YES(?,O(n^1)) * Step 1: ArgumentFilter 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: ArgumentFilter [2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26] + Details: We remove following argument positions: [2,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,D) -> f2(A,B,D) True (1,1) 1. f2(A,B,D) -> f10(A,B,1) [B >= 1 + A] (?,1) 2. f2(A,B,D) -> f2(A,1 + B,D) [A >= B] (?,1) 3. f10(A,B,D) -> f1(A,B,D) [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: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B,D) -> f2(A,B,D) True f2(A,B,D) -> f10(A,B,1) [B >= 1 + A] f2(A,B,D) -> f2(A,1 + B,D) [A >= B] f10(A,B,D) -> f1(A,B,D) [1 + -1*D >= 0 && -1 + D >= 0 && -1 + -1*A + B >= 0 && 0 >= B] Signature: {(f1,27);(f10,27);(f2,27);(start,27)} Rule Graph: [0->{1,2},1->{3},2->{1,2},3->{}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B,D) -> f2(A,B,D) True f2(A,B,D) -> f10(A,B,1) [B >= 1 + A] f2(A,B,D) -> f2(A,1 + B,D) [A >= B] f10(A,B,D) -> f1(A,B,D) [1 + -1*D >= 0 && -1 + D >= 0 && -1 + -1*A + B >= 0 && 0 >= B] f1(A,B,D) -> exitus616(A,B,D) True Signature: {(exitus616,3);(f1,27);(f10,27);(f2,27);(start,27)} Rule Graph: [0->{1,2},1->{3},2->{1,2},3->{4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[2] c: [2] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: start(A,B,D) -> f2(A,B,D) True f2(A,B,D) -> f10(A,B,1) [B >= 1 + A] f2(A,B,D) -> f2(A,1 + B,D) [A >= B] f10(A,B,D) -> f1(A,B,D) [1 + -1*D >= 0 && -1 + D >= 0 && -1 + -1*A + B >= 0 && 0 >= B] f1(A,B,D) -> exitus616(A,B,D) True Signature: {(exitus616,3);(f1,27);(f10,27);(f2,27);(start,27)} Rule Graph: [0->{1,2},1->{3},2->{1,2},3->{4}] ,We construct a looptree: P: [0,1,2,3,4] | `- p:[2] c: [2]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,D,0.0] start ~> f2 [A <= A, B <= B, D <= D] f2 ~> f10 [A <= A, B <= B, D <= K] f2 ~> f2 [A <= A, B <= K + B, D <= D] f10 ~> f1 [A <= A, B <= B, D <= D] f1 ~> exitus616 [A <= A, B <= B, D <= D] + Loop: [0.0 <= A + B] f2 ~> f2 [A <= A, B <= K + B, D <= D] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,D,0.0] start ~> f2 [] f2 ~> f10 [K ~=> D] f2 ~> f2 [B ~+> B,K ~+> B] f10 ~> f1 [] f1 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] f2 ~> f2 [B ~+> B,K ~+> B] + Applied Processor: Lare + Details: start ~> exitus616 [K ~=> D ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,A ~*> B ,B ~*> B ,K ~*> B] + f2> [A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,A ~*> B ,B ~*> B ,K ~*> B] YES(?,O(n^1))