YES(?,PRIMREC) * Step 1: FromIts MAYBE + Considered Problem: Rules: 0. f(A,B,C) -> g(1,1,C) True (1,1) 1. g(A,B,C) -> g(A + B,A + B,-1 + C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && -1 + C >= 0] (?,1) 2. g(A,B,C) -> h(A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 0 >= C] (?,1) 3. h(A,B,C) -> h(A,-1 + B,C) [-1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A >= 0 && -1 + B >= 0] (?,1) Signature: {(f,3);(g,3);(h,3)} 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,C) -> g(1,1,C) True g(A,B,C) -> g(A + B,A + B,-1 + C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && -1 + C >= 0] g(A,B,C) -> h(A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 0 >= C] h(A,B,C) -> h(A,-1 + B,C) [-1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A >= 0 && -1 + B >= 0] Signature: {(f,3);(g,3);(h,3)} 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,C) -> g(1,1,C) True g(A,B,C) -> g(A + B,A + B,-1 + C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && -1 + C >= 0] g(A,B,C) -> h(A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 0 >= C] h(A,B,C) -> h(A,-1 + B,C) [-1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A >= 0 && -1 + B >= 0] h(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f,3);(g,3);(h,3)} 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,C) -> g.1(1,1,C) True f.0(A,B,C) -> g.2(1,1,C) True g.1(A,B,C) -> g.1(A + B,A + B,-1 + C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && -1 + C >= 0] g.1(A,B,C) -> g.2(A + B,A + B,-1 + C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && -1 + C >= 0] g.2(A,B,C) -> h.3(A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 0 >= C] h.3(A,B,C) -> h.3(A,-1 + B,C) [-1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A >= 0 && -1 + B >= 0] h.3(A,B,C) -> h.4(A,-1 + B,C) [-1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A >= 0 && -1 + B >= 0] h.4(A,B,C) -> exitus616.5(A,B,C) True Signature: {(exitus616.5,3);(f.0,3);(g.1,3);(g.2,3);(h.3,3);(h.4,3)} 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,C) -> g.1(1,1,C) True f.0(A,B,C) -> g.2(1,1,C) True g.1(A,B,C) -> g.1(A + B,A + B,-1 + C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && -1 + C >= 0] g.1(A,B,C) -> g.2(A + B,A + B,-1 + C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && -1 + C >= 0] g.2(A,B,C) -> h.3(A,B,C) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 0 >= C] h.3(A,B,C) -> h.3(A,-1 + B,C) [-1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A >= 0 && -1 + B >= 0] h.3(A,B,C) -> h.4(A,-1 + B,C) [-1*C >= 0 && -1 + A + -1*C >= 0 && -1 + A >= 0 && -1 + B >= 0] h.4(A,B,C) -> exitus616.5(A,B,C) True Signature: {(exitus616.5,3);(f.0,3);(g.1,3);(g.2,3);(h.3,3);(h.4,3)} 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,C,0.0,0.1] f.0 ~> g.1 [A <= K, B <= K, C <= C] f.0 ~> g.2 [A <= K, B <= K, C <= C] g.1 ~> g.1 [A <= A + B, B <= A + B, C <= C] g.1 ~> g.2 [A <= A + B, B <= A + B, C <= C] g.2 ~> h.3 [A <= A, B <= B, C <= C] h.3 ~> h.3 [A <= A, B <= B, C <= C] h.3 ~> h.4 [A <= A, B <= B, C <= C] h.4 ~> exitus616.5 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + C] g.1 ~> g.1 [A <= A + B, B <= A + B, C <= C] + Loop: [0.1 <= K + B] h.3 ~> h.3 [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 ~=> A,K ~=> B] f.0 ~> g.2 [K ~=> A,K ~=> B] g.1 ~> g.1 [A ~+> A,A ~+> B,B ~+> A,B ~+> B] g.1 ~> g.2 [A ~+> A,A ~+> B,B ~+> A,B ~+> B] g.2 ~> h.3 [] h.3 ~> h.3 [] h.3 ~> h.4 [] h.4 ~> exitus616.5 [] + Loop: [C ~+> 0.0,K ~+> 0.0] g.1 ~> g.1 [A ~+> A,A ~+> B,B ~+> A,B ~+> B] + Loop: [B ~+> 0.1,K ~+> 0.1] h.3 ~> h.3 [] + Applied Processor: Lare + Details: f.0 ~> exitus616.5 [K ~=> A ,K ~=> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,C ~*> A ,C ~*> B ,C ~*> 0.1 ,C ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.1 ,K ~*> tick ,C ~^> A ,C ~^> B ,C ~^> 0.1 ,C ~^> tick ,K ~^> A ,K ~^> B ,K ~^> 0.1 ,K ~^> tick] + g.1> [A ~+> A ,A ~+> B ,B ~+> A ,B ~+> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,B ~*> A ,B ~*> B ,C ~*> A ,C ~*> B ,K ~*> A ,K ~*> B ,C ~^> A ,C ~^> B ,K ~^> A ,K ~^> B] + h.3> [B ~+> 0.1,B ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] YES(?,PRIMREC)