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: Unfold 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: Unfold + Details: () * Step 4: Decompose MAYBE + Considered Problem: Rules: f.0(A,B,C) -> g.1(A,1,0) True f.0(A,B,C) -> g.3(A,1,0) True g.1(A,B,C) -> g1.2(-1 + A,B,B) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && -1 + A >= 0] g1.2(A,B,C) -> g.1(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] g1.2(A,B,C) -> g.3(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.3(A,B,C) -> h.4(A,B,C) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && 0 >= A] h.4(A,B,C) -> h.4(A,-1 + B,C) [C >= 0 && -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] h.4(A,B,C) -> h.5(A,-1 + B,C) [C >= 0 && -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] h.5(A,B,C) -> exitus616.6(A,B,C) True Signature: {(exitus616.6,3);(f.0,3);(g.1,3);(g.3,3);(g1.2,3);(h.4,3);(h.5,3)} Rule Graph: [0->{2},1->{5},2->{3,4},3->{2},4->{5},5->{6,7},6->{6,7},7->{8},8->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[2,3] c: [2,3] | `- p:[6] c: [6] * Step 5: AbstractSize MAYBE + Considered Problem: (Rules: f.0(A,B,C) -> g.1(A,1,0) True f.0(A,B,C) -> g.3(A,1,0) True g.1(A,B,C) -> g1.2(-1 + A,B,B) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && -1 + A >= 0] g1.2(A,B,C) -> g.1(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] g1.2(A,B,C) -> g.3(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.3(A,B,C) -> h.4(A,B,C) [-1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + B >= 0 && 0 >= A] h.4(A,B,C) -> h.4(A,-1 + B,C) [C >= 0 && -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] h.4(A,B,C) -> h.5(A,-1 + B,C) [C >= 0 && -1*A + C >= 0 && -1*A >= 0 && -1 + B >= 0] h.5(A,B,C) -> exitus616.6(A,B,C) True Signature: {(exitus616.6,3);(f.0,3);(g.1,3);(g.3,3);(g1.2,3);(h.4,3);(h.5,3)} Rule Graph: [0->{2},1->{5},2->{3,4},3->{2},4->{5},5->{6,7},6->{6,7},7->{8},8->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[2,3] c: [2,3] | `- p:[6] c: [6]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow MAYBE + Considered Problem: Program: Domain: [A,B,C,0.0,0.1] f.0 ~> g.1 [A <= A, B <= K, C <= 0*K] f.0 ~> g.3 [A <= A, B <= K, C <= 0*K] g.1 ~> g1.2 [A <= A, B <= B, C <= B] g1.2 ~> g.1 [A <= A, B <= B + C, C <= C] g1.2 ~> g.3 [A <= A, B <= B + C, C <= C] g.3 ~> h.4 [A <= A, B <= B, C <= C] h.4 ~> h.4 [A <= A, B <= B, C <= C] h.4 ~> h.5 [A <= A, B <= B, C <= C] h.5 ~> exitus616.6 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A] g.1 ~> g1.2 [A <= A, B <= B, C <= B] g1.2 ~> g.1 [A <= A, B <= B + C, C <= C] + Loop: [0.1 <= K + B] h.4 ~> h.4 [A <= A, B <= B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.1] f.0 ~> g.1 [K ~=> B,K ~=> C] f.0 ~> g.3 [K ~=> B,K ~=> C] g.1 ~> g1.2 [B ~=> C] g1.2 ~> g.1 [B ~+> B,C ~+> B] g1.2 ~> g.3 [B ~+> B,C ~+> B] g.3 ~> h.4 [] h.4 ~> h.4 [] h.4 ~> h.5 [] h.5 ~> exitus616.6 [] + Loop: [A ~+> 0.0,K ~+> 0.0] g.1 ~> g1.2 [B ~=> C] g1.2 ~> g.1 [B ~+> B,C ~+> B] + Loop: [B ~+> 0.1,K ~+> 0.1] h.4 ~> h.4 [] + Applied Processor: Lare + Details: f.0 ~> exitus616.6 [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 ~*> C ,A ~*> 0.1 ,A ~*> tick ,K ~*> B ,K ~*> C ,K ~*> 0.1 ,K ~*> tick ,A ~^> B ,A ~^> C ,A ~^> 0.1 ,A ~^> tick ,K ~^> B ,K ~^> C ,K ~^> 0.1 ,K ~^> tick] + g1.2> [B ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> C ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,A ~*> C ,B ~*> B ,B ~*> C ,K ~*> B ,K ~*> C ,A ~^> B ,A ~^> C ,K ~^> B ,K ~^> C] + h.4> [B ~+> 0.1,B ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] YES(?,PRIMREC)