YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> m1(A,B,C,D,E,F) [A >= 0 && 2 + A + B >= 2*C && B >= 1 + A && 2*C >= A + B && D >= 0 && 1 + E = C && F = A] (1,1) 1. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && A >= 1 + E && 1 + B >= G && 1 + C >= H && H >= 1 + C && 1 + F >= G && G >= 1 + F] 2. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && 1 + E >= H && C >= 1 + B && 1 + F >= G && G >= 1 + F && 1 + A >= H && H >= 1 + A] 3. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && 1 + B >= H && E >= A && 1 + F >= G && G >= 1 + F && 1 + C >= H && H >= 1 + C] 4. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && B >= C && 1 + E >= H && 1 + A >= H && H >= 1 + A && 1 + F >= G && G >= 1 + F] Signature: {(m1,6);(start,6)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,1),(0,2),(1,2),(1,3),(1,4),(2,3),(2,4),(3,1),(4,2)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C,D,E,F) -> m1(A,B,C,D,E,F) [A >= 0 && 2 + A + B >= 2*C && B >= 1 + A && 2*C >= A + B && D >= 0 && 1 + E = C && F = A] (1,1) 1. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && A >= 1 + E && 1 + B >= G && 1 + C >= H && H >= 1 + C && 1 + F >= G && G >= 1 + F] 2. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && 1 + E >= H && C >= 1 + B && 1 + F >= G && G >= 1 + F && 1 + A >= H && H >= 1 + A] 3. m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && 1 + B >= H && E >= A && 1 + F >= G && G >= 1 + F && 1 + C >= H && H >= 1 + C] 4. m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [F >= 0 (?,1) && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && B >= C && 1 + E >= H && 1 + A >= H && H >= 1 + A && 1 + F >= G && G >= 1 + F] Signature: {(m1,6);(start,6)} Flow Graph: [0->{3,4},1->{1},2->{1,2},3->{2,3,4},4->{1,3,4}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B,C,D,E,F) -> m1(A,B,C,D,E,F) [A >= 0 && 2 + A + B >= 2*C && B >= 1 + A && 2*C >= A + B && D >= 0 && 1 + E = C && F = A] m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && A >= 1 + E && 1 + B >= G && 1 + C >= H && H >= 1 + C && 1 + F >= G && G >= 1 + F] m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && 1 + E >= H && C >= 1 + B && 1 + F >= G && G >= 1 + F && 1 + A >= H && H >= 1 + A] m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && 1 + B >= H && E >= A && 1 + F >= G && G >= 1 + F && 1 + C >= H && H >= 1 + C] m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && B >= C && 1 + E >= H && 1 + A >= H && H >= 1 + A && 1 + F >= G && G >= 1 + F] Signature: {(m1,6);(start,6)} Rule Graph: [0->{3,4},1->{1},2->{1,2},3->{2,3,4},4->{1,3,4}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B,C,D,E,F) -> m1(A,B,C,D,E,F) [A >= 0 && 2 + A + B >= 2*C && B >= 1 + A && 2*C >= A + B && D >= 0 && 1 + E = C && F = A] m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && A >= 1 + E && 1 + B >= G && 1 + C >= H && H >= 1 + C && 1 + F >= G && G >= 1 + F] m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && 1 + E >= H && C >= 1 + B && 1 + F >= G && G >= 1 + F && 1 + A >= H && H >= 1 + A] m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && 1 + B >= H && E >= A && 1 + F >= G && G >= 1 + F && 1 + C >= H && H >= 1 + C] m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && B >= C && 1 + E >= H && 1 + A >= H && H >= 1 + A && 1 + F >= G && G >= 1 + F] m1(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6);(m1,6);(start,6)} Rule Graph: [0->{3,4},1->{1,5},2->{1,2},3->{2,3,4},4->{1,3,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[3,4] c: [3,4] | +- p:[2] c: [2] | `- p:[1] c: [1] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: start(A,B,C,D,E,F) -> m1(A,B,C,D,E,F) [A >= 0 && 2 + A + B >= 2*C && B >= 1 + A && 2*C >= A + B && D >= 0 && 1 + E = C && F = A] m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && A >= 1 + E && 1 + B >= G && 1 + C >= H && H >= 1 + C && 1 + F >= G && G >= 1 + F] m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && 1 + E >= H && C >= 1 + B && 1 + F >= G && G >= 1 + F && 1 + A >= H && H >= 1 + A] m1(A,B,C,D,E,F) -> m1(A,B,H,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && 1 + B >= H && E >= A && 1 + F >= G && G >= 1 + F && 1 + C >= H && H >= 1 + C] m1(A,B,C,D,E,F) -> m1(H,B,C,D,E,G) [F >= 0 && E + F >= 0 && D + F >= 0 && -1 + C + F >= 0 && -1 + B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && -1 + C + -1*E >= 0 && E >= 0 && D + E >= 0 && -1 + C + E >= 0 && -1 + B + E >= 0 && A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0 && B >= 1 && B >= F && B >= C && 1 + E >= H && 1 + A >= H && H >= 1 + A && 1 + F >= G && G >= 1 + F] m1(A,B,C,D,E,F) -> exitus616(A,B,C,D,E,F) True Signature: {(exitus616,6);(m1,6);(start,6)} Rule Graph: [0->{3,4},1->{1,5},2->{1,2},3->{2,3,4},4->{1,3,4}] ,We construct a looptree: P: [0,1,2,3,4,5] | +- p:[3,4] c: [3,4] | +- p:[2] c: [2] | `- p:[1] c: [1]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,E,F,0.0,0.1,0.2] start ~> m1 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] m1 ~> m1 [A <= A, B <= B, C <= C + F, D <= D, E <= E, F <= C + F] m1 ~> m1 [A <= C, B <= B, C <= C, D <= D, E <= E, F <= C] m1 ~> m1 [A <= A, B <= B, C <= B + C, D <= D, E <= E, F <= B + F] m1 ~> m1 [A <= B, B <= B, C <= C, D <= D, E <= E, F <= B + F] m1 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F] + Loop: [0.0 <= A + B + C] m1 ~> m1 [A <= A, B <= B, C <= B + C, D <= D, E <= E, F <= B + F] m1 ~> m1 [A <= B, B <= B, C <= C, D <= D, E <= E, F <= B + F] + Loop: [0.1 <= A + B] m1 ~> m1 [A <= C, B <= B, C <= C, D <= D, E <= E, F <= C] + Loop: [0.2 <= B + F] m1 ~> m1 [A <= A, B <= B, C <= C + F, D <= D, E <= E, F <= C + F] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,0.0,0.1,0.2] start ~> m1 [] m1 ~> m1 [C ~+> C,C ~+> F,F ~+> C,F ~+> F] m1 ~> m1 [C ~=> A,C ~=> F] m1 ~> m1 [B ~+> C,B ~+> F,C ~+> C,F ~+> F] m1 ~> m1 [B ~=> A,B ~+> F,F ~+> F] m1 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0] m1 ~> m1 [B ~+> C,B ~+> F,C ~+> C,F ~+> F] m1 ~> m1 [B ~=> A,B ~+> F,F ~+> F] + Loop: [A ~+> 0.1,B ~+> 0.1] m1 ~> m1 [C ~=> A,C ~=> F] + Loop: [B ~+> 0.2,F ~+> 0.2] m1 ~> m1 [C ~+> C,C ~+> F,F ~+> C,F ~+> F] + Applied Processor: Lare + Details: start ~> exitus616 [B ~=> A ,C ~=> A ,C ~=> F ,A ~+> 0.0 ,A ~+> 0.1 ,A ~+> tick ,B ~+> C ,B ~+> F ,B ~+> 0.0 ,B ~+> 0.1 ,B ~+> 0.2 ,B ~+> tick ,C ~+> C ,C ~+> F ,C ~+> 0.0 ,C ~+> tick ,F ~+> C ,F ~+> F ,F ~+> 0.2 ,F ~+> tick ,tick ~+> tick ,A ~*> C ,A ~*> F ,B ~*> C ,B ~*> F ,C ~*> C ,C ~*> F ,F ~*> C ,F ~*> F ,B ~^> C ,B ~^> F ,F ~^> C ,F ~^> F] + m1> [B ~=> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> C ,B ~+> F ,B ~+> 0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0 ,C ~+> tick ,F ~+> F ,tick ~+> tick ,A ~*> C ,A ~*> F ,B ~*> C ,B ~*> F ,C ~*> C ,C ~*> F] + m1> [C ~=> A,C ~=> F,A ~+> 0.1,A ~+> tick,B ~+> 0.1,B ~+> tick,tick ~+> tick] + m1> [B ~+> 0.2 ,B ~+> tick ,C ~+> C ,C ~+> F ,F ~+> C ,F ~+> F ,F ~+> 0.2 ,F ~+> tick ,tick ~+> tick ,B ~*> C ,B ~*> F ,C ~*> C ,C ~*> F ,F ~*> C ,F ~*> F ,B ~^> C ,B ~^> F ,F ~^> C ,F ~^> F] YES(?,O(n^1))