YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C) -> f3(-1*A,B,C) True (?,1) 1. f3(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 2. f4(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 3. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1) 5. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && C >= 2] (?,1) 6. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && 0 >= C] (?,1) 7. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && C >= 2] (?,1) 8. f4(A,B,C) -> f3(1 + -1*A,B,0) [0 >= 1 + A && C = 1] (?,1) 9. f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) 10. f5(A,B,C) -> f3(1 + -1*A,B,0) [0 >= 1 + A && C = 1] (?,1) 11. f5(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) Signature: {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Flow Graph: [0->{1,4,5,6,7},1->{},2->{},3->{2,8,9},4->{2,8,9},5->{2,8,9},6->{2,8,9},7->{2,8,9},8->{1,4,5,6,7},9->{1,4 ,5,6,7},10->{1,4,5,6,7},11->{1,4,5,6,7}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C) -> f3(-1*A,B,C) True (1,1) 1. f3(A,B,C) -> f7(0,D,C) [A = 0] (1,1) 2. f4(A,B,C) -> f7(0,D,C) [A = 0] (1,1) 3. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1) 5. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && C >= 2] (?,1) 6. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && 0 >= C] (?,1) 7. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && C >= 2] (?,1) 8. f4(A,B,C) -> f3(1 + -1*A,B,0) [0 >= 1 + A && C = 1] (?,1) 9. f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) 10. f5(A,B,C) -> f3(1 + -1*A,B,0) [0 >= 1 + A && C = 1] (1,1) 11. f5(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (1,1) Signature: {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Flow Graph: [0->{1,4,5,6,7},1->{},2->{},3->{2,8,9},4->{2,8,9},5->{2,8,9},6->{2,8,9},7->{2,8,9},8->{1,4,5,6,7},9->{1,4 ,5,6,7},10->{1,4,5,6,7},11->{1,4,5,6,7}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,2) ,(3,8) ,(4,8) ,(5,8) ,(6,2) ,(6,9) ,(7,2) ,(7,9) ,(8,1) ,(8,4) ,(8,5) ,(8,7) ,(9,5) ,(9,6) ,(9,7) ,(10,1) ,(10,4) ,(10,5) ,(10,7) ,(11,5) ,(11,6) ,(11,7)] * Step 3: UnreachableRules WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C) -> f3(-1*A,B,C) True (1,1) 1. f3(A,B,C) -> f7(0,D,C) [A = 0] (1,1) 2. f4(A,B,C) -> f7(0,D,C) [A = 0] (1,1) 3. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1) 5. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && C >= 2] (?,1) 6. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && 0 >= C] (?,1) 7. f3(A,B,C) -> f4(-1 + -1*A,B,1) [A >= 1 && C >= 2] (?,1) 8. f4(A,B,C) -> f3(1 + -1*A,B,0) [0 >= 1 + A && C = 1] (?,1) 9. f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) 10. f5(A,B,C) -> f3(1 + -1*A,B,0) [0 >= 1 + A && C = 1] (1,1) 11. f5(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (1,1) Signature: {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Flow Graph: [0->{1,4,5,6,7},1->{},2->{},3->{9},4->{2,9},5->{2,9},6->{8},7->{8},8->{6},9->{1,4},10->{6},11->{1,4}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [0,5,6,7,8,10,11] * Step 4: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 1. f3(A,B,C) -> f7(0,D,C) [A = 0] (1,1) 2. f4(A,B,C) -> f7(0,D,C) [A = 0] (1,1) 3. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1) 9. f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) Signature: {(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Flow Graph: [1->{},2->{},3->{9},4->{2,9},9->{1,4}] + Applied Processor: AddSinks + Details: () * Step 5: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 1. f3(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 2. f4(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 3. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1) 9. f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) 10. f4(A,B,C) -> exitus616(A,B,C) True (?,1) 11. f3(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Flow Graph: [1->{},2->{},3->{2,9,10},4->{2,9,10},9->{1,4,11},10->{},11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,2)] * Step 6: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 1. f3(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 2. f4(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 3. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1) 9. f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) 10. f4(A,B,C) -> exitus616(A,B,C) True (?,1) 11. f3(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Flow Graph: [1->{},2->{},3->{9,10},4->{2,9,10},9->{1,4,11},10->{},11->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [1,2,3,4,9,10,11] | `- p:[9,4] c: [9] * Step 7: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 1. f3(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 2. f4(A,B,C) -> f7(0,D,C) [A = 0] (?,1) 3. f6(A,B,C) -> f4(A,B,1) [A >= 1] (1,1) 4. f3(A,B,C) -> f4(-1 + -1*A,B,1) [0 >= 1 + A && 0 >= C] (?,1) 9. f4(A,B,C) -> f3(1 + -1*A,B,0) [A >= 1 && C = 1] (?,1) 10. f4(A,B,C) -> exitus616(A,B,C) True (?,1) 11. f3(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f0,3);(f3,3);(f4,3);(f5,3);(f6,3);(f7,3)} Flow Graph: [1->{},2->{},3->{9,10},4->{2,9,10},9->{1,4,11},10->{},11->{}] ,We construct a looptree: P: [1,2,3,4,9,10,11] | `- p:[9,4] c: [9]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 8: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0] f3 ~> f7 [A <= 0*K, B <= unknown, C <= C] f4 ~> f7 [A <= 0*K, B <= unknown, C <= C] f6 ~> f4 [A <= A, B <= B, C <= K] f3 ~> f4 [A <= A, B <= B, C <= K] f4 ~> f3 [A <= A, B <= B, C <= 0*K] f4 ~> exitus616 [A <= A, B <= B, C <= C] f3 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A] f4 ~> f3 [A <= A, B <= B, C <= 0*K] f3 ~> f4 [A <= A, B <= B, C <= K] + Applied Processor: FlowAbstraction + Details: () * Step 9: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] f3 ~> f7 [K ~=> A,huge ~=> B] f4 ~> f7 [K ~=> A,huge ~=> B] f6 ~> f4 [K ~=> C] f3 ~> f4 [K ~=> C] f4 ~> f3 [K ~=> C] f4 ~> exitus616 [] f3 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] f4 ~> f3 [K ~=> C] f3 ~> f4 [K ~=> C] + Applied Processor: LareProcessor + Details: f6 ~> exitus616 [K ~=> C,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick,A ~*> tick,K ~*> tick] f6 ~> f7 [K ~=> A ,K ~=> C ,huge ~=> B ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> tick ,K ~*> tick] + f3> [K ~=> C,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] f4> [K ~=> C,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] YES(?,POLY)