YES(?,PRIMREC) * Step 1: UnsatPaths MAYBE + Considered Problem: Rules: 0. f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B] (?,1) 1. f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] (?,1) 2. f0(A,B,C) -> f4(0,0,C) [C >= 1] (1,1) Signature: {(f0,3);(f4,3)} Flow Graph: [0->{0,1},1->{0,1},2->{0,1}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,0)] * Step 2: FromIts MAYBE + Considered Problem: Rules: 0. f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B] (?,1) 1. f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] (?,1) 2. f0(A,B,C) -> f4(0,0,C) [C >= 1] (1,1) Signature: {(f0,3);(f4,3)} Flow Graph: [0->{0,1},1->{0,1},2->{1}] + Applied Processor: FromIts + Details: () * Step 3: Unfold MAYBE + Considered Problem: Rules: f4(A,B,C) -> f4(A,1 + B,C) [A >= 1 + B] f4(A,B,C) -> f4(1 + A,0,C) [C >= 2 + A && B >= A] f0(A,B,C) -> f4(0,0,C) [C >= 1] Signature: {(f0,3);(f4,3)} Rule Graph: [0->{0,1},1->{0,1},2->{1}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks MAYBE + Considered Problem: Rules: f4.0(A,B,C) -> f4.0(A,1 + B,C) [A >= 1 + B] f4.0(A,B,C) -> f4.1(A,1 + B,C) [A >= 1 + B] f4.1(A,B,C) -> f4.0(1 + A,0,C) [C >= 2 + A && B >= A] f4.1(A,B,C) -> f4.1(1 + A,0,C) [C >= 2 + A && B >= A] f0.2(A,B,C) -> f4.1(0,0,C) [C >= 1] Signature: {(f0.2,3);(f4.0,3);(f4.1,3)} Rule Graph: [0->{0,1},1->{2,3},2->{0,1},3->{2,3},4->{2,3}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose MAYBE + Considered Problem: Rules: f4.0(A,B,C) -> f4.0(A,1 + B,C) [A >= 1 + B] f4.0(A,B,C) -> f4.1(A,1 + B,C) [A >= 1 + B] f4.1(A,B,C) -> f4.0(1 + A,0,C) [C >= 2 + A && B >= A] f4.1(A,B,C) -> f4.1(1 + A,0,C) [C >= 2 + A && B >= A] f0.2(A,B,C) -> f4.1(0,0,C) [C >= 1] f4.0(A,B,C) -> exitus616(A,B,C) True f4.0(A,B,C) -> exitus616(A,B,C) True f4.1(A,B,C) -> exitus616(A,B,C) True f4.1(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f0.2,3);(f4.0,3);(f4.1,3)} Rule Graph: [0->{0,1,5},1->{2,3,7},2->{0,1,6},3->{2,3,8},4->{2,3}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[0,2,1,3] c: [2,3] | `- p:[0] c: [0] * Step 6: AbstractSize MAYBE + Considered Problem: (Rules: f4.0(A,B,C) -> f4.0(A,1 + B,C) [A >= 1 + B] f4.0(A,B,C) -> f4.1(A,1 + B,C) [A >= 1 + B] f4.1(A,B,C) -> f4.0(1 + A,0,C) [C >= 2 + A && B >= A] f4.1(A,B,C) -> f4.1(1 + A,0,C) [C >= 2 + A && B >= A] f0.2(A,B,C) -> f4.1(0,0,C) [C >= 1] f4.0(A,B,C) -> exitus616(A,B,C) True f4.0(A,B,C) -> exitus616(A,B,C) True f4.1(A,B,C) -> exitus616(A,B,C) True f4.1(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f0.2,3);(f4.0,3);(f4.1,3)} Rule Graph: [0->{0,1,5},1->{2,3,7},2->{0,1,6},3->{2,3,8},4->{2,3}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | `- p:[0,2,1,3] c: [2,3] | `- p:[0] c: [0]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow MAYBE + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] f4.0 ~> f4.0 [A <= A, B <= A + B, C <= C] f4.0 ~> f4.1 [A <= A, B <= A + B, C <= C] f4.1 ~> f4.0 [A <= K + A, B <= 0*K, C <= C] f4.1 ~> f4.1 [A <= K + A, B <= 0*K, C <= C] f0.2 ~> f4.1 [A <= 0*K, B <= 0*K, C <= C] f4.0 ~> exitus616 [A <= A, B <= B, C <= C] f4.0 ~> exitus616 [A <= A, B <= B, C <= C] f4.1 ~> exitus616 [A <= A, B <= B, C <= C] f4.1 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 2*K + A + C] f4.0 ~> f4.0 [A <= A, B <= A + B, C <= C] f4.1 ~> f4.0 [A <= K + A, B <= 0*K, C <= C] f4.0 ~> f4.1 [A <= A, B <= A + B, C <= C] f4.1 ~> f4.1 [A <= K + A, B <= 0*K, C <= C] + Loop: [0.0.0 <= K + A + B] f4.0 ~> f4.0 [A <= A, B <= A + B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] f4.0 ~> f4.0 [A ~+> B,B ~+> B] f4.0 ~> f4.1 [A ~+> B,B ~+> B] f4.1 ~> f4.0 [K ~=> B,A ~+> A,K ~+> A] f4.1 ~> f4.1 [K ~=> B,A ~+> A,K ~+> A] f0.2 ~> f4.1 [K ~=> A,K ~=> B] f4.0 ~> exitus616 [] f4.0 ~> exitus616 [] f4.1 ~> exitus616 [] f4.1 ~> exitus616 [] + Loop: [A ~+> 0.0,C ~+> 0.0,K ~*> 0.0] f4.0 ~> f4.0 [A ~+> B,B ~+> B] f4.1 ~> f4.0 [K ~=> B,A ~+> A,K ~+> A] f4.0 ~> f4.1 [A ~+> B,B ~+> B] f4.1 ~> f4.1 [K ~=> B,A ~+> A,K ~+> A] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0,K ~+> 0.0.0] f4.0 ~> f4.0 [A ~+> B,B ~+> B] + Applied Processor: Lare + Details: f0.2 ~> exitus616 [K ~=> A ,K ~=> B ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,C ~*> A ,C ~*> B ,C ~*> 0.0 ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,C ~^> B ,C ~^> 0.0.0 ,C ~^> tick ,K ~^> B ,K ~^> 0.0.0 ,K ~^> tick] + f4.0> [K ~=> B ,A ~+> A ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> B ,C ~*> A ,C ~*> B ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> B ,C ~^> B ,K ~^> B] f4.1> [K ~=> B ,A ~+> A ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> B ,C ~*> A ,C ~*> B ,C ~*> 0.0.0 ,C ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> B ,C ~^> B ,K ~^> B] + f4.0> [A ~+> B ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] YES(?,PRIMREC)