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) -> f12(3,T,3,1,0,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) True (1,1) 1. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f12(A,B,C,T,1 + E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) [C >= 1 + E] (?,1) 2. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,F,1 + G,T,I,J,K,L,M,N,O,P,Q,R,S) [F >= 1 + G] (?,1) 3. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,I,1 + J,T,L,M,N,O,P,Q,R,S) [I >= 1 + J] (?,1) 4. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f46(A,B,C,D,E,F,G,H,I,J,K,K,K,N,O,P,Q,R,S) [J >= I] (?,1) 5. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,A,0,1,L,M,H,H,T,Q,R,S) [G >= F] (?,1) 6. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,A,0,1,I,J,K,L,M,N,O,P,D,D,T) [E >= C] (?,1) Signature: {(f0,19);(f12,19);(f24,19);(f36,19);(f46,19)} Flow Graph: [0->{1,6},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3,4},6->{2,5}] + 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) -> f12(3,T,3,1,0,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) True (1,1) 1. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f12(A,B,C,T,1 + E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) [C >= 1 + E] (?,1) 2. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,F,1 + G,T,I,J,K,L,M,N,O,P,Q,R,S) [F >= 1 + G] (?,1) 3. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,I,1 + J,T,L,M,N,O,P,Q,R,S) [I >= 1 + J] (?,1) 4. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f46(A,B,C,D,E,F,G,H,I,J,K,K,K,N,O,P,Q,R,S) [J >= I] (1,1) 5. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,A,0,1,L,M,H,H,T,Q,R,S) [G >= F] (1,1) 6. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,A,0,1,I,J,K,L,M,N,O,P,D,D,T) [E >= C] (1,1) Signature: {(f0,19);(f12,19);(f24,19);(f36,19);(f46,19)} Flow Graph: [0->{1,6},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3,4},6->{2,5}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,6)] * 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) -> f12(3,T,3,1,0,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) True (1,1) 1. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f12(A,B,C,T,1 + E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) [C >= 1 + E] (?,1) 2. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,F,1 + G,T,I,J,K,L,M,N,O,P,Q,R,S) [F >= 1 + G] (?,1) 3. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,I,1 + J,T,L,M,N,O,P,Q,R,S) [I >= 1 + J] (?,1) 4. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f46(A,B,C,D,E,F,G,H,I,J,K,K,K,N,O,P,Q,R,S) [J >= I] (1,1) 5. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,A,0,1,L,M,H,H,T,Q,R,S) [G >= F] (1,1) 6. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,A,0,1,I,J,K,L,M,N,O,P,D,D,T) [E >= C] (1,1) Signature: {(f0,19);(f12,19);(f24,19);(f36,19);(f46,19)} Flow Graph: [0->{1},1->{1,6},2->{2,5},3->{3,4},4->{},5->{3,4},6->{2,5}] + 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) -> f12(3,T,3,1,0,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) True (1,1) 1. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f12(A,B,C,T,1 + E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) [C >= 1 + E] (?,1) 2. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,F,1 + G,T,I,J,K,L,M,N,O,P,Q,R,S) [F >= 1 + G] (?,1) 3. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,I,1 + J,T,L,M,N,O,P,Q,R,S) [I >= 1 + J] (?,1) 4. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f46(A,B,C,D,E,F,G,H,I,J,K,K,K,N,O,P,Q,R,S) [J >= I] (?,1) 5. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,A,0,1,L,M,H,H,T,Q,R,S) [G >= F] (?,1) 6. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,A,0,1,I,J,K,L,M,N,O,P,D,D,T) [E >= C] (?,1) 7. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> exitus616(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) True (?,1) Signature: {(exitus616,19);(f0,19);(f12,19);(f24,19);(f36,19);(f46,19)} Flow Graph: [0->{1,6},1->{1,6},2->{2,5},3->{3,4,7},4->{},5->{3,4,7},6->{2,5},7->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,6)] * 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) -> f12(3,T,3,1,0,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) True (1,1) 1. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f12(A,B,C,T,1 + E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) [C >= 1 + E] (?,1) 2. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,F,1 + G,T,I,J,K,L,M,N,O,P,Q,R,S) [F >= 1 + G] (?,1) 3. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,I,1 + J,T,L,M,N,O,P,Q,R,S) [I >= 1 + J] (?,1) 4. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f46(A,B,C,D,E,F,G,H,I,J,K,K,K,N,O,P,Q,R,S) [J >= I] (?,1) 5. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,A,0,1,L,M,H,H,T,Q,R,S) [G >= F] (?,1) 6. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,A,0,1,I,J,K,L,M,N,O,P,D,D,T) [E >= C] (?,1) 7. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> exitus616(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) True (?,1) Signature: {(exitus616,19);(f0,19);(f12,19);(f24,19);(f36,19);(f46,19)} Flow Graph: [0->{1},1->{1,6},2->{2,5},3->{3,4,7},4->{},5->{3,4,7},6->{2,5},7->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[1] c: [1] | +- p:[2] c: [2] | `- p:[3] c: [3] * 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) -> f12(3,T,3,1,0,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) True (1,1) 1. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f12(A,B,C,T,1 + E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) [C >= 1 + E] (?,1) 2. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,F,1 + G,T,I,J,K,L,M,N,O,P,Q,R,S) [F >= 1 + G] (?,1) 3. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,I,1 + J,T,L,M,N,O,P,Q,R,S) [I >= 1 + J] (?,1) 4. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f46(A,B,C,D,E,F,G,H,I,J,K,K,K,N,O,P,Q,R,S) [J >= I] (?,1) 5. f24(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f36(A,B,C,D,E,F,G,H,A,0,1,L,M,H,H,T,Q,R,S) [G >= F] (?,1) 6. f12(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> f24(A,B,C,D,E,A,0,1,I,J,K,L,M,N,O,P,D,D,T) [E >= C] (?,1) 7. f36(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) -> exitus616(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S) True (?,1) Signature: {(exitus616,19);(f0,19);(f12,19);(f24,19);(f36,19);(f46,19)} Flow Graph: [0->{1},1->{1,6},2->{2,5},3->{3,4,7},4->{},5->{3,4,7},6->{2,5},7->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[1] c: [1] | +- p:[2] c: [2] | `- p:[3] c: [3]) + 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,0.0,0.1,0.2] f0 ~> f12 [A <= 3*K, B <= unknown, C <= 3*K, D <= K, E <= 0*K, 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] f12 ~> f12 [A <= A, B <= B, C <= C, D <= unknown, E <= C + 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] f24 ~> f24 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= F + G, H <= unknown, I <= I, J <= J, K <= K, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S] f36 ~> f36 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= I + J, K <= unknown, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S] f36 ~> f46 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= J, K <= K, L <= K, M <= K, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S] f24 ~> f36 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= A, J <= 0*K, K <= K, L <= L, M <= M, N <= H, O <= H, P <= unknown, Q <= Q, R <= R, S <= S] f12 ~> f24 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= A, G <= 0*K, H <= K, I <= I, J <= J, K <= K, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= D, R <= D, S <= unknown] f36 ~> 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] + Loop: [0.0 <= C + E] f12 ~> f12 [A <= A, B <= B, C <= C, D <= unknown, E <= C + 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] + Loop: [0.1 <= F + G] f24 ~> f24 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= F + G, H <= unknown, I <= I, J <= J, K <= K, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S] + Loop: [0.2 <= I + J] f36 ~> f36 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G, H <= H, I <= I, J <= I + J, K <= unknown, L <= L, M <= M, N <= N, O <= O, P <= P, Q <= Q, R <= R, S <= S] + 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,0.0,0.1,0.2] f0 ~> f12 [K ~=> A,K ~=> C,K ~=> D,K ~=> E,huge ~=> B] f12 ~> f12 [huge ~=> D,C ~+> E,E ~+> E] f24 ~> f24 [huge ~=> H,F ~+> G,G ~+> G] f36 ~> f36 [huge ~=> K,I ~+> J,J ~+> J] f36 ~> f46 [K ~=> L,K ~=> M] f24 ~> f36 [A ~=> I,H ~=> N,H ~=> O,K ~=> J,K ~=> K,huge ~=> P] f12 ~> f24 [A ~=> F,D ~=> Q,D ~=> R,K ~=> G,K ~=> H,huge ~=> S] f36 ~> exitus616 [] + Loop: [C ~+> 0.0,E ~+> 0.0] f12 ~> f12 [huge ~=> D,C ~+> E,E ~+> E] + Loop: [F ~+> 0.1,G ~+> 0.1] f24 ~> f24 [huge ~=> H,F ~+> G,G ~+> G] + Loop: [I ~+> 0.2,J ~+> 0.2] f36 ~> f36 [huge ~=> K,I ~+> J,J ~+> J] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> A ,K ~=> C ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,K ~=> H ,K ~=> I ,K ~=> J ,K ~=> K ,K ~=> N ,K ~=> O ,K ~=> Q ,K ~=> R ,huge ~=> B ,huge ~=> D ,huge ~=> H ,huge ~=> K ,huge ~=> N ,huge ~=> O ,huge ~=> P ,huge ~=> Q ,huge ~=> R ,huge ~=> S ,tick ~+> tick ,K ~+> E ,K ~+> G ,K ~+> J ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> tick ,K ~*> E ,K ~*> G ,K ~*> J ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> tick] f0 ~> f46 [K ~=> A ,K ~=> C ,K ~=> D ,K ~=> E ,K ~=> F ,K ~=> G ,K ~=> H ,K ~=> I ,K ~=> J ,K ~=> K ,K ~=> L ,K ~=> M ,K ~=> N ,K ~=> O ,K ~=> Q ,K ~=> R ,huge ~=> B ,huge ~=> D ,huge ~=> H ,huge ~=> K ,huge ~=> L ,huge ~=> M ,huge ~=> N ,huge ~=> O ,huge ~=> P ,huge ~=> Q ,huge ~=> R ,huge ~=> S ,tick ~+> tick ,K ~+> E ,K ~+> G ,K ~+> J ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> tick ,K ~*> E ,K ~*> G ,K ~*> J ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> tick] + f12> [huge ~=> D ,C ~+> E ,C ~+> 0.0 ,C ~+> tick ,E ~+> E ,E ~+> 0.0 ,E ~+> tick ,tick ~+> tick ,C ~*> E ,E ~*> E] + f24> [huge ~=> H ,F ~+> G ,F ~+> 0.1 ,F ~+> tick ,G ~+> G ,G ~+> 0.1 ,G ~+> tick ,tick ~+> tick ,F ~*> G ,G ~*> G] + f36> [huge ~=> K ,I ~+> J ,I ~+> 0.2 ,I ~+> tick ,J ~+> J ,J ~+> 0.2 ,J ~+> tick ,tick ~+> tick ,I ~*> J ,J ~*> J] YES(?,O(1))