YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (1,1) 1. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f10(A,B,C,1,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1 + A] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,1 + B,B1*C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= B] (?,1) 3. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 + -1*D >= 0 && -1 + D >= 0 && -1 + -1*A + B >= 0 && 0 >= B] (?,1) Signature: {(f1,27);(f10,27);(f2,27);(start,27)} Flow Graph: [0->{1,2},1->{3},2->{1,2},3->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (1,1) 1. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f10(A,B,C,1,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1 + A] (1,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,1 + B,B1*C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= B] (?,1) 3. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 + -1*D >= 0 && -1 + D >= 0 && -1 + -1*A + B >= 0 && 0 >= B] (1,1) Signature: {(f1,27);(f10,27);(f2,27);(start,27)} Flow Graph: [0->{1,2},1->{3},2->{1,2},3->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (1,1) 1. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f10(A,B,C,1,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1 + A] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,1 + B,B1*C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= B] (?,1) 3. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 + -1*D >= 0 && -1 + D >= 0 && -1 + -1*A + B >= 0 && 0 >= B] (?,1) 4. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> exitus616(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (?,1) Signature: {(exitus616,27);(f1,27);(f10,27);(f2,27);(start,27)} Flow Graph: [0->{1,2},1->{3,4},2->{1,2},3->{},4->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[2] c: [2] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. start(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (1,1) 1. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f10(A,B,C,1,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [B >= 1 + A] (?,1) 2. f2(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f2(A,1 + B,B1*C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [A >= B] (?,1) 3. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [1 + -1*D >= 0 && -1 + D >= 0 && -1 + -1*A + B >= 0 && 0 >= B] (?,1) 4. f10(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) -> exitus616(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) True (?,1) Signature: {(exitus616,27);(f1,27);(f10,27);(f2,27);(start,27)} Flow Graph: [0->{1,2},1->{3,4},2->{1,2},3->{},4->{}] ,We construct a looptree: P: [0,1,2,3,4] | `- p:[2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,0.0] start ~> f2 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J, K <= K, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S, T <= T, U <= U, V <= V, W <= W, X <= X, Y <= Y, Z <= Z, A1 <= A1] f2 ~> f10 [A <= A, B <= B, C <= C, D <= K, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J, K <= K, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S, T <= T, U <= U, V <= V, W <= W, X <= X, Y <= Y, Z <= Z, A1 <= A1] f2 ~> f2 [A <= A, B <= K + B, C <= unknown, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J, K <= K, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S, T <= T, U <= U, V <= V, W <= W, X <= X, Y <= Y, Z <= Z, A1 <= A1] f10 ~> f1 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J, K <= K, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S, T <= T, U <= U, V <= V, W <= W, X <= X, Y <= Y, Z <= Z, A1 <= A1] f10 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J, K <= K, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S, T <= T, U <= U, V <= V, W <= W, X <= X, Y <= Y, Z <= Z, A1 <= A1] + Loop: [0.0 <= K + A + B] f2 ~> f2 [A <= A, B <= K + B, C <= unknown, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J, K <= K, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S, T <= T, U <= U, V <= V, W <= W, X <= X, Y <= Y, Z <= Z, A1 <= A1] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1,0.0] start ~> f2 [] f2 ~> f10 [K ~=> D] f2 ~> f2 [huge ~=> C,B ~+> B,K ~+> B] f10 ~> f1 [] f10 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] f2 ~> f2 [huge ~=> C,B ~+> B,K ~+> B] + Applied Processor: LareProcessor + Details: start ~> f1 [K ~=> D ,huge ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] start ~> exitus616 [K ~=> D ,huge ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] + f2> [huge ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] YES(?,O(n^1))