YES(?,PRIMREC) * Step 1: FromIts MAYBE + Considered Problem: Rules: 0. f(A,B,C) -> g(A,1,0) True (1,1) 1. g(A,B,C) -> g1(-1 + A,B,B) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && -1 + A >= 0] (?,1) 2. g1(A,B,C) -> g(A,B + C,C) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -1*B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0] 3. g(A,B,C) -> h(A,B,C) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && 0 >= A] (?,1) 4. h(A,B,C) -> h(A,-1 + B,C) [C >= 0 && -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] (?,1) Signature: {(f,3);(g,3);(g1,3);(h,3)} Flow Graph: [0->{1,3},1->{2},2->{1,3},3->{4},4->{4}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks MAYBE + Considered Problem: Rules: f(A,B,C) -> g(A,1,0) True g(A,B,C) -> g1(-1 + A,B,B) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && -1 + A >= 0] g1(A,B,C) -> g(A,B + C,C) [B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1*B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0] g(A,B,C) -> h(A,B,C) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && 0 >= A] h(A,B,C) -> h(A,-1 + B,C) [C >= 0 && -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] Signature: {(f,3);(g,3);(g1,3);(h,3)} Rule Graph: [0->{1,3},1->{2},2->{1,3},3->{4},4->{4}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose MAYBE + Considered Problem: Rules: f(A,B,C) -> g(A,1,0) True g(A,B,C) -> g1(-1 + A,B,B) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && -1 + A >= 0] g1(A,B,C) -> g(A,B + C,C) [B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1*B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0] g(A,B,C) -> h(A,B,C) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && 0 >= A] h(A,B,C) -> h(A,-1 + B,C) [C >= 0 && -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] h(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f,3);(g,3);(g1,3);(h,3)} Rule Graph: [0->{1,3},1->{2},2->{1,3},3->{4},4->{4,5}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[1,2] c: [1,2] | `- p:[4] c: [4] * Step 4: AbstractSize MAYBE + Considered Problem: (Rules: f(A,B,C) -> g(A,1,0) True g(A,B,C) -> g1(-1 + A,B,B) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && -1 + A >= 0] g1(A,B,C) -> g(A,B + C,C) [B + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -1*B + C >= 0 && -1 + A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && A >= 0] g(A,B,C) -> h(A,B,C) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && 0 >= A] h(A,B,C) -> h(A,-1 + B,C) [C >= 0 && -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] h(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f,3);(g,3);(g1,3);(h,3)} Rule Graph: [0->{1,3},1->{2},2->{1,3},3->{4},4->{4,5}] ,We construct a looptree: P: [0,1,2,3,4,5] | +- p:[1,2] c: [1,2] | `- p:[4] c: [4]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow MAYBE + Considered Problem: Program: Domain: [A,B,C,0.0,0.1] f ~> g [A <= A, B <= K, C <= 0*K] g ~> g1 [A <= A, B <= B, C <= B] g1 ~> g [A <= A, B <= B + C, C <= C] g ~> h [A <= A, B <= B, C <= C] h ~> h [A <= A, B <= B, C <= C] h ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A] g ~> g1 [A <= A, B <= B, C <= B] g1 ~> g [A <= A, B <= B + C, C <= C] + Loop: [0.1 <= K + B] h ~> h [A <= A, B <= B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.1] f ~> g [K ~=> B,K ~=> C] g ~> g1 [B ~=> C] g1 ~> g [B ~+> B,C ~+> B] g ~> h [] h ~> h [] h ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] g ~> g1 [B ~=> C] g1 ~> g [B ~+> B,C ~+> B] + Loop: [B ~+> 0.1,K ~+> 0.1] h ~> h [] + Applied Processor: Lare + Details: f ~> exitus616 [K ~=> B ,K ~=> C ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,A ~*> 0.1 ,A ~*> tick ,K ~*> B ,K ~*> C ,K ~*> 0.1 ,K ~*> tick ,A ~^> B ,A ~^> 0.1 ,A ~^> tick ,K ~^> B ,K ~^> 0.1 ,K ~^> tick] + g> [B ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> C ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,B ~*> C ,K ~*> B ,A ~^> B ,K ~^> B] + h> [B ~+> 0.1,B ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] YES(?,PRIMREC)