YES(?,PRIMREC) * Step 1: FromIts MAYBE + Considered Problem: Rules: 0. f(A,B) -> g(A,B) True (1,1) 1. g(A,B) -> g(2*A,-1 + B) [-1 + B >= 0] (?,1) 2. g(A,B) -> h(A,B) [0 >= B] (?,1) 3. h(A,B) -> h(-1 + A,B) [-1*B >= 0 && -1 + A >= 0] (?,1) Signature: {(f,2);(g,2);(h,2)} Flow Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks MAYBE + Considered Problem: Rules: f(A,B) -> g(A,B) True g(A,B) -> g(2*A,-1 + B) [-1 + B >= 0] g(A,B) -> h(A,B) [0 >= B] h(A,B) -> h(-1 + A,B) [-1*B >= 0 && -1 + A >= 0] Signature: {(f,2);(g,2);(h,2)} Rule Graph: [0->{1,2},1->{1,2},2->{3},3->{3}] + Applied Processor: AddSinks + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f(A,B) -> g(A,B) True g(A,B) -> g(2*A,-1 + B) [-1 + B >= 0] g(A,B) -> h(A,B) [0 >= B] h(A,B) -> h(-1 + A,B) [-1*B >= 0 && -1 + A >= 0] h(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f,2);(g,2);(h,2)} Rule Graph: [0->{1,2},1->{1,2},2->{3},3->{3,4}] + Applied Processor: Unfold + Details: () * Step 4: Decompose MAYBE + Considered Problem: Rules: f.0(A,B) -> g.1(A,B) True f.0(A,B) -> g.2(A,B) True g.1(A,B) -> g.1(2*A,-1 + B) [-1 + B >= 0] g.1(A,B) -> g.2(2*A,-1 + B) [-1 + B >= 0] g.2(A,B) -> h.3(A,B) [0 >= B] h.3(A,B) -> h.3(-1 + A,B) [-1*B >= 0 && -1 + A >= 0] h.3(A,B) -> h.4(-1 + A,B) [-1*B >= 0 && -1 + A >= 0] h.4(A,B) -> exitus616.5(A,B) True Signature: {(exitus616.5,2);(f.0,2);(g.1,2);(g.2,2);(h.3,2);(h.4,2)} Rule Graph: [0->{2,3},1->{4},2->{2,3},3->{4},4->{5,6},5->{5,6},6->{7},7->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[2] c: [2] | `- p:[5] c: [5] * Step 5: AbstractSize MAYBE + Considered Problem: (Rules: f.0(A,B) -> g.1(A,B) True f.0(A,B) -> g.2(A,B) True g.1(A,B) -> g.1(2*A,-1 + B) [-1 + B >= 0] g.1(A,B) -> g.2(2*A,-1 + B) [-1 + B >= 0] g.2(A,B) -> h.3(A,B) [0 >= B] h.3(A,B) -> h.3(-1 + A,B) [-1*B >= 0 && -1 + A >= 0] h.3(A,B) -> h.4(-1 + A,B) [-1*B >= 0 && -1 + A >= 0] h.4(A,B) -> exitus616.5(A,B) True Signature: {(exitus616.5,2);(f.0,2);(g.1,2);(g.2,2);(h.3,2);(h.4,2)} Rule Graph: [0->{2,3},1->{4},2->{2,3},3->{4},4->{5,6},5->{5,6},6->{7},7->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[2] c: [2] | `- p:[5] c: [5]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow MAYBE + Considered Problem: Program: Domain: [A,B,0.0,0.1] f.0 ~> g.1 [A <= A, B <= B] f.0 ~> g.2 [A <= A, B <= B] g.1 ~> g.1 [A <= 2*A, B <= B] g.1 ~> g.2 [A <= 2*A, B <= B] g.2 ~> h.3 [A <= A, B <= B] h.3 ~> h.3 [A <= A, B <= B] h.3 ~> h.4 [A <= A, B <= B] h.4 ~> exitus616.5 [A <= A, B <= B] + Loop: [0.0 <= K + B] g.1 ~> g.1 [A <= 2*A, B <= B] + Loop: [0.1 <= K + A] h.3 ~> h.3 [A <= A, B <= B] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.1] f.0 ~> g.1 [] f.0 ~> g.2 [] g.1 ~> g.1 [A ~*> A] g.1 ~> g.2 [A ~*> A] g.2 ~> h.3 [] h.3 ~> h.3 [] h.3 ~> h.4 [] h.4 ~> exitus616.5 [] + Loop: [B ~+> 0.0,K ~+> 0.0] g.1 ~> g.1 [A ~*> A] + Loop: [A ~+> 0.1,K ~+> 0.1] h.3 ~> h.3 [] + Applied Processor: Lare + Details: f.0 ~> exitus616.5 [A ~+> 0.1 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> A ,A ~*> 0.1 ,A ~*> tick ,K ~*> tick ,B ~^> A ,B ~^> 0.1 ,B ~^> tick ,K ~^> A ,K ~^> 0.1 ,K ~^> tick] + g.1> [B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick,A ~*> A,B ~^> A,K ~^> A] + h.3> [A ~+> 0.1,A ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] YES(?,PRIMREC)