YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> lbl71(A,B,1,D,0,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 2 && B = A && C = D && E = F] 1. start(A,B,C,D,E,F) -> stop(A,B,0,D,1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 1 >= A && B = A && C = D && E = F] 2. lbl71(A,B,C,D,E,F) -> lbl71(A,B,1 + C,D,E,F) [-2 + B + -1*E >= 0 (?,1) && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 2 + C && A >= 1 + C && A >= 2 + E && C >= 1 && B = A] 3. lbl71(A,B,C,D,E,F) -> cut(A,B,C,D,1 + E,F) [-2 + B + -1*E >= 0 (?,1) && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 3 + E && A >= 2 + E && A >= 2 && 1 + C = A && B = A] 4. lbl71(A,B,C,D,E,F) -> stop(A,B,C,D,1 + E,F) [-2 + B + -1*E >= 0 (?,1) && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 2 && 2 + E = A && 1 + C = A && B = A] 5. cut(A,B,C,D,E,F) -> lbl71(A,B,1,D,E,F) [-1 + C + -1*E >= 0 (?,1) && -2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && -1 + E >= 0 && -3 + C + E >= 0 && -4 + B + E >= 0 && -4 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -2 + C >= 0 && -5 + B + C >= 0 && 1 + -1*B + C >= 0 && -5 + A + C >= 0 && 1 + -1*A + C >= 0 && A + -1*B >= 0 && -3 + B >= 0 && -6 + A + B >= 0 && -1*A + B >= 0 && -3 + A >= 0 && A >= 2 && A >= 2 + E && E >= 1 && 1 + C = A && B = A] 6. start0(A,B,C,D,E,F) -> start(A,A,D,D,F,F) True (1,1) Signature: {(cut,6);(lbl71,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{2,3,4},1->{},2->{2,3,4},3->{5},4->{},5->{2,3,4},6->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3),(5,3),(5,4)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> lbl71(A,B,1,D,0,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 2 && B = A && C = D && E = F] 1. start(A,B,C,D,E,F) -> stop(A,B,0,D,1,F) [E + -1*F >= 0 (?,1) && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 1 >= A && B = A && C = D && E = F] 2. lbl71(A,B,C,D,E,F) -> lbl71(A,B,1 + C,D,E,F) [-2 + B + -1*E >= 0 (?,1) && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 2 + C && A >= 1 + C && A >= 2 + E && C >= 1 && B = A] 3. lbl71(A,B,C,D,E,F) -> cut(A,B,C,D,1 + E,F) [-2 + B + -1*E >= 0 (?,1) && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 3 + E && A >= 2 + E && A >= 2 && 1 + C = A && B = A] 4. lbl71(A,B,C,D,E,F) -> stop(A,B,C,D,1 + E,F) [-2 + B + -1*E >= 0 (?,1) && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 2 && 2 + E = A && 1 + C = A && B = A] 5. cut(A,B,C,D,E,F) -> lbl71(A,B,1,D,E,F) [-1 + C + -1*E >= 0 (?,1) && -2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && -1 + E >= 0 && -3 + C + E >= 0 && -4 + B + E >= 0 && -4 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -2 + C >= 0 && -5 + B + C >= 0 && 1 + -1*B + C >= 0 && -5 + A + C >= 0 && 1 + -1*A + C >= 0 && A + -1*B >= 0 && -3 + B >= 0 && -6 + A + B >= 0 && -1*A + B >= 0 && -3 + A >= 0 && A >= 2 && A >= 2 + E && E >= 1 && 1 + C = A && B = A] 6. start0(A,B,C,D,E,F) -> start(A,A,D,D,F,F) True (1,1) Signature: {(cut,6);(lbl71,6);(start,6);(start0,6);(stop,6)} Flow Graph: [0->{2,4},1->{},2->{2,3,4},3->{5},4->{},5->{2},6->{0,1}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D,E,F) -> lbl71(A,B,1,D,0,F) [E + -1*F >= 0 && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 2 && B = A && C = D && E = F] start(A,B,C,D,E,F) -> stop(A,B,0,D,1,F) [E + -1*F >= 0 && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 1 >= A && B = A && C = D && E = F] lbl71(A,B,C,D,E,F) -> lbl71(A,B,1 + C,D,E,F) [-2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 2 + C && A >= 1 + C && A >= 2 + E && C >= 1 && B = A] lbl71(A,B,C,D,E,F) -> cut(A,B,C,D,1 + E,F) [-2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 3 + E && A >= 2 + E && A >= 2 && 1 + C = A && B = A] lbl71(A,B,C,D,E,F) -> stop(A,B,C,D,1 + E,F) [-2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 2 && 2 + E = A && 1 + C = A && B = A] cut(A,B,C,D,E,F) -> lbl71(A,B,1,D,E,F) [-1 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && -1 + E >= 0 && -3 + C + E >= 0 && -4 + B + E >= 0 && -4 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -2 + C >= 0 && -5 + B + C >= 0 && 1 + -1*B + C >= 0 && -5 + A + C >= 0 && 1 + -1*A + C >= 0 && A + -1*B >= 0 && -3 + B >= 0 && -6 + A + B >= 0 && -1*A + B >= 0 && -3 + A >= 0 && A >= 2 && A >= 2 + E && E >= 1 && 1 + C = A && B = A] start0(A,B,C,D,E,F) -> start(A,A,D,D,F,F) True Signature: {(cut,6);(lbl71,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{2,4},1->{},2->{2,3,4},3->{5},4->{},5->{2},6->{0,1}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: start(A,B,C,D,E,F) -> lbl71(A,B,1,D,0,F) [E + -1*F >= 0 && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 2 && B = A && C = D && E = F] start(A,B,C,D,E,F) -> stop(A,B,0,D,1,F) [E + -1*F >= 0 && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 1 >= A && B = A && C = D && E = F] lbl71(A,B,C,D,E,F) -> lbl71(A,B,1 + C,D,E,F) [-2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 2 + C && A >= 1 + C && A >= 2 + E && C >= 1 && B = A] lbl71(A,B,C,D,E,F) -> cut(A,B,C,D,1 + E,F) [-2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 3 + E && A >= 2 + E && A >= 2 && 1 + C = A && B = A] lbl71(A,B,C,D,E,F) -> stop(A,B,C,D,1 + E,F) [-2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 2 && 2 + E = A && 1 + C = A && B = A] cut(A,B,C,D,E,F) -> lbl71(A,B,1,D,E,F) [-1 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && -1 + E >= 0 && -3 + C + E >= 0 && -4 + B + E >= 0 && -4 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -2 + C >= 0 && -5 + B + C >= 0 && 1 + -1*B + C >= 0 && -5 + A + C >= 0 && 1 + -1*A + C >= 0 && A + -1*B >= 0 && -3 + B >= 0 && -6 + A + B >= 0 && -1*A + B >= 0 && -3 + A >= 0 && A >= 2 && A >= 2 + E && E >= 1 && 1 + C = A && B = A] start0(A,B,C,D,E,F) -> start(A,A,D,D,F,F) 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: {(cut,6);(exitus616,6);(lbl71,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{2,4},1->{7},2->{2,3,4},3->{5},4->{8},5->{2},6->{0,1}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[2,5,3] c: [3,5] | `- p:[2] c: [2] * Step 5: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: start(A,B,C,D,E,F) -> lbl71(A,B,1,D,0,F) [E + -1*F >= 0 && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && A >= 2 && B = A && C = D && E = F] start(A,B,C,D,E,F) -> stop(A,B,0,D,1,F) [E + -1*F >= 0 && -1*E + F >= 0 && C + -1*D >= 0 && -1*C + D >= 0 && A + -1*B >= 0 && -1*A + B >= 0 && 1 >= A && B = A && C = D && E = F] lbl71(A,B,C,D,E,F) -> lbl71(A,B,1 + C,D,E,F) [-2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 2 + C && A >= 1 + C && A >= 2 + E && C >= 1 && B = A] lbl71(A,B,C,D,E,F) -> cut(A,B,C,D,1 + E,F) [-2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 3 + E && A >= 2 + E && A >= 2 && 1 + C = A && B = A] lbl71(A,B,C,D,E,F) -> stop(A,B,C,D,1 + E,F) [-2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && E >= 0 && -1 + C + E >= 0 && -2 + B + E >= 0 && -2 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -3 + A + C >= 0 && A + -1*B >= 0 && -2 + B >= 0 && -4 + A + B >= 0 && -1*A + B >= 0 && -2 + A >= 0 && A >= 2 && 2 + E = A && 1 + C = A && B = A] cut(A,B,C,D,E,F) -> lbl71(A,B,1,D,E,F) [-1 + C + -1*E >= 0 && -2 + B + -1*E >= 0 && -2 + A + -1*E >= 0 && -1 + E >= 0 && -3 + C + E >= 0 && -4 + B + E >= 0 && -4 + A + E >= 0 && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -2 + C >= 0 && -5 + B + C >= 0 && 1 + -1*B + C >= 0 && -5 + A + C >= 0 && 1 + -1*A + C >= 0 && A + -1*B >= 0 && -3 + B >= 0 && -6 + A + B >= 0 && -1*A + B >= 0 && -3 + A >= 0 && A >= 2 && A >= 2 + E && E >= 1 && 1 + C = A && B = A] start0(A,B,C,D,E,F) -> start(A,A,D,D,F,F) 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: {(cut,6);(exitus616,6);(lbl71,6);(start,6);(start0,6);(stop,6)} Rule Graph: [0->{2,4},1->{7},2->{2,3,4},3->{5},4->{8},5->{2},6->{0,1}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[2,5,3] c: [3,5] | `- p:[2] c: [2]) + 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 ~> lbl71 [A <= A, B <= B, C <= K, D <= D, E <= 0*K, F <= F] start ~> stop [A <= A, B <= B, C <= 0*K, D <= D, E <= K, F <= F] lbl71 ~> lbl71 [A <= A, B <= B, C <= B, D <= D, E <= E, F <= F] lbl71 ~> cut [A <= A, B <= B, C <= C, D <= D, E <= B, F <= F] lbl71 ~> stop [A <= A, B <= B, C <= C, D <= D, E <= B, F <= F] cut ~> lbl71 [A <= A, B <= B, C <= K, D <= D, E <= E, F <= F] start0 ~> start [A <= A, B <= A, C <= D, D <= D, E <= F, F <= F] 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 <= 3*K + B + E] lbl71 ~> lbl71 [A <= A, B <= B, C <= B, D <= D, E <= E, F <= F] cut ~> lbl71 [A <= A, B <= B, C <= K, D <= D, E <= E, F <= F] lbl71 ~> cut [A <= A, B <= B, C <= C, D <= D, E <= B, F <= F] + Loop: [0.0.0 <= K + B + C] lbl71 ~> lbl71 [A <= A, B <= B, C <= B, 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 ~> lbl71 [K ~=> C,K ~=> E] start ~> stop [K ~=> C,K ~=> E] lbl71 ~> lbl71 [B ~=> C] lbl71 ~> cut [B ~=> E] lbl71 ~> stop [B ~=> E] cut ~> lbl71 [K ~=> C] start0 ~> start [A ~=> B,D ~=> C,F ~=> E] stop ~> exitus616 [] stop ~> exitus616 [] + Loop: [B ~+> 0.0,E ~+> 0.0,K ~*> 0.0] lbl71 ~> lbl71 [B ~=> C] cut ~> lbl71 [K ~=> C] lbl71 ~> cut [B ~=> E] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0,K ~+> 0.0.0] lbl71 ~> lbl71 [B ~=> C] + Applied Processor: Lare + Details: start0 ~> exitus616 [A ~=> B ,A ~=> C ,A ~=> E ,K ~=> C ,K ~=> E ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + lbl71> [B ~=> C ,B ~=> E ,K ~=> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,E ~+> 0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0.0 ,B ~*> tick ,C ~*> tick ,E ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + lbl71> [B ~=> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)