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) -> lbl62(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] (?,1) 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] (?,1) 3. lbl72(A,B,C,D,E,F) -> lbl72(A,F,C,-1 + D,E,F) [D >= 1 && 0 >= A && D >= 0 && A >= 1 + D && B = 0 && F = A] (?,1) 4. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] (?,1) 5. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] (?,1) 6. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] (?,1) 7. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{5,6},2->{},3->{2,3,4},4->{5,6},5->{2,3,4},6->{5,6},7->{0,1}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [3] * 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) -> lbl62(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] (?,1) 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] (?,1) 4. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] (?,1) 5. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] (?,1) 6. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] (?,1) 7. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{5,6},2->{},4->{5,6},5->{2,4},6->{5,6},7->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,5)] * 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) -> lbl62(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] (?,1) 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] (?,1) 4. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] (?,1) 5. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] (?,1) 6. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] (?,1) 7. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{5,6},2->{},4->{6},5->{2,4},6->{5,6},7->{0,1}] + 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) -> lbl62(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{5,6},2->{},4->{6},5->{2,4},6->{5,6},7->{0,1}] + Applied Processor: Unfold + Details: () * Step 5: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: start.0(A,B,C,D,E,F) -> stop.8(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl62.5(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl62.6(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] lbl72.2(A,B,C,D,E,F) -> stop.8(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] lbl72.4(A,B,C,D,E,F) -> lbl62.6(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] lbl62.5(A,B,C,D,E,F) -> lbl72.2(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62.5(A,B,C,D,E,F) -> lbl72.4(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62.6(A,B,C,D,E,F) -> lbl62.5(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] lbl62.6(A,B,C,D,E,F) -> lbl62.6(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] start0.7(A,B,C,D,E,F) -> start.0(A,C,C,E,E,A) True start0.7(A,B,C,D,E,F) -> start.1(A,C,C,E,E,A) True Signature: {(lbl62.5,6);(lbl62.6,6);(lbl72.2,6);(lbl72.4,6);(start.0,6);(start.1,6);(start0.7,6);(stop.8,6)} Rule Graph: [0->{},1->{5,6},2->{7,8},3->{},4->{7,8},5->{3},6->{4},7->{5,6},8->{7,8},9->{0},10->{1,2}] + Applied Processor: AddSinks + Details: () * Step 6: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: start.0(A,B,C,D,E,F) -> stop.8(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl62.5(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl62.6(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] lbl72.2(A,B,C,D,E,F) -> stop.8(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] lbl72.4(A,B,C,D,E,F) -> lbl62.6(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] lbl62.5(A,B,C,D,E,F) -> lbl72.2(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62.5(A,B,C,D,E,F) -> lbl72.4(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62.6(A,B,C,D,E,F) -> lbl62.5(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] lbl62.6(A,B,C,D,E,F) -> lbl62.6(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] start0.7(A,B,C,D,E,F) -> start.0(A,C,C,E,E,A) True start0.7(A,B,C,D,E,F) -> start.1(A,C,C,E,E,A) True stop.8(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.8(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.8(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6) ;(lbl62.5,6) ;(lbl62.6,6) ;(lbl72.2,6) ;(lbl72.4,6) ;(start.0,6) ;(start.1,6) ;(start0.7,6) ;(stop.8,6)} Rule Graph: [0->{13},1->{5,6},2->{7,8},3->{11,12},4->{7,8},5->{3},6->{4},7->{5,6},8->{7,8},9->{0},10->{1,2}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[6,7,4,8] c: [4,6,7] | `- p:[8] c: [8] * Step 7: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: start.0(A,B,C,D,E,F) -> stop.8(A,B,C,F,E,F) [0 >= A && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl62.5(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] start.1(A,B,C,D,E,F) -> lbl62.6(A,-1 + F,C,F,E,F) [A >= 1 && B = C && D = E && F = A] lbl72.2(A,B,C,D,E,F) -> stop.8(A,B,C,D,E,F) [A >= 1 && D = 0 && B = 0 && F = A] lbl72.4(A,B,C,D,E,F) -> lbl62.6(A,-1 + F,C,D,E,F) [A >= 1 && D >= 1 && D >= 0 && A >= 1 + D && B = 0 && F = A] lbl62.5(A,B,C,D,E,F) -> lbl72.2(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62.5(A,B,C,D,E,F) -> lbl72.4(A,B,C,-1 + D,E,F) [A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62.6(A,B,C,D,E,F) -> lbl62.5(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] lbl62.6(A,B,C,D,E,F) -> lbl62.6(A,-1 + B,C,D,E,F) [B >= 1 && A >= D && A >= 1 + B && B >= 0 && D >= 1 && F = A] start0.7(A,B,C,D,E,F) -> start.0(A,C,C,E,E,A) True start0.7(A,B,C,D,E,F) -> start.1(A,C,C,E,E,A) True stop.8(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.8(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop.8(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6) ;(lbl62.5,6) ;(lbl62.6,6) ;(lbl72.2,6) ;(lbl72.4,6) ;(start.0,6) ;(start.1,6) ;(start0.7,6) ;(stop.8,6)} Rule Graph: [0->{13},1->{5,6},2->{7,8},3->{11,12},4->{7,8},5->{3},6->{4},7->{5,6},8->{7,8},9->{0},10->{1,2}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[6,7,4,8] c: [4,6,7] | `- p:[8] c: [8]) + 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.8 [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] start.1 ~> lbl62.5 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] start.1 ~> lbl62.6 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] lbl72.2 ~> stop.8 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl72.4 ~> lbl62.6 [A <= A, B <= F, C <= C, D <= D, E <= E, F <= F] lbl62.5 ~> lbl72.2 [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] lbl62.5 ~> lbl72.4 [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] lbl62.6 ~> lbl62.5 [A <= A, B <= F, C <= C, D <= D, E <= E, F <= F] lbl62.6 ~> lbl62.6 [A <= A, B <= F, C <= C, D <= D, E <= E, F <= F] start0.7 ~> start.0 [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] start0.7 ~> start.1 [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] stop.8 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop.8 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop.8 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= 2*K + D] lbl62.5 ~> lbl72.4 [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] lbl62.6 ~> lbl62.5 [A <= A, B <= F, C <= C, D <= D, E <= E, F <= F] lbl72.4 ~> lbl62.6 [A <= A, B <= F, C <= C, D <= D, E <= E, F <= F] lbl62.6 ~> lbl62.6 [A <= A, B <= F, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0.0 <= B] lbl62.6 ~> lbl62.6 [A <= A, B <= F, 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.8 [F ~=> D] start.1 ~> lbl62.5 [F ~=> B,F ~=> D] start.1 ~> lbl62.6 [F ~=> B,F ~=> D] lbl72.2 ~> stop.8 [] lbl72.4 ~> lbl62.6 [F ~=> B] lbl62.5 ~> lbl72.2 [F ~=> D] lbl62.5 ~> lbl72.4 [F ~=> D] lbl62.6 ~> lbl62.5 [F ~=> B] lbl62.6 ~> lbl62.6 [F ~=> B] start0.7 ~> start.0 [A ~=> F,C ~=> B,E ~=> D] start0.7 ~> start.1 [A ~=> F,C ~=> B,E ~=> D] stop.8 ~> exitus616 [] stop.8 ~> exitus616 [] stop.8 ~> exitus616 [] + Loop: [D ~+> 0.0,K ~*> 0.0] lbl62.5 ~> lbl72.4 [F ~=> D] lbl62.6 ~> lbl62.5 [F ~=> B] lbl72.4 ~> lbl62.6 [F ~=> B] lbl62.6 ~> lbl62.6 [F ~=> B] + Loop: [B ~=> 0.0.0] lbl62.6 ~> lbl62.6 [F ~=> B] + Applied Processor: Lare + Details: start0.7 ~> exitus616 [A ~=> B ,A ~=> D ,A ~=> F ,A ~=> 0.0.0 ,C ~=> B ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,A ~*> tick ,K ~*> 0.0 ,K ~*> tick] + lbl62.5> [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] lbl62.5> [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] + lbl62.6> [B ~=> 0.0.0,F ~=> B,B ~+> tick,tick ~+> tick] YES(?,POLY)