WORST_CASE(?,O(1)) * Step 1: RestrictVarsProcessor WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [99 >= A] (?,1) 2. f17(A,B,C,D,E,F,G) -> f17(A,B,C,D,E,F,G) True (?,1) 3. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) [0 >= 1 + H] (?,1) 4. f17(A,B,C,D,E,F,G) -> f17(A,1 + B,C,D,E,F,G) True (?,1) 5. f32(A,B,C,D,E,F,G) -> f32(A,B,C,D,E,F,G) True (?,1) 6. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) [0 >= 1 + H] (?,1) 7. f32(A,B,C,D,E,F,G) -> f32(A,B,1 + C,D,E,F,G) True (?,1) 8. f32(A,B,C,D,E,F,G) -> f13(A,B,C,C,C,F,G) True (?,1) 9. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) [0 >= 1 + I] (?,1) 10. f17(A,B,C,D,E,F,G) -> f32(A,B,B,B,E,B,H) True (?,1) 11. f17(A,B,C,D,E,F,G) -> f13(A,B,C,B,E,B,H) True (?,1) 12. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 100] (?,1) 13. f5(A,B,C,D,E,F,G) -> f17(A,-2 + A,C,-2 + A,E,F,G) [0 >= 1 + A && A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f17,7);(f32,7);(f5,7)} Flow Graph: [0->{1,12,13},1->{1,12,13},2->{2,3,4,9,10,11},3->{2,3,4,9,10,11},4->{2,3,4,9,10,11},5->{5,6,7,8},6->{5,6,7 ,8},7->{5,6,7,8},8->{},9->{5,6,7,8},10->{5,6,7,8},11->{},12->{},13->{2,3,4,9,10,11}] + Applied Processor: RestrictVarsProcessor + Details: We removed the arguments [D,E,F,G] . * Step 2: UnsatRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(0,B,C) True (1,1) 1. f5(A,B,C) -> f5(1 + A,B,C) [99 >= A] (?,1) 2. f17(A,B,C) -> f17(A,B,C) True (?,1) 3. f17(A,B,C) -> f17(A,1 + B,C) [0 >= 1 + H] (?,1) 4. f17(A,B,C) -> f17(A,1 + B,C) True (?,1) 5. f32(A,B,C) -> f32(A,B,C) True (?,1) 6. f32(A,B,C) -> f32(A,B,1 + C) [0 >= 1 + H] (?,1) 7. f32(A,B,C) -> f32(A,B,1 + C) True (?,1) 8. f32(A,B,C) -> f13(A,B,C) True (?,1) 9. f17(A,B,C) -> f32(A,B,B) [0 >= 1 + I] (?,1) 10. f17(A,B,C) -> f32(A,B,B) True (?,1) 11. f17(A,B,C) -> f13(A,B,C) True (?,1) 12. f5(A,B,C) -> f13(A,B,C) [A >= 100] (?,1) 13. f5(A,B,C) -> f17(A,-2 + A,C) [0 >= 1 + A && A >= 100] (?,1) Signature: {(f0,3);(f13,3);(f17,3);(f32,3);(f5,3)} Flow Graph: [0->{1,12,13},1->{1,12,13},2->{2,3,4,9,10,11},3->{2,3,4,9,10,11},4->{2,3,4,9,10,11},5->{5,6,7,8},6->{5,6,7 ,8},7->{5,6,7,8},8->{},9->{5,6,7,8},10->{5,6,7,8},11->{},12->{},13->{2,3,4,9,10,11}] + Applied Processor: UnsatRules + Details: The following transitions have unsatisfiable constraints and are removed: [13] * Step 3: UnreachableRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(0,B,C) True (1,1) 1. f5(A,B,C) -> f5(1 + A,B,C) [99 >= A] (?,1) 2. f17(A,B,C) -> f17(A,B,C) True (?,1) 3. f17(A,B,C) -> f17(A,1 + B,C) [0 >= 1 + H] (?,1) 4. f17(A,B,C) -> f17(A,1 + B,C) True (?,1) 5. f32(A,B,C) -> f32(A,B,C) True (?,1) 6. f32(A,B,C) -> f32(A,B,1 + C) [0 >= 1 + H] (?,1) 7. f32(A,B,C) -> f32(A,B,1 + C) True (?,1) 8. f32(A,B,C) -> f13(A,B,C) True (?,1) 9. f17(A,B,C) -> f32(A,B,B) [0 >= 1 + I] (?,1) 10. f17(A,B,C) -> f32(A,B,B) True (?,1) 11. f17(A,B,C) -> f13(A,B,C) True (?,1) 12. f5(A,B,C) -> f13(A,B,C) [A >= 100] (?,1) Signature: {(f0,3);(f13,3);(f17,3);(f32,3);(f5,3)} Flow Graph: [0->{1,12},1->{1,12},2->{2,3,4,9,10,11},3->{2,3,4,9,10,11},4->{2,3,4,9,10,11},5->{5,6,7,8},6->{5,6,7,8} ,7->{5,6,7,8},8->{},9->{5,6,7,8},10->{5,6,7,8},11->{},12->{}] + Applied Processor: UnreachableRules + Details: The following transitions are not reachable from the starting states and are removed: [2 ,3 ,4 ,5 ,6 ,7 ,8 ,9 ,10 ,11] * Step 4: LocalSizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(0,B,C) True (1,1) 1. f5(A,B,C) -> f5(1 + A,B,C) [99 >= A] (?,1) 12. f5(A,B,C) -> f13(A,B,C) [A >= 100] (?,1) Signature: {(f0,3);(f13,3);(f17,3);(f32,3);(f5,3)} Flow Graph: [0->{1,12},1->{1,12},12->{}] + Applied Processor: LocalSizeboundsProc + Details: LocalSizebounds generated; rvgraph (< 0,0,A>, 0, .= 0) (< 0,0,B>, B, .= 0) (< 0,0,C>, C, .= 0) (< 1,0,A>, 1 + A, .+ 1) (< 1,0,B>, B, .= 0) (< 1,0,C>, C, .= 0) (<12,0,A>, A, .= 0) (<12,0,B>, B, .= 0) (<12,0,C>, C, .= 0) * Step 5: SizeboundsProc WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(0,B,C) True (1,1) 1. f5(A,B,C) -> f5(1 + A,B,C) [99 >= A] (?,1) 12. f5(A,B,C) -> f13(A,B,C) [A >= 100] (?,1) Signature: {(f0,3);(f13,3);(f17,3);(f32,3);(f5,3)} Flow Graph: [0->{1,12},1->{1,12},12->{}] Sizebounds: (< 0,0,A>, ?) (< 0,0,B>, ?) (< 0,0,C>, ?) (< 1,0,A>, ?) (< 1,0,B>, ?) (< 1,0,C>, ?) (<12,0,A>, ?) (<12,0,B>, ?) (<12,0,C>, ?) + Applied Processor: SizeboundsProc + Details: Sizebounds computed: (< 0,0,A>, 0) (< 0,0,B>, B) (< 0,0,C>, C) (< 1,0,A>, 100) (< 1,0,B>, B) (< 1,0,C>, C) (<12,0,A>, 100) (<12,0,B>, B) (<12,0,C>, C) * Step 6: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(0,B,C) True (1,1) 1. f5(A,B,C) -> f5(1 + A,B,C) [99 >= A] (?,1) 12. f5(A,B,C) -> f13(A,B,C) [A >= 100] (?,1) Signature: {(f0,3);(f13,3);(f17,3);(f32,3);(f5,3)} Flow Graph: [0->{1,12},1->{1,12},12->{}] Sizebounds: (< 0,0,A>, 0) (< 0,0,B>, B) (< 0,0,C>, C) (< 1,0,A>, 100) (< 1,0,B>, B) (< 1,0,C>, C) (<12,0,A>, 100) (<12,0,B>, B) (<12,0,C>, C) + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,12)] * Step 7: LeafRules WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(0,B,C) True (1,1) 1. f5(A,B,C) -> f5(1 + A,B,C) [99 >= A] (?,1) 12. f5(A,B,C) -> f13(A,B,C) [A >= 100] (?,1) Signature: {(f0,3);(f13,3);(f17,3);(f32,3);(f5,3)} Flow Graph: [0->{1},1->{1,12},12->{}] Sizebounds: (< 0,0,A>, 0) (< 0,0,B>, B) (< 0,0,C>, C) (< 1,0,A>, 100) (< 1,0,B>, B) (< 1,0,C>, C) (<12,0,A>, 100) (<12,0,B>, B) (<12,0,C>, C) + Applied Processor: LeafRules + Details: The following transitions are estimated by its predecessors and are removed [12] * Step 8: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(0,B,C) True (1,1) 1. f5(A,B,C) -> f5(1 + A,B,C) [99 >= A] (?,1) Signature: {(f0,3);(f13,3);(f17,3);(f32,3);(f5,3)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, B) (<0,0,C>, C) (<1,0,A>, 100) (<1,0,B>, B) (<1,0,C>, C) + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 100 p(f5) = 100 + -1*x1 The following rules are strictly oriented: [99 >= A] ==> f5(A,B,C) = 100 + -1*A > 99 + -1*A = f5(1 + A,B,C) The following rules are weakly oriented: True ==> f0(A,B,C) = 100 >= 100 = f5(0,B,C) * Step 9: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f5(0,B,C) True (1,1) 1. f5(A,B,C) -> f5(1 + A,B,C) [99 >= A] (100,1) Signature: {(f0,3);(f13,3);(f17,3);(f32,3);(f5,3)} Flow Graph: [0->{1},1->{1}] Sizebounds: (<0,0,A>, 0) (<0,0,B>, B) (<0,0,C>, C) (<1,0,A>, 100) (<1,0,B>, B) (<1,0,C>, C) + Applied Processor: KnowledgePropagation + Details: The problem is already solved. WORST_CASE(?,O(1))