YES(?,O(n^1)) * Step 1: ArgumentFilter WORST_CASE(?,O(n^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,U,V,W,X,Y,Z,A1) -> f16(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. f16(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) -> f26(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) [B >= 1 + A] (?,1) 2. f16(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) -> f18(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) [A >= B] (?,1) 3. f26(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) -> f35(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*A + B >= 0 && B >= 1 + A] (?,1) 4. f18(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) -> f16(A,1 + 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) [A + -1*B >= 0 && C >= 1 + A] (?,1) 5. f18(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) -> f18(A,B,1 + 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 + -1*B >= 0 && A >= C] (?,1) 6. f35(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) -> f52(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*A + B >= 0 && E >= 51] (?,1) 7. f35(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) -> f38(A,B,C,D,E,0,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1 + -1*A + B >= 0 && 50 >= E] (?,1) 8. f38(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) -> f52(A,B,C,D,E,0,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,A1) [-1*F >= 0 (?,1) && 50 + -1*E + -1*F >= 0 && F >= 0 && 50 + -1*E + F >= 0 && 50 + -1*E >= 0 && -1 + -1*A + B >= 0 && B >= A && F = 0] Signature: {(f0,27);(f16,27);(f18,27);(f26,27);(f35,27);(f38,27);(f52,27)} Flow Graph: [0->{1,2},1->{3},2->{4,5},3->{6,7},4->{1,2},5->{4,5},6->{},7->{8},8->{}] + Applied Processor: ArgumentFilter [3,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] + Details: We remove following argument positions: [3,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A,B,C,E,F) -> f16(A,B,C,E,F) True (1,1) 1. f16(A,B,C,E,F) -> f26(A,B,C,E,F) [B >= 1 + A] (?,1) 2. f16(A,B,C,E,F) -> f18(A,B,C,E,F) [A >= B] (?,1) 3. f26(A,B,C,E,F) -> f35(A,B,C,E,F) [-1 + -1*A + B >= 0 && B >= 1 + A] (?,1) 4. f18(A,B,C,E,F) -> f16(A,1 + B,C,E,F) [A + -1*B >= 0 && C >= 1 + A] (?,1) 5. f18(A,B,C,E,F) -> f18(A,B,1 + C,E,F) [A + -1*B >= 0 && A >= C] (?,1) 6. f35(A,B,C,E,F) -> f52(A,B,C,E,F) [-1 + -1*A + B >= 0 && E >= 51] (?,1) 7. f35(A,B,C,E,F) -> f38(A,B,C,E,0) [-1 + -1*A + B >= 0 && 50 >= E] (?,1) 8. f38(A,B,C,E,F) -> f52(A,B,C,E,0) [-1*F >= 0 (?,1) && 50 + -1*E + -1*F >= 0 && F >= 0 && 50 + -1*E + F >= 0 && 50 + -1*E >= 0 && -1 + -1*A + B >= 0 && B >= A && F = 0] Signature: {(f0,27);(f16,27);(f18,27);(f26,27);(f35,27);(f38,27);(f52,27)} Flow Graph: [0->{1,2},1->{3},2->{4,5},3->{6,7},4->{1,2},5->{4,5},6->{},7->{8},8->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f0(A,B,C,E,F) -> f16(A,B,C,E,F) True f16(A,B,C,E,F) -> f26(A,B,C,E,F) [B >= 1 + A] f16(A,B,C,E,F) -> f18(A,B,C,E,F) [A >= B] f26(A,B,C,E,F) -> f35(A,B,C,E,F) [-1 + -1*A + B >= 0 && B >= 1 + A] f18(A,B,C,E,F) -> f16(A,1 + B,C,E,F) [A + -1*B >= 0 && C >= 1 + A] f18(A,B,C,E,F) -> f18(A,B,1 + C,E,F) [A + -1*B >= 0 && A >= C] f35(A,B,C,E,F) -> f52(A,B,C,E,F) [-1 + -1*A + B >= 0 && E >= 51] f35(A,B,C,E,F) -> f38(A,B,C,E,0) [-1 + -1*A + B >= 0 && 50 >= E] f38(A,B,C,E,F) -> f52(A,B,C,E,0) [-1*F >= 0 && 50 + -1*E + -1*F >= 0 && F >= 0 && 50 + -1*E + F >= 0 && 50 + -1*E >= 0 && -1 + -1*A + B >= 0 && B >= A && F = 0] Signature: {(f0,27);(f16,27);(f18,27);(f26,27);(f35,27);(f38,27);(f52,27)} Rule Graph: [0->{1,2},1->{3},2->{4,5},3->{6,7},4->{1,2},5->{4,5},6->{},7->{8},8->{}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f0(A,B,C,E,F) -> f16(A,B,C,E,F) True f16(A,B,C,E,F) -> f26(A,B,C,E,F) [B >= 1 + A] f16(A,B,C,E,F) -> f18(A,B,C,E,F) [A >= B] f26(A,B,C,E,F) -> f35(A,B,C,E,F) [-1 + -1*A + B >= 0 && B >= 1 + A] f18(A,B,C,E,F) -> f16(A,1 + B,C,E,F) [A + -1*B >= 0 && C >= 1 + A] f18(A,B,C,E,F) -> f18(A,B,1 + C,E,F) [A + -1*B >= 0 && A >= C] f35(A,B,C,E,F) -> f52(A,B,C,E,F) [-1 + -1*A + B >= 0 && E >= 51] f35(A,B,C,E,F) -> f38(A,B,C,E,0) [-1 + -1*A + B >= 0 && 50 >= E] f38(A,B,C,E,F) -> f52(A,B,C,E,0) [-1*F >= 0 && 50 + -1*E + -1*F >= 0 && F >= 0 && 50 + -1*E + F >= 0 && 50 + -1*E >= 0 && -1 + -1*A + B >= 0 && B >= A && F = 0] f52(A,B,C,E,F) -> exitus616(A,B,C,E,F) True f52(A,B,C,E,F) -> exitus616(A,B,C,E,F) True Signature: {(exitus616,5);(f0,27);(f16,27);(f18,27);(f26,27);(f35,27);(f38,27);(f52,27)} Rule Graph: [0->{1,2},1->{3},2->{4,5},3->{6,7},4->{1,2},5->{4,5},6->{10},7->{8},8->{9}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[2,4,5] c: [2,4,5] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: f0(A,B,C,E,F) -> f16(A,B,C,E,F) True f16(A,B,C,E,F) -> f26(A,B,C,E,F) [B >= 1 + A] f16(A,B,C,E,F) -> f18(A,B,C,E,F) [A >= B] f26(A,B,C,E,F) -> f35(A,B,C,E,F) [-1 + -1*A + B >= 0 && B >= 1 + A] f18(A,B,C,E,F) -> f16(A,1 + B,C,E,F) [A + -1*B >= 0 && C >= 1 + A] f18(A,B,C,E,F) -> f18(A,B,1 + C,E,F) [A + -1*B >= 0 && A >= C] f35(A,B,C,E,F) -> f52(A,B,C,E,F) [-1 + -1*A + B >= 0 && E >= 51] f35(A,B,C,E,F) -> f38(A,B,C,E,0) [-1 + -1*A + B >= 0 && 50 >= E] f38(A,B,C,E,F) -> f52(A,B,C,E,0) [-1*F >= 0 && 50 + -1*E + -1*F >= 0 && F >= 0 && 50 + -1*E + F >= 0 && 50 + -1*E >= 0 && -1 + -1*A + B >= 0 && B >= A && F = 0] f52(A,B,C,E,F) -> exitus616(A,B,C,E,F) True f52(A,B,C,E,F) -> exitus616(A,B,C,E,F) True Signature: {(exitus616,5);(f0,27);(f16,27);(f18,27);(f26,27);(f35,27);(f38,27);(f52,27)} Rule Graph: [0->{1,2},1->{3},2->{4,5},3->{6,7},4->{1,2},5->{4,5},6->{10},7->{8},8->{9}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[2,4,5] c: [2,4,5]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,E,F,0.0] f0 ~> f16 [A <= A, B <= B, C <= C, E <= E, F <= F] f16 ~> f26 [A <= A, B <= B, C <= C, E <= E, F <= F] f16 ~> f18 [A <= A, B <= B, C <= C, E <= E, F <= F] f26 ~> f35 [A <= A, B <= B, C <= C, E <= E, F <= F] f18 ~> f16 [A <= A, B <= K + B, C <= C, E <= E, F <= F] f18 ~> f18 [A <= A, B <= B, C <= K + C, E <= E, F <= F] f35 ~> f52 [A <= A, B <= B, C <= C, E <= E, F <= F] f35 ~> f38 [A <= A, B <= B, C <= C, E <= E, F <= 0*K] f38 ~> f52 [A <= A, B <= B, C <= C, E <= E, F <= 0*K] f52 ~> exitus616 [A <= A, B <= B, C <= C, E <= E, F <= F] f52 ~> exitus616 [A <= A, B <= B, C <= C, E <= E, F <= F] + Loop: [0.0 <= A + B + C] f16 ~> f18 [A <= A, B <= B, C <= C, E <= E, F <= F] f18 ~> f16 [A <= A, B <= K + B, C <= C, E <= E, F <= F] f18 ~> f18 [A <= A, B <= B, C <= K + C, E <= E, F <= F] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,E,F,0.0] f0 ~> f16 [] f16 ~> f26 [] f16 ~> f18 [] f26 ~> f35 [] f18 ~> f16 [B ~+> B,K ~+> B] f18 ~> f18 [C ~+> C,K ~+> C] f35 ~> f52 [] f35 ~> f38 [K ~=> F] f38 ~> f52 [K ~=> F] f52 ~> exitus616 [] f52 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0] f16 ~> f18 [] f18 ~> f16 [B ~+> B,K ~+> B] f18 ~> f18 [C ~+> C,K ~+> C] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> F ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,A ~*> B ,A ~*> C ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C ,K ~*> B ,K ~*> C] + f16> [A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,A ~*> B ,A ~*> C ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C ,K ~*> B ,K ~*> C] YES(?,O(n^1))