YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f8(0,B,C) True (1,1) 1. f8(A,B,C) -> f14(A,A,C) [A >= 0 && 9 >= A && 9 >= D] (?,1) 2. f8(A,B,C) -> f14(A,A,C) [A >= 0 && 9 >= A] (?,1) 3. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 9 >= A && 0 >= 1 + E] (?,1) 4. f23(A,B,C) -> f28(A,B,D) [A >= 0 && 9 >= A] (?,1) 5. f23(A,B,C) -> f23(1 + A,B,C) [A >= 0 && 9 >= A] (?,1) 6. f28(A,B,C) -> f23(1 + A,B,C) [9 + -1*A >= 0 && A >= 0] (?,1) 7. f28(A,B,C) -> f23(1 + A,B,C) [9 + -1*A >= 0 && A >= 0 && 8 >= D] (?,1) 8. f23(A,B,C) -> f38(A,B,C) [A >= 0 && A >= 10] (?,1) 9. f8(A,B,C) -> f8(1 + A,A,C) [A >= 0 && 9 >= A] (?,1) 10. f14(A,B,C) -> f8(1 + A,B,C) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0] 11. f14(A,B,C) -> f8(1 + A,B,C) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0 && 8 >= D] 12. f8(A,B,C) -> f23(0,B,C) [A >= 0 && A >= 10] (?,1) Signature: {(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Flow Graph: [0->{1,2,9,12},1->{10,11},2->{10,11},3->{6,7},4->{6,7},5->{3,4,5,8},6->{3,4,5,8},7->{3,4,5,8},8->{},9->{1 ,2,9,12},10->{1,2,9,12},11->{1,2,9,12},12->{3,4,5,8}] + Applied Processor: ArgumentFilter [2] + Details: We remove following argument positions: [2]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f8(0,B) True (1,1) 1. f8(A,B) -> f14(A,A) [A >= 0 && 9 >= A && 9 >= D] (?,1) 2. f8(A,B) -> f14(A,A) [A >= 0 && 9 >= A] (?,1) 3. f23(A,B) -> f28(A,B) [A >= 0 && 9 >= A && 0 >= 1 + E] (?,1) 4. f23(A,B) -> f28(A,B) [A >= 0 && 9 >= A] (?,1) 5. f23(A,B) -> f23(1 + A,B) [A >= 0 && 9 >= A] (?,1) 6. f28(A,B) -> f23(1 + A,B) [9 + -1*A >= 0 && A >= 0] (?,1) 7. f28(A,B) -> f23(1 + A,B) [9 + -1*A >= 0 && A >= 0 && 8 >= D] (?,1) 8. f23(A,B) -> f38(A,B) [A >= 0 && A >= 10] (?,1) 9. f8(A,B) -> f8(1 + A,A) [A >= 0 && 9 >= A] (?,1) 10. f14(A,B) -> f8(1 + A,B) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0] 11. f14(A,B) -> f8(1 + A,B) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0 && 8 >= D] 12. f8(A,B) -> f23(0,B) [A >= 0 && A >= 10] (?,1) Signature: {(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Flow Graph: [0->{1,2,9,12},1->{10,11},2->{10,11},3->{6,7},4->{6,7},5->{3,4,5,8},6->{3,4,5,8},7->{3,4,5,8},8->{},9->{1 ,2,9,12},10->{1,2,9,12},11->{1,2,9,12},12->{3,4,5,8}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,12),(12,8)] * Step 3: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f8(0,B) True (1,1) 1. f8(A,B) -> f14(A,A) [A >= 0 && 9 >= A && 9 >= D] (?,1) 2. f8(A,B) -> f14(A,A) [A >= 0 && 9 >= A] (?,1) 3. f23(A,B) -> f28(A,B) [A >= 0 && 9 >= A && 0 >= 1 + E] (?,1) 4. f23(A,B) -> f28(A,B) [A >= 0 && 9 >= A] (?,1) 5. f23(A,B) -> f23(1 + A,B) [A >= 0 && 9 >= A] (?,1) 6. f28(A,B) -> f23(1 + A,B) [9 + -1*A >= 0 && A >= 0] (?,1) 7. f28(A,B) -> f23(1 + A,B) [9 + -1*A >= 0 && A >= 0 && 8 >= D] (?,1) 8. f23(A,B) -> f38(A,B) [A >= 0 && A >= 10] (?,1) 9. f8(A,B) -> f8(1 + A,A) [A >= 0 && 9 >= A] (?,1) 10. f14(A,B) -> f8(1 + A,B) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0] 11. f14(A,B) -> f8(1 + A,B) [9 + -1*B >= 0 (?,1) && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0 && 8 >= D] 12. f8(A,B) -> f23(0,B) [A >= 0 && A >= 10] (?,1) Signature: {(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Flow Graph: [0->{1,2,9},1->{10,11},2->{10,11},3->{6,7},4->{6,7},5->{3,4,5,8},6->{3,4,5,8},7->{3,4,5,8},8->{},9->{1,2,9 ,12},10->{1,2,9,12},11->{1,2,9,12},12->{3,4,5}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A,B) -> f8(0,B) True f8(A,B) -> f14(A,A) [A >= 0 && 9 >= A && 9 >= D] f8(A,B) -> f14(A,A) [A >= 0 && 9 >= A] f23(A,B) -> f28(A,B) [A >= 0 && 9 >= A && 0 >= 1 + E] f23(A,B) -> f28(A,B) [A >= 0 && 9 >= A] f23(A,B) -> f23(1 + A,B) [A >= 0 && 9 >= A] f28(A,B) -> f23(1 + A,B) [9 + -1*A >= 0 && A >= 0] f28(A,B) -> f23(1 + A,B) [9 + -1*A >= 0 && A >= 0 && 8 >= D] f23(A,B) -> f38(A,B) [A >= 0 && A >= 10] f8(A,B) -> f8(1 + A,A) [A >= 0 && 9 >= A] f14(A,B) -> f8(1 + A,B) [9 + -1*B >= 0 && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0] f14(A,B) -> f8(1 + A,B) [9 + -1*B >= 0 && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0 && 8 >= D] f8(A,B) -> f23(0,B) [A >= 0 && A >= 10] Signature: {(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Rule Graph: [0->{1,2,9},1->{10,11},2->{10,11},3->{6,7},4->{6,7},5->{3,4,5,8},6->{3,4,5,8},7->{3,4,5,8},8->{},9->{1,2,9 ,12},10->{1,2,9,12},11->{1,2,9,12},12->{3,4,5}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A,B) -> f8(0,B) True f8(A,B) -> f14(A,A) [A >= 0 && 9 >= A && 9 >= D] f8(A,B) -> f14(A,A) [A >= 0 && 9 >= A] f23(A,B) -> f28(A,B) [A >= 0 && 9 >= A && 0 >= 1 + E] f23(A,B) -> f28(A,B) [A >= 0 && 9 >= A] f23(A,B) -> f23(1 + A,B) [A >= 0 && 9 >= A] f28(A,B) -> f23(1 + A,B) [9 + -1*A >= 0 && A >= 0] f28(A,B) -> f23(1 + A,B) [9 + -1*A >= 0 && A >= 0 && 8 >= D] f23(A,B) -> f38(A,B) [A >= 0 && A >= 10] f8(A,B) -> f8(1 + A,A) [A >= 0 && 9 >= A] f14(A,B) -> f8(1 + A,B) [9 + -1*B >= 0 && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0] f14(A,B) -> f8(1 + A,B) [9 + -1*B >= 0 && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0 && 8 >= D] f8(A,B) -> f23(0,B) [A >= 0 && A >= 10] f38(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Rule Graph: [0->{1,2,9},1->{10,11},2->{10,11},3->{6,7},4->{6,7},5->{3,4,5,8},6->{3,4,5,8},7->{3,4,5,8},8->{13},9->{1,2 ,9,12},10->{1,2,9,12},11->{1,2,9,12},12->{3,4,5}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | +- p:[1,9,10,2,11] c: [1,2,9,10,11] | `- p:[3,5,6,4,7] c: [3,4,5,6,7] * Step 6: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f0(A,B) -> f8(0,B) True f8(A,B) -> f14(A,A) [A >= 0 && 9 >= A && 9 >= D] f8(A,B) -> f14(A,A) [A >= 0 && 9 >= A] f23(A,B) -> f28(A,B) [A >= 0 && 9 >= A && 0 >= 1 + E] f23(A,B) -> f28(A,B) [A >= 0 && 9 >= A] f23(A,B) -> f23(1 + A,B) [A >= 0 && 9 >= A] f28(A,B) -> f23(1 + A,B) [9 + -1*A >= 0 && A >= 0] f28(A,B) -> f23(1 + A,B) [9 + -1*A >= 0 && A >= 0 && 8 >= D] f23(A,B) -> f38(A,B) [A >= 0 && A >= 10] f8(A,B) -> f8(1 + A,A) [A >= 0 && 9 >= A] f14(A,B) -> f8(1 + A,B) [9 + -1*B >= 0 && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0] f14(A,B) -> f8(1 + A,B) [9 + -1*B >= 0 && A + -1*B >= 0 && 18 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && -1*A + B >= 0 && 9 + -1*A >= 0 && A >= 0 && 8 >= D] f8(A,B) -> f23(0,B) [A >= 0 && A >= 10] f38(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f0,3);(f14,3);(f23,3);(f28,3);(f38,3);(f8,3)} Rule Graph: [0->{1,2,9},1->{10,11},2->{10,11},3->{6,7},4->{6,7},5->{3,4,5,8},6->{3,4,5,8},7->{3,4,5,8},8->{13},9->{1,2 ,9,12},10->{1,2,9,12},11->{1,2,9,12},12->{3,4,5}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | +- p:[1,9,10,2,11] c: [1,2,9,10,11] | `- p:[3,5,6,4,7] c: [3,4,5,6,7]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,0.0,0.1] f0 ~> f8 [A <= 0*K, B <= B] f8 ~> f14 [A <= A, B <= A] f8 ~> f14 [A <= A, B <= A] f23 ~> f28 [A <= A, B <= B] f23 ~> f28 [A <= A, B <= B] f23 ~> f23 [A <= 10*K, B <= B] f28 ~> f23 [A <= 10*K, B <= B] f28 ~> f23 [A <= 10*K, B <= B] f23 ~> f38 [A <= A, B <= B] f8 ~> f8 [A <= 10*K, B <= A] f14 ~> f8 [A <= 10*K, B <= B] f14 ~> f8 [A <= 10*K, B <= B] f8 ~> f23 [A <= 0*K, B <= B] f38 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= 423*K + 46*A] f8 ~> f14 [A <= A, B <= A] f8 ~> f8 [A <= 10*K, B <= A] f14 ~> f8 [A <= 10*K, B <= B] f8 ~> f14 [A <= A, B <= A] f14 ~> f8 [A <= 10*K, B <= B] + Loop: [0.1 <= 89*K + 9*A] f23 ~> f28 [A <= A, B <= B] f23 ~> f23 [A <= 10*K, B <= B] f28 ~> f23 [A <= 10*K, B <= B] f23 ~> f28 [A <= A, B <= B] f28 ~> f23 [A <= 10*K, B <= B] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.1] f0 ~> f8 [K ~=> A] f8 ~> f14 [A ~=> B] f8 ~> f14 [A ~=> B] f23 ~> f28 [] f23 ~> f28 [] f23 ~> f23 [K ~=> A] f28 ~> f23 [K ~=> A] f28 ~> f23 [K ~=> A] f23 ~> f38 [] f8 ~> f8 [A ~=> B,K ~=> A] f14 ~> f8 [K ~=> A] f14 ~> f8 [K ~=> A] f8 ~> f23 [K ~=> A] f38 ~> exitus616 [] + Loop: [A ~*> 0.0,K ~*> 0.0] f8 ~> f14 [A ~=> B] f8 ~> f8 [A ~=> B,K ~=> A] f14 ~> f8 [K ~=> A] f8 ~> f14 [A ~=> B] f14 ~> f8 [K ~=> A] + Loop: [A ~*> 0.1,K ~*> 0.1] f23 ~> f28 [] f23 ~> f23 [K ~=> A] f28 ~> f23 [K ~=> A] f23 ~> f28 [] f28 ~> f23 [K ~=> A] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> A,K ~=> B,tick ~+> tick,K ~*> 0.0,K ~*> 0.1,K ~*> tick] + f8> [A ~=> B,K ~=> A,K ~=> B,tick ~+> tick,A ~*> 0.0,A ~*> tick,K ~*> 0.0,K ~*> tick] + f23> [K ~=> A,tick ~+> tick,A ~*> 0.1,A ~*> tick,K ~*> 0.1,K ~*> tick] YES(?,O(1))