YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = C && D = A && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl6(A,B,C,D,E,F) [A >= 1 && A >= C && B = C && D = A && E = F] (?,1) 2. start(A,B,C,D,E,F) -> lbl121(A,B,C,D,B + -1*D,F) [A >= 1 && C >= 1 + A && B = C && D = A && E = F] (?,1) 3. lbl6(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && A >= C && E = F && D = A && B = C] (?,1) 4. lbl111(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 2 && E = 0 && D = A && B = C] (?,1) 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && E >= 0 && C >= 1 + A + E && A >= 2 + E && D = A && B = C] (?,1) 6. lbl111(A,B,C,D,E,F) -> lbl121(A,B,C,D,-1*D + E,F) [E >= 1 && E >= A && E >= 0 && C >= 1 + A + E && A >= 2 + E && D = A && B = C] (?,1) 7. lbl121(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 1 && C >= A && E = 0 && D = A && B = C] (?,1) 8. lbl121(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 9. lbl121(A,B,C,D,E,F) -> lbl121(A,B,C,D,-1*D + E,F) [E >= 1 && E >= A && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 10. cut(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && C >= 1 + A && E = 0 && D = A && B = C] (?,1) 11. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) Signature: {(cut,6);(lbl111,6);(lbl121,6);(lbl6,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3},2->{7,8,9},3->{},4->{10},5->{4,5,6},6->{7,8,9},7->{10},8->{4,5,6},9->{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(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = C && D = A && E = F] (1,1) 1. start(A,B,C,D,E,F) -> lbl6(A,B,C,D,E,F) [A >= 1 && A >= C && B = C && D = A && E = F] (1,1) 2. start(A,B,C,D,E,F) -> lbl121(A,B,C,D,B + -1*D,F) [A >= 1 && C >= 1 + A && B = C && D = A && E = F] (1,1) 3. lbl6(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && A >= C && E = F && D = A && B = C] (1,1) 4. lbl111(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 2 && E = 0 && D = A && B = C] (1,1) 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && E >= 0 && C >= 1 + A + E && A >= 2 + E && D = A && B = C] (?,1) 6. lbl111(A,B,C,D,E,F) -> lbl121(A,B,C,D,-1*D + E,F) [E >= 1 && E >= A && E >= 0 && C >= 1 + A + E && A >= 2 + E && D = A && B = C] (?,1) 7. lbl121(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 1 && C >= A && E = 0 && D = A && B = C] (1,1) 8. lbl121(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 9. lbl121(A,B,C,D,E,F) -> lbl121(A,B,C,D,-1*D + E,F) [E >= 1 && E >= A && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 10. cut(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && C >= 1 + A && E = 0 && D = A && B = C] (1,1) 11. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) Signature: {(cut,6);(lbl111,6);(lbl121,6);(lbl6,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3},2->{7,8,9},3->{},4->{10},5->{4,5,6},6->{7,8,9},7->{10},8->{4,5,6},9->{7,8,9},10->{},11->{0,1 ,2}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [6] * Step 3: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = C && D = A && E = F] (1,1) 1. start(A,B,C,D,E,F) -> lbl6(A,B,C,D,E,F) [A >= 1 && A >= C && B = C && D = A && E = F] (1,1) 2. start(A,B,C,D,E,F) -> lbl121(A,B,C,D,B + -1*D,F) [A >= 1 && C >= 1 + A && B = C && D = A && E = F] (1,1) 3. lbl6(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && A >= C && E = F && D = A && B = C] (1,1) 4. lbl111(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 2 && E = 0 && D = A && B = C] (1,1) 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && E >= 0 && C >= 1 + A + E && A >= 2 + E && D = A && B = C] (?,1) 7. lbl121(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 1 && C >= A && E = 0 && D = A && B = C] (1,1) 8. lbl121(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 9. lbl121(A,B,C,D,E,F) -> lbl121(A,B,C,D,-1*D + E,F) [E >= 1 && E >= A && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 10. cut(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && C >= 1 + A && E = 0 && D = A && B = C] (1,1) 11. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) Signature: {(cut,6);(lbl111,6);(lbl121,6);(lbl6,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3},2->{7,8,9},3->{},4->{10},5->{4,5},7->{10},8->{4,5},9->{7,8,9},10->{},11->{0,1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,7)] * Step 4: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = C && D = A && E = F] (1,1) 1. start(A,B,C,D,E,F) -> lbl6(A,B,C,D,E,F) [A >= 1 && A >= C && B = C && D = A && E = F] (1,1) 2. start(A,B,C,D,E,F) -> lbl121(A,B,C,D,B + -1*D,F) [A >= 1 && C >= 1 + A && B = C && D = A && E = F] (1,1) 3. lbl6(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && A >= C && E = F && D = A && B = C] (1,1) 4. lbl111(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 2 && E = 0 && D = A && B = C] (1,1) 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && E >= 0 && C >= 1 + A + E && A >= 2 + E && D = A && B = C] (?,1) 7. lbl121(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 1 && C >= A && E = 0 && D = A && B = C] (1,1) 8. lbl121(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 9. lbl121(A,B,C,D,E,F) -> lbl121(A,B,C,D,-1*D + E,F) [E >= 1 && E >= A && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 10. cut(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && C >= 1 + A && E = 0 && D = A && B = C] (1,1) 11. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) Signature: {(cut,6);(lbl111,6);(lbl121,6);(lbl6,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3},2->{8,9},3->{},4->{10},5->{4,5},7->{10},8->{4,5},9->{7,8,9},10->{},11->{0,1,2}] + Applied Processor: AddSinks + Details: () * Step 5: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = C && D = A && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl6(A,B,C,D,E,F) [A >= 1 && A >= C && B = C && D = A && E = F] (?,1) 2. start(A,B,C,D,E,F) -> lbl121(A,B,C,D,B + -1*D,F) [A >= 1 && C >= 1 + A && B = C && D = A && E = F] (?,1) 3. lbl6(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && A >= C && E = F && D = A && B = C] (?,1) 4. lbl111(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 2 && E = 0 && D = A && B = C] (?,1) 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && E >= 0 && C >= 1 + A + E && A >= 2 + E && D = A && B = C] (?,1) 7. lbl121(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 1 && C >= A && E = 0 && D = A && B = C] (?,1) 8. lbl121(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 9. lbl121(A,B,C,D,E,F) -> lbl121(A,B,C,D,-1*D + E,F) [E >= 1 && E >= A && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 10. cut(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && C >= 1 + A && E = 0 && D = A && B = C] (?,1) 11. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) 12. cut(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 13. lbl6(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 14. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(cut,6);(exitus616,6);(lbl111,6);(lbl121,6);(lbl6,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,13},2->{7,8,9},3->{},4->{10,12},5->{4,5},7->{10,12},8->{4,5},9->{7,8,9},10->{},11->{0,1,2,14} ,12->{},13->{},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,7)] * Step 6: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = C && D = A && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl6(A,B,C,D,E,F) [A >= 1 && A >= C && B = C && D = A && E = F] (?,1) 2. start(A,B,C,D,E,F) -> lbl121(A,B,C,D,B + -1*D,F) [A >= 1 && C >= 1 + A && B = C && D = A && E = F] (?,1) 3. lbl6(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && A >= C && E = F && D = A && B = C] (?,1) 4. lbl111(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 2 && E = 0 && D = A && B = C] (?,1) 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && E >= 0 && C >= 1 + A + E && A >= 2 + E && D = A && B = C] (?,1) 7. lbl121(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 1 && C >= A && E = 0 && D = A && B = C] (?,1) 8. lbl121(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 9. lbl121(A,B,C,D,E,F) -> lbl121(A,B,C,D,-1*D + E,F) [E >= 1 && E >= A && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 10. cut(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && C >= 1 + A && E = 0 && D = A && B = C] (?,1) 11. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) 12. cut(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 13. lbl6(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 14. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(cut,6);(exitus616,6);(lbl111,6);(lbl121,6);(lbl6,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,13},2->{8,9},3->{},4->{10,12},5->{4,5},7->{10,12},8->{4,5},9->{7,8,9},10->{},11->{0,1,2,14} ,12->{},13->{},14->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,7,8,9,10,11,12,13,14] | +- p:[9] c: [9] | `- p:[5] c: [5] * Step 7: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [0 >= A && B = C && D = A && E = F] (?,1) 1. start(A,B,C,D,E,F) -> lbl6(A,B,C,D,E,F) [A >= 1 && A >= C && B = C && D = A && E = F] (?,1) 2. start(A,B,C,D,E,F) -> lbl121(A,B,C,D,B + -1*D,F) [A >= 1 && C >= 1 + A && B = C && D = A && E = F] (?,1) 3. lbl6(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && A >= C && E = F && D = A && B = C] (?,1) 4. lbl111(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 2 && E = 0 && D = A && B = C] (?,1) 5. lbl111(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && E >= 0 && C >= 1 + A + E && A >= 2 + E && D = A && B = C] (?,1) 7. lbl121(A,B,C,D,E,F) -> cut(A,B,C,D,E,F) [C >= 1 + A && A >= 1 && C >= A && E = 0 && D = A && B = C] (?,1) 8. lbl121(A,B,C,D,E,F) -> lbl111(A,B,C,D,-1 + E,F) [E >= 1 && A >= 1 + E && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 9. lbl121(A,B,C,D,E,F) -> lbl121(A,B,C,D,-1*D + E,F) [E >= 1 && E >= A && C >= 1 + A && A >= 1 && E >= 0 && C >= A + E && D = A && B = C] (?,1) 10. cut(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A >= 1 && C >= 1 + A && E = 0 && D = A && B = C] (?,1) 11. start0(A,B,C,D,E,F) -> start(A,C,C,A,F,F) True (1,1) 12. cut(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 13. lbl6(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) 14. start(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True (?,1) Signature: {(cut,6);(exitus616,6);(lbl111,6);(lbl121,6);(lbl6,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{3,13},2->{8,9},3->{},4->{10,12},5->{4,5},7->{10,12},8->{4,5},9->{7,8,9},10->{},11->{0,1,2,14} ,12->{},13->{},14->{}] ,We construct a looptree: P: [0,1,2,3,4,5,7,8,9,10,11,12,13,14] | +- p:[9] c: [9] | `- p:[5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 8: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.1] start ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] start ~> lbl6 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] start ~> lbl121 [A <= A, B <= B, C <= C, D <= D, E <= B, F <= F] lbl6 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl111 ~> cut [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= D, E <= B, F <= F] lbl121 ~> cut [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl121 ~> lbl111 [A <= A, B <= B, C <= C, D <= D, E <= B, F <= F] lbl121 ~> lbl121 [A <= A, B <= B, C <= C, D <= D, E <= C, F <= F] cut ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] start0 ~> start [A <= A, B <= C, C <= C, D <= A, E <= F, F <= F] cut ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl6 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] start ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= K + E] lbl121 ~> lbl121 [A <= A, B <= B, C <= C, D <= D, E <= C, F <= F] + Loop: [0.1 <= K + E] lbl111 ~> lbl111 [A <= A, B <= B, C <= C, D <= D, E <= B, F <= F] + Applied Processor: FlowAbstraction + Details: () * Step 9: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.1] start ~> stop [] start ~> lbl6 [] start ~> lbl121 [B ~=> E] lbl6 ~> stop [] lbl111 ~> cut [] lbl111 ~> lbl111 [B ~=> E] lbl121 ~> cut [] lbl121 ~> lbl111 [B ~=> E] lbl121 ~> lbl121 [C ~=> E] cut ~> stop [] start0 ~> start [A ~=> D,C ~=> B,F ~=> E] cut ~> exitus616 [] lbl6 ~> exitus616 [] start ~> exitus616 [] + Loop: [E ~+> 0.0,K ~+> 0.0] lbl121 ~> lbl121 [C ~=> E] + Loop: [E ~+> 0.1,K ~+> 0.1] lbl111 ~> lbl111 [B ~=> E] + Applied Processor: LareProcessor + Details: start0 ~> exitus616 [A ~=> D ,C ~=> B ,C ~=> E ,F ~=> E ,C ~+> 0.0 ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,C ~*> tick ,K ~*> tick] start0 ~> stop [A ~=> D ,C ~=> B ,C ~=> E ,F ~=> E ,C ~+> 0.0 ,C ~+> 0.1 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,C ~*> tick ,K ~*> tick] + lbl121> [C ~=> E,E ~+> 0.0,E ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] + lbl111> [B ~=> E,E ~+> 0.1,E ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] YES(?,POLY)