YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = A] 1. start(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = E && F = A] 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && B = 0 && F = A] 3. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && A >= 1 + D && B = 0 && F = A] 4. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && A >= 1 && D >= 1 && B = 0 && F = A] 5. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 1 && A >= D && A >= 1 + B && D >= 1 && F = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{},3->{4,5},4->{2,3},5->{4,5},6->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,4)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = A] 1. start(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,F,E,F) [A + -1*F >= 0 (?,1) && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = E && F = A] 2. lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && B = 0 && F = A] 3. lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && A >= 1 + D && B = 0 && F = A] 4. lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && A >= 1 && D >= 1 && B = 0 && F = A] 5. lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [A + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 1 && A >= D && A >= 1 + B && D >= 1 && F = A] 6. start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True (1,1) Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{},1->{4,5},2->{},3->{5},4->{2,3},5->{4,5},6->{0,1}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = E && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && A >= 1 + D && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 1 && A >= D && A >= 1 + B && D >= 1 && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True Signature: {(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{},1->{4,5},2->{},3->{5},4->{2,3},5->{4,5},6->{0,1}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = E && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && A >= 1 + D && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 1 && A >= D && A >= 1 + B && D >= 1 && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6);(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{8},1->{4,5},2->{7},3->{5},4->{2,3},5->{4,5},6->{0,1}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[4,5,3] c: [3,4] | `- p:[5] c: [5] * Step 5: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: start(A,B,C,D,E,F) -> stop(A,B,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && 0 >= A && B = C && D = E && F = A] start(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,F,E,F) [A + -1*F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && -1*D + E >= 0 && B + -1*C >= 0 && -1*B + C >= 0 && A >= 1 && B = C && D = E && F = A] lbl72(A,B,C,D,E,F) -> stop(A,B,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D = 0 && B = 0 && F = A] lbl72(A,B,C,D,E,F) -> lbl62(A,-1 + F,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -1 + D + F >= 0 && -1 + -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && -1 + A + -1*D >= 0 && D >= 0 && B + D >= 0 && -1*B + D >= 0 && -1 + A + D >= 0 && -1*B >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= 1 && D >= 1 && A >= 1 + D && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl72(A,B,C,-1 + D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && A >= D && A >= 1 && D >= 1 && B = 0 && F = A] lbl62(A,B,C,D,E,F) -> lbl62(A,-1 + B,C,D,E,F) [A + -1*F >= 0 && -1 + F >= 0 && -2 + D + F >= 0 && -1*D + F >= 0 && -1 + B + F >= 0 && -1 + -1*B + F >= 0 && -2 + A + F >= 0 && -1*A + F >= 0 && A + -1*D >= 0 && -1 + D >= 0 && -1 + B + D >= 0 && -2 + A + D >= 0 && -1 + A + -1*B >= 0 && B >= 0 && -1 + A + B >= 0 && -1 + A >= 0 && B >= 1 && A >= D && A >= 1 + B && D >= 1 && F = A] start0(A,B,C,D,E,F) -> start(A,C,C,E,E,A) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True stop(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6);(lbl62,6);(lbl72,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{8},1->{4,5},2->{7},3->{5},4->{2,3},5->{4,5},6->{0,1}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[4,5,3] c: [3,4] | `- p:[5] c: [5]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.0.0] start ~> stop [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] start ~> lbl62 [A <= A, B <= F, C <= C, D <= F, E <= E, F <= F] lbl72 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] lbl72 ~> lbl62 [A <= A, B <= F, C <= C, D <= D, E <= E, F <= F] lbl62 ~> lbl72 [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] lbl62 ~> lbl62 [A <= A, B <= A, C <= C, D <= D, E <= E, F <= F] start0 ~> start [A <= A, B <= C, C <= C, D <= E, E <= E, F <= A] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] stop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= 2*K + A + D] lbl62 ~> lbl72 [A <= A, B <= B, C <= C, D <= F, E <= E, F <= F] lbl62 ~> lbl62 [A <= A, B <= A, C <= C, D <= D, E <= E, F <= F] lbl72 ~> lbl62 [A <= A, B <= F, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0.0 <= K + B + F] lbl62 ~> lbl62 [A <= A, B <= A, C <= C, D <= D, E <= E, F <= F] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.0.0] start ~> stop [F ~=> D] start ~> lbl62 [F ~=> B,F ~=> D] lbl72 ~> stop [] lbl72 ~> lbl62 [F ~=> B] lbl62 ~> lbl72 [F ~=> D] lbl62 ~> lbl62 [A ~=> B] start0 ~> start [A ~=> F,C ~=> B,E ~=> D] stop ~> exitus616 [] stop ~> exitus616 [] + Loop: [A ~+> 0.0,D ~+> 0.0,K ~*> 0.0] lbl62 ~> lbl72 [F ~=> D] lbl62 ~> lbl62 [A ~=> B] lbl72 ~> lbl62 [F ~=> B] + Loop: [B ~+> 0.0.0,F ~+> 0.0.0,K ~+> 0.0.0] lbl62 ~> lbl62 [A ~=> B] + Applied Processor: Lare + Details: start0 ~> exitus616 [A ~=> B ,A ~=> D ,A ~=> F ,C ~=> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0 ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> 0.0 ,K ~*> tick] + lbl72> [A ~=> B ,F ~=> B ,F ~=> D ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,D ~+> 0.0 ,D ~+> tick ,F ~+> 0.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> tick ,D ~*> tick ,F ~*> 0.0.0 ,F ~*> tick ,K ~*> 0.0 ,K ~*> tick] + lbl62> [A ~=> B ,B ~+> 0.0.0 ,B ~+> tick ,F ~+> 0.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)