YES(?,PRIMREC) * Step 1: FromIts MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D) -> f4(0,B,C,D) True (1,1) 1. f4(A,B,C,D) -> f7(A,B,1 + A,D) [B >= 1 + A] (?,1) 2. f7(A,B,C,D) -> f7(A,B,1 + C,0) [B >= 1 + C] (?,1) 3. f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B >= 1 + C && 0 >= 1 + E] (?,1) 4. f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B >= 1 + C && E >= 1] (?,1) 5. f7(A,B,C,D) -> f4(1 + A,B,C,D) [C >= B] (?,1) 6. f4(A,B,C,D) -> f19(A,B,C,D) [A >= B] (?,1) Signature: {(f0,4);(f19,4);(f4,4);(f7,4)} Flow Graph: [0->{1,6},1->{2,3,4,5},2->{2,3,4,5},3->{2,3,4,5},4->{2,3,4,5},5->{1,6},6->{}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks MAYBE + Considered Problem: Rules: f0(A,B,C,D) -> f4(0,B,C,D) True f4(A,B,C,D) -> f7(A,B,1 + A,D) [B >= 1 + A] f7(A,B,C,D) -> f7(A,B,1 + C,0) [B >= 1 + C] f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B >= 1 + C && 0 >= 1 + E] f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B >= 1 + C && E >= 1] f7(A,B,C,D) -> f4(1 + A,B,C,D) [C >= B] f4(A,B,C,D) -> f19(A,B,C,D) [A >= B] Signature: {(f0,4);(f19,4);(f4,4);(f7,4)} Rule Graph: [0->{1,6},1->{2,3,4,5},2->{2,3,4,5},3->{2,3,4,5},4->{2,3,4,5},5->{1,6},6->{}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose MAYBE + Considered Problem: Rules: f0(A,B,C,D) -> f4(0,B,C,D) True f4(A,B,C,D) -> f7(A,B,1 + A,D) [B >= 1 + A] f7(A,B,C,D) -> f7(A,B,1 + C,0) [B >= 1 + C] f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B >= 1 + C && 0 >= 1 + E] f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B >= 1 + C && E >= 1] f7(A,B,C,D) -> f4(1 + A,B,C,D) [C >= B] f4(A,B,C,D) -> f19(A,B,C,D) [A >= B] f19(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f0,4);(f19,4);(f4,4);(f7,4)} Rule Graph: [0->{1,6},1->{2,3,4,5},2->{2,3,4,5},3->{2,3,4,5},4->{2,3,4,5},5->{1,6},6->{7}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[1,5,2,3,4] c: [1,5] | `- p:[2,3,4] c: [2,3,4] * Step 4: AbstractSize MAYBE + Considered Problem: (Rules: f0(A,B,C,D) -> f4(0,B,C,D) True f4(A,B,C,D) -> f7(A,B,1 + A,D) [B >= 1 + A] f7(A,B,C,D) -> f7(A,B,1 + C,0) [B >= 1 + C] f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B >= 1 + C && 0 >= 1 + E] f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B >= 1 + C && E >= 1] f7(A,B,C,D) -> f4(1 + A,B,C,D) [C >= B] f4(A,B,C,D) -> f19(A,B,C,D) [A >= B] f19(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(exitus616,4);(f0,4);(f19,4);(f4,4);(f7,4)} Rule Graph: [0->{1,6},1->{2,3,4,5},2->{2,3,4,5},3->{2,3,4,5},4->{2,3,4,5},5->{1,6},6->{7}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | `- p:[1,5,2,3,4] c: [1,5] | `- p:[2,3,4] c: [2,3,4]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow MAYBE + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0] f0 ~> f4 [A <= 0*K, B <= B, C <= C, D <= D] f4 ~> f7 [A <= A, B <= B, C <= A + B, D <= D] f7 ~> f7 [A <= A, B <= B, C <= B + C, D <= 0*K] f7 ~> f7 [A <= A, B <= B + C, C <= C, D <= unknown] f7 ~> f7 [A <= A, B <= B + C, C <= C, D <= unknown] f7 ~> f4 [A <= K + A, B <= B, C <= C, D <= D] f4 ~> f19 [A <= A, B <= B, C <= C, D <= D] f19 ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= K + A + B] f4 ~> f7 [A <= A, B <= B, C <= A + B, D <= D] f7 ~> f4 [A <= K + A, B <= B, C <= C, D <= D] f7 ~> f7 [A <= A, B <= B, C <= B + C, D <= 0*K] f7 ~> f7 [A <= A, B <= B + C, C <= C, D <= unknown] f7 ~> f7 [A <= A, B <= B + C, C <= C, D <= unknown] + Loop: [0.0.0 <= K + B + C] f7 ~> f7 [A <= A, B <= B, C <= B + C, D <= 0*K] f7 ~> f7 [A <= A, B <= B + C, C <= C, D <= unknown] f7 ~> f7 [A <= A, B <= B + C, C <= C, D <= unknown] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.0.0] f0 ~> f4 [K ~=> A] f4 ~> f7 [A ~+> C,B ~+> C] f7 ~> f7 [K ~=> D,B ~+> C,C ~+> C] f7 ~> f7 [huge ~=> D,B ~+> B,C ~+> B] f7 ~> f7 [huge ~=> D,B ~+> B,C ~+> B] f7 ~> f4 [A ~+> A,K ~+> A] f4 ~> f19 [] f19 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] f4 ~> f7 [A ~+> C,B ~+> C] f7 ~> f4 [A ~+> A,K ~+> A] f7 ~> f7 [K ~=> D,B ~+> C,C ~+> C] f7 ~> f7 [huge ~=> D,B ~+> B,C ~+> B] f7 ~> f7 [huge ~=> D,B ~+> B,C ~+> B] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0,K ~+> 0.0.0] f7 ~> f7 [K ~=> D,B ~+> C,C ~+> C] f7 ~> f7 [huge ~=> D,B ~+> B,C ~+> B] f7 ~> f7 [huge ~=> D,B ~+> B,C ~+> B] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> A ,K ~=> D ,huge ~=> D ,B ~+> B ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> A ,B ~*> B ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> B ,K ~*> C ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,B ~^> B ,B ~^> C ,B ~^> 0.0.0 ,B ~^> tick ,K ~^> B ,K ~^> C ,K ~^> 0.0.0 ,K ~^> tick] + f4> [K ~=> D ,huge ~=> D ,A ~+> A ,A ~+> B ,A ~+> C ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> A ,B ~*> B ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> B ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> B ,A ~^> C ,A ~^> 0.0.0 ,A ~^> tick ,B ~^> B ,B ~^> C ,B ~^> 0.0.0 ,B ~^> tick ,K ~^> B ,K ~^> C ,K ~^> 0.0.0 ,K ~^> tick] + f7> [K ~=> D ,huge ~=> D ,B ~+> B ,B ~+> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> B ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> B ,B ~*> C ,C ~*> B ,C ~*> C ,K ~*> B ,K ~*> C ,B ~^> B ,B ~^> C ,C ~^> B ,C ~^> C ,K ~^> B ,K ~^> C] YES(?,PRIMREC)