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] lbl72.7(A,B,C,D,E,F) -> lbl52.4(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] start0.9(A,B,C,D,E,F) -> start.0(A,C,C,E,E,A) True start0.9(A,B,C,D,E,F) -> start.1(A,C,C,E,E,A) True start0.9(A,B,C,D,E,F) -> start.2(A,C,C,E,E,A) True Signature: {(lbl52.4,6) ;(lbl52.5,6) ;(lbl72.6,6) ;(lbl72.7,6) ;(start.0,6) ;(start.1,6) ;(start.2,6) ;(start0.9,6) ;(stop.10,6)} Rule Graph: [0->{},1->{5,6},2->{7,8},3->{9},4->{10},5->{5,6},6->{7,8},7->{9},8->{10},9->{},10->{5,6},11->{0},12->{1,2} ,13->{3,4}] + Applied Processor: AddSinks + Details: () * Step 6: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: start.0(A,B,C,D,E,F) -> stop.10(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl52.4(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl52.5(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] start.2(A,B,C,D,E,F) -> lbl72.6(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] start.2(A,B,C,D,E,F) -> lbl72.7(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] lbl52.4(A,B,C,D,E,F) -> lbl52.4(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] lbl52.4(A,B,C,D,E,F) -> lbl52.5(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] lbl52.5(A,B,C,D,E,F) -> lbl72.6(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] lbl52.5(A,B,C,D,E,F) -> lbl72.7(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] lbl72.6(A,B,C,D,E,F) -> stop.10(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] lbl72.7(A,B,C,D,E,F) -> lbl52.4(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] start0.9(A,B,C,D,E,F) -> start.0(A,C,C,E,E,A) True start0.9(A,B,C,D,E,F) -> start.1(A,C,C,E,E,A) True start0.9(A,B,C,D,E,F) -> start.2(A,C,C,E,E,A) True stop.10(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.10(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.10(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.10(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.10(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6) ;(lbl52.4,6) ;(lbl52.5,6) ;(lbl72.6,6) ;(lbl72.7,6) ;(start.0,6) ;(start.1,6) ;(start.2,6) ;(start0.9,6) ;(stop.10,6)} Rule Graph: [0->{18},1->{5,6},2->{7,8},3->{9},4->{10},5->{5,6},6->{7,8},7->{9},8->{10},9->{14,15,16,17},10->{5,6} ,11->{0},12->{1,2},13->{3,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[5,10,8,6] c: [6,8,10] | `- p:[5] c: [5] * Step 7: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: start.0(A,B,C,D,E,F) -> stop.10(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl52.4(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl52.5(A,-1 + B,C,F,E,F) [A >= 1 && C >= 1 && B = C && D = E && F = A] start.2(A,B,C,D,E,F) -> lbl72.6(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] start.2(A,B,C,D,E,F) -> lbl72.7(A,F,C,-1 + F,E,F) [A >= 1 && 0 >= C && B = C && D = E && F = A] lbl52.4(A,B,C,D,E,F) -> lbl52.4(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] lbl52.4(A,B,C,D,E,F) -> lbl52.5(A,-1 + B,C,D,E,F) [D >= 1 && B >= 1 && B >= 0 && A >= D && F = A] lbl52.5(A,B,C,D,E,F) -> lbl72.6(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] lbl52.5(A,B,C,D,E,F) -> lbl72.7(A,F,C,-1 + D,E,F) [D >= 1 && A >= D && B = 0 && F = A] lbl72.6(A,B,C,D,E,F) -> stop.10(A,B,C,D,E,F) [A >= 1 && D = 0 && F = A && B = A] lbl72.7(A,B,C,D,E,F) -> lbl52.4(A,-1 + B,C,D,E,F) [D >= 1 && A >= 1 && D >= 0 && A >= 1 + D && F = A && B = A] start0.9(A,B,C,D,E,F) -> start.0(A,C,C,E,E,A) True start0.9(A,B,C,D,E,F) -> start.1(A,C,C,E,E,A) True start0.9(A,B,C,D,E,F) -> start.2(A,C,C,E,E,A) True stop.10(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.10(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.10(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.10(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.10(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6) ;(lbl52.4,6) ;(lbl52.5,6) ;(lbl72.6,6) ;(lbl72.7,6) ;(start.0,6) ;(start.1,6) ;(start.2,6) ;(start0.9,6) ;(stop.10,6)} Rule Graph: [0->{18},1->{5,6},2->{7,8},3->{9},4->{10},5->{5,6},6->{7,8},7->{9},8->{10},9->{14,15,16,17},10->{5,6} ,11->{0},12->{1,2},13->{3,4}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[5,10,8,6] c: [6,8,10] | `- p:[5] c: [5]) + Applied Processor: AbstractSize Minimize + Details: () * Step 8: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.0.0] start.0 ~> stop.10 [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] start.1 ~> lbl52.4 [A <= A, B <= C, C <= C, D <= F, E <= E, F <= F] start.1 ~> lbl52.5 [A <= A, B <= C, C <= C, D <= F, E <= E, F <= F] start.2 ~> lbl72.6 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] start.2 ~> lbl72.7 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] lbl52.4 ~> lbl52.4 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl52.4 ~> lbl52.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl52.5 ~> lbl72.6 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] lbl52.5 ~> lbl72.7 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] lbl72.6 ~> stop.10 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl72.7 ~> lbl52.4 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] start0.9 ~> start.0 [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] start0.9 ~> start.1 [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] start0.9 ~> start.2 [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] stop.10 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop.10 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop.10 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop.10 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop.10 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= 2*K + D] lbl52.4 ~> lbl52.4 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl72.7 ~> lbl52.4 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl52.5 ~> lbl72.7 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] lbl52.4 ~> lbl52.5 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0.0 <= B] lbl52.4 ~> lbl52.4 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Applied Processor: AbstractFlow + Details: () * Step 9: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.0.0] start.0 ~> stop.10 [F ~=> D] start.1 ~> lbl52.4 [C ~=> B,F ~=> D] start.1 ~> lbl52.5 [C ~=> B,F ~=> D] start.2 ~> lbl72.6 [F ~=> B,F ~=> D] start.2 ~> lbl72.7 [F ~=> B,F ~=> D] lbl52.4 ~> lbl52.4 [] lbl52.4 ~> lbl52.5 [] lbl52.5 ~> lbl72.6 [F ~=> B,F ~=> D] lbl52.5 ~> lbl72.7 [F ~=> B,F ~=> D] lbl72.6 ~> stop.10 [] lbl72.7 ~> lbl52.4 [] start0.9 ~> start.0 [A ~=> F,C ~=> B,E ~=> D] start0.9 ~> start.1 [A ~=> F,C ~=> B,E ~=> D] start0.9 ~> start.2 [A ~=> F,C ~=> B,E ~=> D] stop.10 ~> exitus616 [] stop.10 ~> exitus616 [] stop.10 ~> exitus616 [] stop.10 ~> exitus616 [] stop.10 ~> exitus616 [] + Loop: [D ~+> 0.0,K ~*> 0.0] lbl52.4 ~> lbl52.4 [] lbl72.7 ~> lbl52.4 [] lbl52.5 ~> lbl72.7 [F ~=> B,F ~=> D] lbl52.4 ~> lbl52.5 [] + Loop: [B ~=> 0.0.0] lbl52.4 ~> lbl52.4 [] + Applied Processor: Lare + Details: start0.9 ~> exitus616 [A ~=> B ,A ~=> D ,A ~=> F ,A ~=> 0.0.0 ,C ~=> B ,C ~=> 0.0.0 ,A ~+> 0.0 ,A ~+> tick ,C ~+> tick ,tick ~+> tick ,A ~*> tick ,C ~*> tick ,K ~*> 0.0 ,K ~*> tick] + lbl52.5> [F ~=> B ,F ~=> D ,F ~=> 0.0.0 ,D ~+> 0.0 ,D ~+> tick ,F ~+> tick ,tick ~+> tick ,D ~*> tick ,F ~*> tick ,K ~*> 0.0 ,K ~*> tick] lbl52.5> [B ~=> 0.0.0 ,F ~=> B ,F ~=> D ,F ~=> 0.0.0 ,B ~+> tick ,D ~+> 0.0 ,D ~+> tick ,F ~+> tick ,tick ~+> tick ,B ~*> tick ,D ~*> tick ,F ~*> tick ,K ~*> 0.0 ,K ~*> tick] lbl52.5> [B ~=> 0.0.0 ,F ~=> B ,F ~=> D ,F ~=> 0.0.0 ,B ~+> tick ,D ~+> 0.0 ,D ~+> tick ,F ~+> tick ,tick ~+> tick ,B ~*> tick ,D ~*> tick ,F ~*> tick ,K ~*> 0.0 ,K ~*> tick] + lbl52.4> [B ~=> 0.0.0,B ~+> tick,tick ~+> tick] YES(?,POLY)