YES(?,POLY) * Step 1: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A] (?,1) 1. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + C && B = C && D = A] (?,1) 2. start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 (?,1) && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 2 + A >= C && C >= 0 && 2 + C >= A && B = C && D = A] 3. start(A,B,C,D) -> lbl81(A,B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 3 + A && B = C && D = A] (?,1) 4. start(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 3 + C && C >= 0 && B = C && D = A] (?,1) 5. lbl81(A,B,C,D) -> stop(A,B,C,D) [-2 + C + -1*D >= 0 (?,1) && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + A && 2 + D = C && B = C] 6. lbl81(A,B,C,D) -> lbl81(A,B,C,1 + D) [-2 + C + -1*D >= 0 (?,1) && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + D && D >= 1 + A && C >= 2 + D && B = C] 7. lbl91(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 (?,1) && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + C && 2 + B = A && D = A] 8. lbl91(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 (?,1) && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + B && A >= 2 + B && B >= 1 + C && D = A] 9. start0(A,B,C,D) -> start(A,C,C,A) True (1,1) Signature: {(lbl81,4);(lbl91,4);(start,4);(start0,4);(stop,4)} Flow Graph: [0->{},1->{},2->{},3->{5,6},4->{7,8},5->{},6->{5,6},7->{},8->{7,8},9->{0,1,2,3,4}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A] start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + C && B = C && D = A] start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 2 + A >= C && C >= 0 && 2 + C >= A && B = C && D = A] start(A,B,C,D) -> lbl81(A,B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 3 + A && B = C && D = A] start(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 3 + C && C >= 0 && B = C && D = A] lbl81(A,B,C,D) -> stop(A,B,C,D) [-2 + C + -1*D >= 0 && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + A && 2 + D = C && B = C] lbl81(A,B,C,D) -> lbl81(A,B,C,1 + D) [-2 + C + -1*D >= 0 && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + D && D >= 1 + A && C >= 2 + D && B = C] lbl91(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + C && 2 + B = A && D = A] lbl91(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + B && A >= 2 + B && B >= 1 + C && D = A] start0(A,B,C,D) -> start(A,C,C,A) True Signature: {(lbl81,4);(lbl91,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{},1->{},2->{},3->{5,6},4->{7,8},5->{},6->{5,6},7->{},8->{7,8},9->{0,1,2,3,4}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A] start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + C && B = C && D = A] start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 2 + A >= C && C >= 0 && 2 + C >= A && B = C && D = A] start(A,B,C,D) -> lbl81(A,B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 3 + A && B = C && D = A] start(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 3 + C && C >= 0 && B = C && D = A] lbl81(A,B,C,D) -> stop(A,B,C,D) [-2 + C + -1*D >= 0 && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + A && 2 + D = C && B = C] lbl81(A,B,C,D) -> lbl81(A,B,C,1 + D) [-2 + C + -1*D >= 0 && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + D && D >= 1 + A && C >= 2 + D && B = C] lbl91(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + C && 2 + B = A && D = A] lbl91(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + B && A >= 2 + B && B >= 1 + C && D = A] start0(A,B,C,D) -> start(A,C,C,A) True stop(A,B,C,D) -> exitus616(A,B,C,D) True stop(A,B,C,D) -> exitus616(A,B,C,D) True stop(A,B,C,D) -> exitus616(A,B,C,D) True stop(A,B,C,D) -> exitus616(A,B,C,D) True stop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(lbl81,4);(lbl91,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{14},1->{13},2->{12},3->{5,6},4->{7,8},5->{11},6->{5,6},7->{10},8->{7,8},9->{0,1,2,3,4}] + 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] | +- p:[8] c: [8] | `- p:[6] c: [6] * Step 4: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + A && B = C && D = A] start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= 1 + C && B = C && D = A] start(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && 2 + A >= C && C >= 0 && 2 + C >= A && B = C && D = A] start(A,B,C,D) -> lbl81(A,B,C,1 + D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 0 && C >= 3 + A && B = C && D = A] start(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -1*A + D >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 3 + C && C >= 0 && B = C && D = A] lbl81(A,B,C,D) -> stop(A,B,C,D) [-2 + C + -1*D >= 0 && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + A && 2 + D = C && B = C] lbl81(A,B,C,D) -> lbl81(A,B,C,1 + D) [-2 + C + -1*D >= 0 && -2 + B + -1*D >= 0 && -1 + D >= 0 && -4 + C + D >= 0 && -4 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && -3 + C >= 0 && -6 + B + C >= 0 && -1*B + C >= 0 && -3 + A + C >= 0 && -3 + -1*A + C >= 0 && -3 + B >= 0 && -3 + A + B >= 0 && -3 + -1*A + B >= 0 && A >= 0 && C >= 3 + D && D >= 1 + A && C >= 2 + D && B = C] lbl91(A,B,C,D) -> stop(A,B,C,D) [A + -1*D >= 0 && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + C && 2 + B = A && D = A] lbl91(A,B,C,D) -> lbl91(A,1 + B,C,D) [A + -1*D >= 0 && -3 + D >= 0 && -3 + C + D >= 0 && -3 + -1*C + D >= 0 && -4 + B + D >= 0 && -2 + -1*B + D >= 0 && -6 + A + D >= 0 && -1*A + D >= 0 && -1 + B + -1*C >= 0 && -3 + A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -3 + A + C >= 0 && -2 + A + -1*B >= 0 && -1 + B >= 0 && -4 + A + B >= 0 && -3 + A >= 0 && A >= 3 + B && A >= 2 + B && B >= 1 + C && D = A] start0(A,B,C,D) -> start(A,C,C,A) True stop(A,B,C,D) -> exitus616(A,B,C,D) True stop(A,B,C,D) -> exitus616(A,B,C,D) True stop(A,B,C,D) -> exitus616(A,B,C,D) True stop(A,B,C,D) -> exitus616(A,B,C,D) True stop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(lbl81,4);(lbl91,4);(start,4);(start0,4);(stop,4)} Rule Graph: [0->{14},1->{13},2->{12},3->{5,6},4->{7,8},5->{11},6->{5,6},7->{10},8->{7,8},9->{0,1,2,3,4}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | +- p:[8] c: [8] | `- p:[6] c: [6]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.1] start ~> stop [A <= A, B <= B, C <= C, D <= D] start ~> stop [A <= A, B <= B, C <= C, D <= D] start ~> stop [A <= A, B <= B, C <= C, D <= D] start ~> lbl81 [A <= A, B <= B, C <= C, D <= C] start ~> lbl91 [A <= A, B <= A, C <= C, D <= D] lbl81 ~> stop [A <= A, B <= B, C <= C, D <= D] lbl81 ~> lbl81 [A <= A, B <= B, C <= C, D <= C] lbl91 ~> stop [A <= A, B <= B, C <= C, D <= D] lbl91 ~> lbl91 [A <= A, B <= A, C <= C, D <= D] start0 ~> start [A <= A, B <= C, C <= C, D <= A] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= 2*K + B + D] lbl91 ~> lbl91 [A <= A, B <= A, C <= C, D <= D] + Loop: [0.1 <= 2*K + C + D] lbl81 ~> lbl81 [A <= A, B <= B, C <= C, D <= C] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.1] start ~> stop [] start ~> stop [] start ~> stop [] start ~> lbl81 [C ~=> D] start ~> lbl91 [A ~=> B] lbl81 ~> stop [] lbl81 ~> lbl81 [C ~=> D] lbl91 ~> stop [] lbl91 ~> lbl91 [A ~=> B] start0 ~> start [A ~=> D,C ~=> B] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] stop ~> exitus616 [] + Loop: [B ~+> 0.0,D ~+> 0.0,K ~*> 0.0] lbl91 ~> lbl91 [A ~=> B] + Loop: [C ~+> 0.1,D ~+> 0.1,K ~*> 0.1] lbl81 ~> lbl81 [C ~=> D] + Applied Processor: Lare + Details: start0 ~> exitus616 [A ~=> B ,A ~=> D ,C ~=> B ,C ~=> D ,A ~+> 0.0 ,A ~+> tick ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,A ~*> 0.0 ,A ~*> tick ,C ~*> 0.1 ,C ~*> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + lbl91> [A ~=> B,B ~+> 0.0,B ~+> tick,D ~+> 0.0,D ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + lbl81> [C ~=> D,C ~+> 0.1,C ~+> tick,D ~+> 0.1,D ~+> tick,tick ~+> tick,K ~*> 0.1,K ~*> tick] YES(?,POLY)