YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D) -> f19(A,999,C,1) True (1,1) 1. f19(A,B,C,D) -> f19(A,-1 + B,C,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && B >= 0] 2. f19(A,B,C,D) -> f28(A,B,999,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && 0 >= 1 + B] 3. f28(A,B,C,D) -> f28(A,B,-1 + C,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && C >= 0] 4. f28(A,B,C,D) -> f36(A,B,C,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && 0 >= 1 + C] Signature: {(f0,4);(f19,4);(f28,4);(f36,4)} Flow Graph: [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{}] + Applied Processor: ArgumentFilter [0] + Details: We remove following argument positions: [0]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C,D) -> f19(999,C,1) True (1,1) 1. f19(B,C,D) -> f19(-1 + B,C,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && B >= 0] 2. f19(B,C,D) -> f28(B,999,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && 0 >= 1 + B] 3. f28(B,C,D) -> f28(B,-1 + C,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && C >= 0] 4. f28(B,C,D) -> f36(B,C,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && 0 >= 1 + C] Signature: {(f0,4);(f19,4);(f28,4);(f36,4)} Flow Graph: [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2),(2,4)] * Step 3: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(B,C,D) -> f19(999,C,1) True (1,1) 1. f19(B,C,D) -> f19(-1 + B,C,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && B >= 0] 2. f19(B,C,D) -> f28(B,999,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && 0 >= 1 + B] 3. f28(B,C,D) -> f28(B,-1 + C,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && C >= 0] 4. f28(B,C,D) -> f36(B,C,D) [1 + -1*D >= 0 (?,1) && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && 0 >= 1 + C] Signature: {(f0,4);(f19,4);(f28,4);(f36,4)} Flow Graph: [0->{1},1->{1,2},2->{3},3->{3,4},4->{}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(B,C,D) -> f19(999,C,1) True f19(B,C,D) -> f19(-1 + B,C,D) [1 + -1*D >= 0 && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && B >= 0] f19(B,C,D) -> f28(B,999,D) [1 + -1*D >= 0 && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && 0 >= 1 + B] f28(B,C,D) -> f28(B,-1 + C,D) [1 + -1*D >= 0 && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && C >= 0] f28(B,C,D) -> f36(B,C,D) [1 + -1*D >= 0 && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && 0 >= 1 + C] Signature: {(f0,4);(f19,4);(f28,4);(f36,4)} Rule Graph: [0->{1},1->{1,2},2->{3},3->{3,4},4->{}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(B,C,D) -> f19(999,C,1) True f19(B,C,D) -> f19(-1 + B,C,D) [1 + -1*D >= 0 && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && B >= 0] f19(B,C,D) -> f28(B,999,D) [1 + -1*D >= 0 && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && 0 >= 1 + B] f28(B,C,D) -> f28(B,-1 + C,D) [1 + -1*D >= 0 && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && C >= 0] f28(B,C,D) -> f36(B,C,D) [1 + -1*D >= 0 && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && 0 >= 1 + C] f36(B,C,D) -> exitus616(B,C,D) True Signature: {(exitus616,3);(f0,4);(f19,4);(f28,4);(f36,4)} Rule Graph: [0->{1},1->{1,2},2->{3},3->{3,4},4->{5}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[1] c: [1] | `- p:[3] c: [3] * Step 6: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0(B,C,D) -> f19(999,C,1) True f19(B,C,D) -> f19(-1 + B,C,D) [1 + -1*D >= 0 && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && B >= 0] f19(B,C,D) -> f28(B,999,D) [1 + -1*D >= 0 && 1000 + -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*B + D >= 0 && 999 + -1*B >= 0 && 0 >= 1 + B] f28(B,C,D) -> f28(B,-1 + C,D) [1 + -1*D >= 0 && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && C >= 0] f28(B,C,D) -> f36(B,C,D) [1 + -1*D >= 0 && 1000 + -1*C + -1*D >= 0 && -1*B + -1*D >= 0 && -1 + D >= 0 && 998 + -1*C + D >= 0 && -2 + -1*B + D >= 0 && 999 + -1*C >= 0 && 998 + -1*B + -1*C >= 0 && -1 + -1*B >= 0 && 0 >= 1 + C] f36(B,C,D) -> exitus616(B,C,D) True Signature: {(exitus616,3);(f0,4);(f19,4);(f28,4);(f36,4)} Rule Graph: [0->{1},1->{1,2},2->{3},3->{3,4},4->{5}] ,We construct a looptree: P: [0,1,2,3,4,5] | +- p:[1] c: [1] | `- p:[3] c: [3]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [B,C,D,0.0,0.1] f0 ~> f19 [B <= 999*K, C <= C, D <= K] f19 ~> f19 [B <= 998*K, C <= C, D <= D] f19 ~> f28 [B <= B, C <= 999*K, D <= D] f28 ~> f28 [B <= B, C <= 998*K, D <= D] f28 ~> f36 [B <= B, C <= C, D <= D] f36 ~> exitus616 [B <= B, C <= C, D <= D] + Loop: [0.0 <= B] f19 ~> f19 [B <= 998*K, C <= C, D <= D] + Loop: [0.1 <= C] f28 ~> f28 [B <= B, C <= 998*K, D <= D] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,B,C,D,0.0,0.1] f0 ~> f19 [K ~=> B,K ~=> D] f19 ~> f19 [K ~=> B] f19 ~> f28 [K ~=> C] f28 ~> f28 [K ~=> C] f28 ~> f36 [] f36 ~> exitus616 [] + Loop: [B ~=> 0.0] f19 ~> f19 [K ~=> B] + Loop: [C ~=> 0.1] f28 ~> f28 [K ~=> C] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> B,K ~=> C,K ~=> D,K ~=> 0.0,K ~=> 0.1,tick ~+> tick,K ~+> tick,K ~*> tick] + f19> [B ~=> 0.0,K ~=> B,B ~+> tick,tick ~+> tick] + f28> [C ~=> 0.1,K ~=> C,C ~+> tick,tick ~+> tick] YES(?,O(1))