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