YES(?,PRIMREC) * Step 1: TrivialSCCs MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f10(H,0,C,D,E,F,G) True (1,1) 1. f10(A,B,C,D,E,F,G) -> f10(A,1 + B,C,D,E,F,G) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,0,G) [D >= 2 + E] (?,1) 3. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,G) [D >= 2 + E + F] (?,1) 4. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,H) [D >= 2 + E + F] (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,1 + E,F,G) [D >= 2 + E] (?,1) 6. f32(A,B,C,D,E,F,G) -> f41(A,B,C,D,E,F,G) [1 + E >= D] (?,1) 7. f21(A,B,C,D,E,F,G) -> f18(A,B,C,D,1 + E,F,G) [1 + E + F >= D] (?,1) 8. f18(A,B,C,D,E,F,G) -> f32(A,B,C,D,0,F,G) [1 + E >= D] (?,1) 9. f10(A,B,C,D,E,F,G) -> f18(A,B,C,C,0,F,G) [B >= C] (?,1) Signature: {(f0,7);(f10,7);(f18,7);(f21,7);(f32,7);(f41,7)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f10(H,0,C,D,E,F,G) True (1,1) 1. f10(A,B,C,D,E,F,G) -> f10(A,1 + B,C,D,E,F,G) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,0,G) [D >= 2 + E] (?,1) 3. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,G) [D >= 2 + E + F] (?,1) 4. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,H) [D >= 2 + E + F] (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,1 + E,F,G) [D >= 2 + E] (?,1) 6. f32(A,B,C,D,E,F,G) -> f41(A,B,C,D,E,F,G) [1 + E >= D] (1,1) 7. f21(A,B,C,D,E,F,G) -> f18(A,B,C,D,1 + E,F,G) [1 + E + F >= D] (?,1) 8. f18(A,B,C,D,E,F,G) -> f32(A,B,C,D,0,F,G) [1 + E >= D] (1,1) 9. f10(A,B,C,D,E,F,G) -> f18(A,B,C,C,0,F,G) [B >= C] (1,1) Signature: {(f0,7);(f10,7);(f18,7);(f21,7);(f32,7);(f41,7)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,7)] * Step 3: AddSinks MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f10(H,0,C,D,E,F,G) True (1,1) 1. f10(A,B,C,D,E,F,G) -> f10(A,1 + B,C,D,E,F,G) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,0,G) [D >= 2 + E] (?,1) 3. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,G) [D >= 2 + E + F] (?,1) 4. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,H) [D >= 2 + E + F] (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,1 + E,F,G) [D >= 2 + E] (?,1) 6. f32(A,B,C,D,E,F,G) -> f41(A,B,C,D,E,F,G) [1 + E >= D] (1,1) 7. f21(A,B,C,D,E,F,G) -> f18(A,B,C,D,1 + E,F,G) [1 + E + F >= D] (?,1) 8. f18(A,B,C,D,E,F,G) -> f32(A,B,C,D,0,F,G) [1 + E >= D] (1,1) 9. f10(A,B,C,D,E,F,G) -> f18(A,B,C,C,0,F,G) [B >= C] (1,1) Signature: {(f0,7);(f10,7);(f18,7);(f21,7);(f32,7);(f41,7)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6},6->{},7->{2,8},8->{5,6},9->{2,8}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f10(H,0,C,D,E,F,G) True (1,1) 1. f10(A,B,C,D,E,F,G) -> f10(A,1 + B,C,D,E,F,G) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,0,G) [D >= 2 + E] (?,1) 3. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,G) [D >= 2 + E + F] (?,1) 4. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,H) [D >= 2 + E + F] (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,1 + E,F,G) [D >= 2 + E] (?,1) 6. f32(A,B,C,D,E,F,G) -> f41(A,B,C,D,E,F,G) [1 + E >= D] (?,1) 7. f21(A,B,C,D,E,F,G) -> f18(A,B,C,D,1 + E,F,G) [1 + E + F >= D] (?,1) 8. f18(A,B,C,D,E,F,G) -> f32(A,B,C,D,0,F,G) [1 + E >= D] (?,1) 9. f10(A,B,C,D,E,F,G) -> f18(A,B,C,C,0,F,G) [B >= C] (?,1) 10. f32(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f10,7);(f18,7);(f21,7);(f32,7);(f41,7)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4,7},3->{3,4,7},4->{3,4,7},5->{5,6,10},6->{},7->{2,8},8->{5,6,10},9->{2,8} ,10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,7)] * Step 5: LooptreeTransformer MAYBE + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f10(H,0,C,D,E,F,G) True (1,1) 1. f10(A,B,C,D,E,F,G) -> f10(A,1 + B,C,D,E,F,G) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,0,G) [D >= 2 + E] (?,1) 3. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,G) [D >= 2 + E + F] (?,1) 4. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,H) [D >= 2 + E + F] (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,1 + E,F,G) [D >= 2 + E] (?,1) 6. f32(A,B,C,D,E,F,G) -> f41(A,B,C,D,E,F,G) [1 + E >= D] (?,1) 7. f21(A,B,C,D,E,F,G) -> f18(A,B,C,D,1 + E,F,G) [1 + E + F >= D] (?,1) 8. f18(A,B,C,D,E,F,G) -> f32(A,B,C,D,0,F,G) [1 + E >= D] (?,1) 9. f10(A,B,C,D,E,F,G) -> f18(A,B,C,C,0,F,G) [B >= C] (?,1) 10. f32(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f10,7);(f18,7);(f21,7);(f32,7);(f41,7)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6,10},6->{},7->{2,8},8->{5,6,10},9->{2,8},10->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[1] c: [1] | +- p:[2,7,3,4] c: [2] | | | `- p:[3,4] c: [4] | | | `- p:[3] c: [3] | `- p:[5] c: [5] * Step 6: SizeAbstraction MAYBE + Considered Problem: (Rules: 0. f0(A,B,C,D,E,F,G) -> f10(H,0,C,D,E,F,G) True (1,1) 1. f10(A,B,C,D,E,F,G) -> f10(A,1 + B,C,D,E,F,G) [C >= 1 + B] (?,1) 2. f18(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,0,G) [D >= 2 + E] (?,1) 3. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,G) [D >= 2 + E + F] (?,1) 4. f21(A,B,C,D,E,F,G) -> f21(A,B,C,D,E,1 + F,H) [D >= 2 + E + F] (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,1 + E,F,G) [D >= 2 + E] (?,1) 6. f32(A,B,C,D,E,F,G) -> f41(A,B,C,D,E,F,G) [1 + E >= D] (?,1) 7. f21(A,B,C,D,E,F,G) -> f18(A,B,C,D,1 + E,F,G) [1 + E + F >= D] (?,1) 8. f18(A,B,C,D,E,F,G) -> f32(A,B,C,D,0,F,G) [1 + E >= D] (?,1) 9. f10(A,B,C,D,E,F,G) -> f18(A,B,C,C,0,F,G) [B >= C] (?,1) 10. f32(A,B,C,D,E,F,G) -> exitus616(A,B,C,D,E,F,G) True (?,1) Signature: {(exitus616,7);(f0,7);(f10,7);(f18,7);(f21,7);(f32,7);(f41,7)} Flow Graph: [0->{1,9},1->{1,9},2->{3,4},3->{3,4,7},4->{3,4,7},5->{5,6,10},6->{},7->{2,8},8->{5,6,10},9->{2,8},10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | +- p:[1] c: [1] | +- p:[2,7,3,4] c: [2] | | | `- p:[3,4] c: [4] | | | `- p:[3] c: [3] | `- p:[5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction MAYBE + Considered Problem: Program: Domain: [A,B,C,D,E,F,G,0.0,0.1,0.1.0,0.1.0.0,0.2] f0 ~> f10 [A <= unknown, B <= 0*K, C <= C, D <= D, E <= E, F <= F, G <= G] f10 ~> f10 [A <= A, B <= B + C, C <= C, D <= D, E <= E, F <= F, G <= G] f18 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f21 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] f21 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= unknown] f32 ~> f32 [A <= A, B <= B, C <= C, D <= D, E <= D + E, F <= F, G <= G] f32 ~> f41 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] f21 ~> f18 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] f18 ~> f32 [A <= A, B <= B, C <= C, D <= D, E <= 0*K, F <= F, G <= G] f10 ~> f18 [A <= A, B <= B, C <= C, D <= C, E <= 0*K, F <= F, G <= G] f32 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.0 <= B + C] f10 ~> f10 [A <= A, B <= B + C, C <= C, D <= D, E <= E, F <= F, G <= G] + Loop: [0.1 <= 2*K + D + E] f18 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= 0*K, G <= G] f21 ~> f18 [A <= A, B <= B, C <= C, D <= D, E <= K + E, F <= F, G <= G] f21 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] f21 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= unknown] + Loop: [0.1.0 <= D + E + F] f21 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] f21 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= unknown] + Loop: [0.1.0.0 <= K + D + E + F] f21 ~> f21 [A <= A, B <= B, C <= C, D <= D, E <= E, F <= K + F, G <= G] + Loop: [0.2 <= K + D + E] f32 ~> f32 [A <= A, B <= B, C <= C, D <= D, E <= D + E, F <= F, G <= G] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor MAYBE + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,F,G,0.0,0.1,0.1.0,0.1.0.0,0.2] f0 ~> f10 [K ~=> B,huge ~=> A] f10 ~> f10 [B ~+> B,C ~+> B] f18 ~> f21 [K ~=> F] f21 ~> f21 [F ~+> F,K ~+> F] f21 ~> f21 [huge ~=> G,F ~+> F,K ~+> F] f32 ~> f32 [D ~+> E,E ~+> E] f32 ~> f41 [] f21 ~> f18 [E ~+> E,K ~+> E] f18 ~> f32 [K ~=> E] f10 ~> f18 [C ~=> D,K ~=> E] f32 ~> exitus616 [] + Loop: [B ~+> 0.0,C ~+> 0.0] f10 ~> f10 [B ~+> B,C ~+> B] + Loop: [D ~+> 0.1,E ~+> 0.1,K ~*> 0.1] f18 ~> f21 [K ~=> F] f21 ~> f18 [E ~+> E,K ~+> E] f21 ~> f21 [F ~+> F,K ~+> F] f21 ~> f21 [huge ~=> G,F ~+> F,K ~+> F] + Loop: [D ~+> 0.1.0,E ~+> 0.1.0,F ~+> 0.1.0] f21 ~> f21 [F ~+> F,K ~+> F] f21 ~> f21 [huge ~=> G,F ~+> F,K ~+> F] + Loop: [D ~+> 0.1.0.0,E ~+> 0.1.0.0,F ~+> 0.1.0.0,K ~+> 0.1.0.0] f21 ~> f21 [F ~+> F,K ~+> F] + Loop: [D ~+> 0.2,E ~+> 0.2,K ~+> 0.2] f32 ~> f32 [D ~+> E,E ~+> E] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [C ~=> D ,K ~=> B ,K ~=> E ,K ~=> F ,huge ~=> A ,huge ~=> G ,C ~+> B ,C ~+> E ,C ~+> 0.0 ,C ~+> 0.1 ,C ~+> 0.1.0 ,C ~+> 0.1.0.0 ,C ~+> 0.2 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> E ,K ~+> F ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> 0.2 ,K ~+> tick ,C ~*> B ,C ~*> E ,C ~*> F ,C ~*> 0.1.0 ,C ~*> 0.1.0.0 ,C ~*> tick ,K ~*> B ,K ~*> E ,K ~*> F ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> 0.2 ,K ~*> tick ,C ~^> F ,C ~^> 0.1.0 ,C ~^> 0.1.0.0 ,C ~^> tick ,K ~^> F ,K ~^> 0.1.0 ,K ~^> 0.1.0.0 ,K ~^> tick] f0 ~> f41 [C ~=> D ,K ~=> B ,K ~=> E ,K ~=> F ,huge ~=> A ,huge ~=> G ,C ~+> B ,C ~+> E ,C ~+> 0.0 ,C ~+> 0.1 ,C ~+> 0.1.0 ,C ~+> 0.1.0.0 ,C ~+> 0.2 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> E ,K ~+> F ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> 0.2 ,K ~+> tick ,C ~*> B ,C ~*> E ,C ~*> F ,C ~*> 0.1.0 ,C ~*> 0.1.0.0 ,C ~*> tick ,K ~*> B ,K ~*> E ,K ~*> F ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> 0.2 ,K ~*> tick ,C ~^> F ,C ~^> 0.1.0 ,C ~^> 0.1.0.0 ,C ~^> tick ,K ~^> F ,K ~^> 0.1.0 ,K ~^> 0.1.0.0 ,K ~^> tick] + f10> [B ~+> B,B ~+> 0.0,B ~+> tick,C ~+> B,C ~+> 0.0,C ~+> tick,tick ~+> tick,B ~*> B,C ~*> B] + f18> [K ~=> F ,huge ~=> G ,D ~+> 0.1 ,D ~+> 0.1.0 ,D ~+> 0.1.0.0 ,D ~+> tick ,E ~+> E ,E ~+> 0.1 ,E ~+> 0.1.0 ,E ~+> 0.1.0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> E ,K ~+> F ,K ~+> 0.1.0 ,K ~+> 0.1.0.0 ,K ~+> tick ,D ~*> E ,D ~*> F ,D ~*> 0.1.0 ,D ~*> 0.1.0.0 ,D ~*> tick ,E ~*> E ,E ~*> F ,E ~*> 0.1.0 ,E ~*> 0.1.0.0 ,E ~*> tick ,K ~*> E ,K ~*> F ,K ~*> 0.1 ,K ~*> 0.1.0 ,K ~*> 0.1.0.0 ,K ~*> tick ,D ~^> F ,D ~^> 0.1.0 ,D ~^> 0.1.0.0 ,D ~^> tick ,E ~^> F ,E ~^> 0.1.0 ,E ~^> 0.1.0.0 ,E ~^> tick ,K ~^> F ,K ~^> 0.1.0 ,K ~^> 0.1.0.0 ,K ~^> tick] + f21> [huge ~=> G ,D ~+> 0.1.0 ,D ~+> 0.1.0.0 ,D ~+> tick ,E ~+> 0.1.0 ,E ~+> 0.1.0.0 ,E ~+> tick ,F ~+> F ,F ~+> 0.1.0 ,F ~+> 0.1.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> F ,K ~+> 0.1.0.0 ,K ~+> tick ,D ~*> F ,D ~*> 0.1.0.0 ,D ~*> tick ,E ~*> F ,E ~*> 0.1.0.0 ,E ~*> tick ,F ~*> F ,F ~*> 0.1.0.0 ,F ~*> tick ,K ~*> F ,K ~*> 0.1.0.0 ,K ~*> tick ,D ~^> F ,E ~^> F ,F ~^> F] + f21> [D ~+> 0.1.0.0 ,D ~+> tick ,E ~+> 0.1.0.0 ,E ~+> tick ,F ~+> F ,F ~+> 0.1.0.0 ,F ~+> tick ,tick ~+> tick ,K ~+> F ,K ~+> 0.1.0.0 ,K ~+> tick ,D ~*> F ,E ~*> F ,F ~*> F ,K ~*> F] + f32> [D ~+> E ,D ~+> 0.2 ,D ~+> tick ,E ~+> E ,E ~+> 0.2 ,E ~+> tick ,tick ~+> tick ,K ~+> 0.2 ,K ~+> tick ,D ~*> E ,E ~*> E ,K ~*> E] YES(?,PRIMREC)