YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [A = 0 && B = 0 && C = D && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [0 >= 1 + B && A = B && C = D && E = F] (?,1) 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [B >= 1 && A = B && C = D && E = F] (?,1) 3. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E = 40 && C = 100 && A = 0 && B = 0] (?,1) 4. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] (?,1) 5. lbl91(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 && 39 >= E && E >= 1 && 40 >= E && C = 100 && A = 0 && B = 0] (?,1) 6. lbl91(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 && 39 >= E && E >= 1 && 40 >= E && C = 100 && A = 0 && B = 0] (?,1) 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 8. lbl111(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 2 && 41 >= E && A = 0 && C = 100 && B = 0] (?,1) 9. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 10. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 11. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{3,4,5,6},1->{7,8,9,10},2->{7,8,9,10},3->{},4->{3,4,5,6},5->{7,8,9,10},6->{7,8,9,10},7->{},8->{3,4,5 ,6},9->{7,8,9,10},10->{7,8,9,10},11->{0,1,2}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [A = 0 && B = 0 && C = D && E = F] (1,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [0 >= 1 + B && A = B && C = D && E = F] (1,1) 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [B >= 1 && A = B && C = D && E = F] (1,1) 3. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E = 40 && C = 100 && A = 0 && B = 0] (1,1) 4. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] (?,1) 5. lbl91(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 && 39 >= E && E >= 1 && 40 >= E && C = 100 && A = 0 && B = 0] (?,1) 6. lbl91(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 && 39 >= E && E >= 1 && 40 >= E && C = 100 && A = 0 && B = 0] (?,1) 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] (1,1) 8. lbl111(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 2 && 41 >= E && A = 0 && C = 100 && B = 0] (?,1) 9. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 10. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 11. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{3,4,5,6},1->{7,8,9,10},2->{7,8,9,10},3->{},4->{3,4,5,6},5->{7,8,9,10},6->{7,8,9,10},7->{},8->{3,4,5 ,6},9->{7,8,9,10},10->{7,8,9,10},11->{0,1,2}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [5,6] * Step 3: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [A = 0 && B = 0 && C = D && E = F] (1,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [0 >= 1 + B && A = B && C = D && E = F] (1,1) 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [B >= 1 && A = B && C = D && E = F] (1,1) 3. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E = 40 && C = 100 && A = 0 && B = 0] (1,1) 4. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] (?,1) 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] (1,1) 8. lbl111(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 2 && 41 >= E && A = 0 && C = 100 && B = 0] (?,1) 9. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 10. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 11. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{3,4},1->{7,8,9,10},2->{7,8,9,10},3->{},4->{3,4},7->{},8->{3,4},9->{7,8,9,10},10->{7,8,9,10},11->{0,1 ,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3) ,(1,7) ,(1,8) ,(1,10) ,(2,7) ,(2,8) ,(2,9) ,(9,8) ,(9,10) ,(10,8) ,(10,9)] * Step 4: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [A = 0 && B = 0 && C = D && E = F] (1,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [0 >= 1 + B && A = B && C = D && E = F] (1,1) 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [B >= 1 && A = B && C = D && E = F] (1,1) 3. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E = 40 && C = 100 && A = 0 && B = 0] (1,1) 4. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] (?,1) 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] (1,1) 8. lbl111(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 2 && 41 >= E && A = 0 && C = 100 && B = 0] (?,1) 9. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 10. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 11. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{4},1->{9},2->{10},3->{},4->{3,4},7->{},8->{3,4},9->{7,9},10->{7,10},11->{0,1,2}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [8] * Step 5: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [A = 0 && B = 0 && C = D && E = F] (1,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [0 >= 1 + B && A = B && C = D && E = F] (1,1) 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [B >= 1 && A = B && C = D && E = F] (1,1) 3. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E = 40 && C = 100 && A = 0 && B = 0] (1,1) 4. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] (?,1) 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] (1,1) 9. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 10. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 11. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) Signature: {(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{4},1->{9},2->{10},3->{},4->{3,4},7->{},9->{7,9},10->{7,10},11->{0,1,2}] + Applied Processor: AddSinks + Details: () * Step 6: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [A = 0 && B = 0 && C = D && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [0 >= 1 + B && A = B && C = D && E = F] (?,1) 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [B >= 1 && A = B && C = D && E = F] (?,1) 3. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E = 40 && C = 100 && A = 0 && B = 0] (?,1) 4. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] (?,1) 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 9. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 10. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 11. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) 12. lbl111(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 13. lbl91(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{3,4,13},1->{7,9,10,12},2->{7,9,10,12},3->{},4->{3,4,13},7->{},9->{7,9,10,12},10->{7,9,10,12},11->{0,1 ,2},12->{},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3),(1,7),(1,10),(2,7),(2,9),(9,10),(10,9)] * Step 7: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [A = 0 && B = 0 && C = D && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [0 >= 1 + B && A = B && C = D && E = F] (?,1) 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [B >= 1 && A = B && C = D && E = F] (?,1) 3. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E = 40 && C = 100 && A = 0 && B = 0] (?,1) 4. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] (?,1) 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 9. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 10. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 11. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) 12. lbl111(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 13. lbl91(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{4,13},1->{9,12},2->{10,12},3->{},4->{3,4,13},7->{},9->{7,9,12},10->{7,10,12},11->{0,1,2},12->{} ,13->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,7,9,10,11,12,13] | +- p:[10] c: [10] | +- p:[9] c: [9] | `- p:[4] c: [4] * Step 8: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. start(A,B,C,D,E,F) -> lbl91(A,B,100,D,1,F) [A = 0 && B = 0 && C = D && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [0 >= 1 + B && A = B && C = D && E = F] (?,1) 2. start(A,B,C,D,E,F) -> lbl111(A,B,100,D,2,F) [B >= 1 && A = B && C = D && E = F] (?,1) 3. lbl91(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E = 40 && C = 100 && A = 0 && B = 0] (?,1) 4. lbl91(A,B,C,D,E,F) -> lbl91(A,B,C,D,1 + E,F) [39 >= E && E >= 1 && 40 >= E && A = 0 && C = 100 && B = 0] (?,1) 7. lbl111(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [E >= 40 && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 9. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [0 >= 1 + B && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 10. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,2 + E,F) [B >= 1 && 39 >= E && E >= 2 && 41 >= E && C = 100 && A = B] (?,1) 11. start0(A,B,C,D,E,F) -> start(B,B,D,D,F,F) True (1,1) 12. lbl111(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 13. lbl91(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(exitus616,6);(lbl111,6);(lbl91,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{4,13},1->{9,12},2->{10,12},3->{},4->{3,4,13},7->{},9->{7,9,12},10->{7,10,12},11->{0,1,2},12->{} ,13->{}] ,We construct a looptree: P: [0,1,2,3,4,7,9,10,11,12,13] | +- p:[10] c: [10] | +- p:[9] c: [9] | `- p:[4] c: [4]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 9: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.1,0.2] start ~> lbl91 [A <= A, B <= B, C <= 100*K, D <= D, E <= K, F <= F] start ~> lbl111 [A <= A, B <= B, C <= 100*K, D <= D, E <= 2*K, F <= F] start ~> lbl111 [A <= A, B <= B, C <= 100*K, D <= D, E <= 2*K, F <= F] lbl91 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl91 ~> lbl91 [A <= A, B <= B, C <= C, D <= D, E <= 40*K, F <= F] lbl111 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= D, E <= 41*K, F <= F] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= D, E <= 41*K, F <= F] start0 ~> start [A <= B, B <= B, C <= D, D <= D, E <= F, F <= F] lbl111 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl91 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= 42*K + E] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= D, E <= 41*K, F <= F] + Loop: [0.1 <= 42*K + E] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= D, E <= 41*K, F <= F] + Loop: [0.2 <= 41*K + E] lbl91 ~> lbl91 [A <= A, B <= B, C <= C, D <= D, E <= 40*K, F <= F] + Applied Processor: FlowAbstraction + Details: () * Step 10: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.1,0.2] start ~> lbl91 [K ~=> C,K ~=> E] start ~> lbl111 [K ~=> C,K ~=> E] start ~> lbl111 [K ~=> C,K ~=> E] lbl91 ~> stop [] lbl91 ~> lbl91 [K ~=> E] lbl111 ~> stop [] lbl111 ~> lbl111 [K ~=> E] lbl111 ~> lbl111 [K ~=> E] start0 ~> start [B ~=> A,D ~=> C,F ~=> E] lbl111 ~> exitus616 [] lbl91 ~> exitus616 [] + Loop: [E ~+> 0.0,K ~*> 0.0] lbl111 ~> lbl111 [K ~=> E] + Loop: [E ~+> 0.1,K ~*> 0.1] lbl111 ~> lbl111 [K ~=> E] + Loop: [E ~+> 0.2,K ~*> 0.2] lbl91 ~> lbl91 [K ~=> E] + Applied Processor: LareProcessor + Details: start0 ~> exitus616 [B ~=> A ,K ~=> C ,K ~=> E ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> tick] start0 ~> stop [B ~=> A ,K ~=> C ,K ~=> E ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.2 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> 0.2 ,K ~*> tick] + lbl111> [K ~=> E,E ~+> 0.0,E ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + lbl111> [K ~=> E,E ~+> 0.1,E ~+> tick,tick ~+> tick,K ~*> 0.1,K ~*> tick] + lbl91> [K ~=> E,E ~+> 0.2,E ~+> tick,tick ~+> tick,K ~*> 0.2,K ~*> tick] YES(?,O(1))