YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y [7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 2. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y[7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 3. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (?,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (?,1) Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1,4},1->{1,4},2->{2,3},3->{},4->{2,3}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y [7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 2. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y[7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 3. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (1,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (1,1) Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1,4},1->{1,4},2->{2,3},3->{},4->{2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(4,3)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y [7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 2. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y[7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 3. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (1,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (1,1) Signature: {(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1},1->{1,4},2->{2,3},3->{},4->{2}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y [7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 2. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y[7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 3. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (?,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (?,1) 5. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> exitus616(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (?,1) Signature: {(exitus616,20);(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1,4},1->{1,4},2->{2,3,5},3->{},4->{2,3,5},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,4),(4,3)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y [7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 2. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y[7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 3. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (?,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (?,1) 5. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> exitus616(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (?,1) Signature: {(exitus616,20);(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1},1->{1,4},2->{2,3,5},3->{},4->{2,5},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[1] c: [1] | `- p:[2] c: [2] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(8,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (1,1) 1. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f7(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y [7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 2. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,1 + B,U + V,W,X + Y,Z,A1 + B1,C1,D1 + E1,F1,D1 + E1 + U + V,-1*D1 + -1*E1 + U + V,A1 + B1 + X + Y[7 >= B] (?,1) ,-1*A1 + -1*B1 + X + Y,-3196,G1,H1,I1 + J1,J1 + K1,J1) 3. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f118(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (?,1) 4. f7(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> f62(A,0,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) [B >= 8] (?,1) 5. f62(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) -> exitus616(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T) True (?,1) Signature: {(exitus616,20);(f0,20);(f118,20);(f62,20);(f7,20)} Flow Graph: [0->{1},1->{1,4},2->{2,3,5},3->{},4->{2,5},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | +- p:[1] c: [1] | `- p:[2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(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,0.0,0.1] f0 ~> f7 [A <= 8*K, B <= 0*K, 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] f7 ~> f7 [A <= A, B <= K + B, C <= unknown, D <= unknown, E <= unknown, F <= unknown, G <= unknown, H <= unknown, I <= unknown, J <= unknown, K <= unknown, L <= unknown, M <= unknown, N <= unknown, O <= 3196*K, P <= unknown, Q <= unknown, R <= unknown, S <= unknown, T <= unknown] f62 ~> f62 [A <= A, B <= K + B, C <= unknown, D <= unknown, E <= unknown, F <= unknown, G <= unknown, H <= unknown, I <= unknown, J <= unknown, K <= unknown, L <= unknown, M <= unknown, N <= unknown, O <= 3196*K, P <= unknown, Q <= unknown, R <= unknown, S <= unknown, T <= unknown] f62 ~> f118 [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] f7 ~> f62 [A <= A, B <= 0*K, 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] f62 ~> 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] + Loop: [0.0 <= 8*K + B] f7 ~> f7 [A <= A, B <= K + B, C <= unknown, D <= unknown, E <= unknown, F <= unknown, G <= unknown, H <= unknown, I <= unknown, J <= unknown, K <= unknown, L <= unknown, M <= unknown, N <= unknown, O <= 3196*K, P <= unknown, Q <= unknown, R <= unknown, S <= unknown, T <= unknown] + Loop: [0.1 <= 8*K + B] f62 ~> f62 [A <= A, B <= K + B, C <= unknown, D <= unknown, E <= unknown, F <= unknown, G <= unknown, H <= unknown, I <= unknown, J <= unknown, K <= unknown, L <= unknown, M <= unknown, N <= unknown, O <= 3196*K, P <= unknown, Q <= unknown, R <= unknown, S <= unknown, T <= unknown] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(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,0.0,0.1] f0 ~> f7 [K ~=> A,K ~=> B] f7 ~> f7 [K ~=> O ,huge ~=> C ,huge ~=> D ,huge ~=> E ,huge ~=> F ,huge ~=> G ,huge ~=> H ,huge ~=> I ,huge ~=> J ,huge ~=> K ,huge ~=> L ,huge ~=> M ,huge ~=> N ,huge ~=> P ,huge ~=> Q ,huge ~=> R ,huge ~=> S ,huge ~=> T ,B ~+> B ,K ~+> B] f62 ~> f62 [K ~=> O ,huge ~=> C ,huge ~=> D ,huge ~=> E ,huge ~=> F ,huge ~=> G ,huge ~=> H ,huge ~=> I ,huge ~=> J ,huge ~=> K ,huge ~=> L ,huge ~=> M ,huge ~=> N ,huge ~=> P ,huge ~=> Q ,huge ~=> R ,huge ~=> S ,huge ~=> T ,B ~+> B ,K ~+> B] f62 ~> f118 [] f7 ~> f62 [K ~=> B] f62 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f7 ~> f7 [K ~=> O ,huge ~=> C ,huge ~=> D ,huge ~=> E ,huge ~=> F ,huge ~=> G ,huge ~=> H ,huge ~=> I ,huge ~=> J ,huge ~=> K ,huge ~=> L ,huge ~=> M ,huge ~=> N ,huge ~=> P ,huge ~=> Q ,huge ~=> R ,huge ~=> S ,huge ~=> T ,B ~+> B ,K ~+> B] + Loop: [B ~+> 0.1,K ~*> 0.1] f62 ~> f62 [K ~=> O ,huge ~=> C ,huge ~=> D ,huge ~=> E ,huge ~=> F ,huge ~=> G ,huge ~=> H ,huge ~=> I ,huge ~=> J ,huge ~=> K ,huge ~=> L ,huge ~=> M ,huge ~=> N ,huge ~=> P ,huge ~=> Q ,huge ~=> R ,huge ~=> S ,huge ~=> T ,B ~+> B ,K ~+> B] + Applied Processor: LareProcessor + Details: f0 ~> f118 [K ~=> A ,K ~=> B ,K ~=> O ,huge ~=> C ,huge ~=> D ,huge ~=> E ,huge ~=> F ,huge ~=> G ,huge ~=> H ,huge ~=> I ,huge ~=> J ,huge ~=> K ,huge ~=> L ,huge ~=> M ,huge ~=> N ,huge ~=> P ,huge ~=> Q ,huge ~=> R ,huge ~=> S ,huge ~=> T ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] f0 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> O ,huge ~=> C ,huge ~=> D ,huge ~=> E ,huge ~=> F ,huge ~=> G ,huge ~=> H ,huge ~=> I ,huge ~=> J ,huge ~=> K ,huge ~=> L ,huge ~=> M ,huge ~=> N ,huge ~=> P ,huge ~=> Q ,huge ~=> R ,huge ~=> S ,huge ~=> T ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + f7> [K ~=> O ,huge ~=> C ,huge ~=> D ,huge ~=> E ,huge ~=> F ,huge ~=> G ,huge ~=> H ,huge ~=> I ,huge ~=> J ,huge ~=> K ,huge ~=> L ,huge ~=> M ,huge ~=> N ,huge ~=> P ,huge ~=> Q ,huge ~=> R ,huge ~=> S ,huge ~=> T ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,B ~*> B ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] + f62> [K ~=> O ,huge ~=> C ,huge ~=> D ,huge ~=> E ,huge ~=> F ,huge ~=> G ,huge ~=> H ,huge ~=> I ,huge ~=> J ,huge ~=> K ,huge ~=> L ,huge ~=> M ,huge ~=> N ,huge ~=> P ,huge ~=> Q ,huge ~=> R ,huge ~=> S ,huge ~=> T ,B ~+> B ,B ~+> 0.1 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,B ~*> B ,K ~*> B ,K ~*> 0.1 ,K ~*> tick] YES(?,O(1))