1124.61/291.69 WORST_CASE(Omega(n^1), O(n^4)) 1124.61/291.70 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1124.61/291.70 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1124.61/291.70 1124.61/291.70 1124.61/291.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^4). 1124.61/291.70 1124.61/291.70 (0) CpxTRS 1124.61/291.70 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.61/291.70 (2) CpxWeightedTrs 1124.61/291.70 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.61/291.70 (4) CpxTypedWeightedTrs 1124.61/291.70 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1124.61/291.70 (6) CpxTypedWeightedCompleteTrs 1124.61/291.70 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1124.61/291.70 (8) CpxRNTS 1124.61/291.70 (9) CompleteCoflocoProof [FINISHED, 8211 ms] 1124.61/291.70 (10) BOUNDS(1, n^4) 1124.61/291.70 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1124.61/291.70 (12) TRS for Loop Detection 1124.61/291.70 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1124.61/291.70 (14) BEST 1124.61/291.70 (15) proven lower bound 1124.61/291.70 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1124.61/291.70 (17) BOUNDS(n^1, INF) 1124.61/291.70 (18) TRS for Loop Detection 1124.61/291.70 1124.61/291.70 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (0) 1124.61/291.70 Obligation: 1124.61/291.70 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^4). 1124.61/291.70 1124.61/291.70 1124.61/291.70 The TRS R consists of the following rules: 1124.61/291.70 1124.61/291.70 eq(0, 0) -> true 1124.61/291.70 eq(0, s(x)) -> false 1124.61/291.70 eq(s(x), 0) -> false 1124.61/291.70 eq(s(x), s(y)) -> eq(x, y) 1124.61/291.70 le(0, y) -> true 1124.61/291.70 le(s(x), 0) -> false 1124.61/291.70 le(s(x), s(y)) -> le(x, y) 1124.61/291.70 app(nil, y) -> y 1124.61/291.70 app(add(n, x), y) -> add(n, app(x, y)) 1124.61/291.70 min(add(n, nil)) -> n 1124.61/291.70 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 1124.61/291.70 if_min(true, add(n, add(m, x))) -> min(add(n, x)) 1124.61/291.70 if_min(false, add(n, add(m, x))) -> min(add(m, x)) 1124.61/291.70 rm(n, nil) -> nil 1124.61/291.70 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 1124.61/291.70 if_rm(true, n, add(m, x)) -> rm(n, x) 1124.61/291.70 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) 1124.61/291.70 minsort(nil, nil) -> nil 1124.61/291.70 minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) 1124.61/291.70 if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) 1124.61/291.70 if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) 1124.61/291.70 1124.61/291.70 S is empty. 1124.61/291.70 Rewrite Strategy: INNERMOST 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1124.61/291.70 Transformed relative TRS to weighted TRS 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (2) 1124.61/291.70 Obligation: 1124.61/291.70 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^4). 1124.61/291.70 1124.61/291.70 1124.61/291.70 The TRS R consists of the following rules: 1124.61/291.70 1124.61/291.70 eq(0, 0) -> true [1] 1124.61/291.70 eq(0, s(x)) -> false [1] 1124.61/291.70 eq(s(x), 0) -> false [1] 1124.61/291.70 eq(s(x), s(y)) -> eq(x, y) [1] 1124.61/291.70 le(0, y) -> true [1] 1124.61/291.70 le(s(x), 0) -> false [1] 1124.61/291.70 le(s(x), s(y)) -> le(x, y) [1] 1124.61/291.70 app(nil, y) -> y [1] 1124.61/291.70 app(add(n, x), y) -> add(n, app(x, y)) [1] 1124.61/291.70 min(add(n, nil)) -> n [1] 1124.61/291.70 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) [1] 1124.61/291.70 if_min(true, add(n, add(m, x))) -> min(add(n, x)) [1] 1124.61/291.70 if_min(false, add(n, add(m, x))) -> min(add(m, x)) [1] 1124.61/291.70 rm(n, nil) -> nil [1] 1124.61/291.70 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) [1] 1124.61/291.70 if_rm(true, n, add(m, x)) -> rm(n, x) [1] 1124.61/291.70 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) [1] 1124.61/291.70 minsort(nil, nil) -> nil [1] 1124.61/291.70 minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) [1] 1124.61/291.70 if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) [1] 1124.61/291.70 if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) [1] 1124.61/291.70 1124.61/291.70 Rewrite Strategy: INNERMOST 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1124.61/291.70 Infered types. 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (4) 1124.61/291.70 Obligation: 1124.61/291.70 Runtime Complexity Weighted TRS with Types. 1124.61/291.70 The TRS R consists of the following rules: 1124.61/291.70 1124.61/291.70 eq(0, 0) -> true [1] 1124.61/291.70 eq(0, s(x)) -> false [1] 1124.61/291.70 eq(s(x), 0) -> false [1] 1124.61/291.70 eq(s(x), s(y)) -> eq(x, y) [1] 1124.61/291.70 le(0, y) -> true [1] 1124.61/291.70 le(s(x), 0) -> false [1] 1124.61/291.70 le(s(x), s(y)) -> le(x, y) [1] 1124.61/291.70 app(nil, y) -> y [1] 1124.61/291.70 app(add(n, x), y) -> add(n, app(x, y)) [1] 1124.61/291.70 min(add(n, nil)) -> n [1] 1124.61/291.70 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) [1] 1124.61/291.70 if_min(true, add(n, add(m, x))) -> min(add(n, x)) [1] 1124.61/291.70 if_min(false, add(n, add(m, x))) -> min(add(m, x)) [1] 1124.61/291.70 rm(n, nil) -> nil [1] 1124.61/291.70 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) [1] 1124.61/291.70 if_rm(true, n, add(m, x)) -> rm(n, x) [1] 1124.61/291.70 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) [1] 1124.61/291.70 minsort(nil, nil) -> nil [1] 1124.61/291.70 minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) [1] 1124.61/291.70 if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) [1] 1124.61/291.70 if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) [1] 1124.61/291.70 1124.61/291.70 The TRS has the following type information: 1124.61/291.70 eq :: 0:s -> 0:s -> true:false 1124.61/291.70 0 :: 0:s 1124.61/291.70 true :: true:false 1124.61/291.70 s :: 0:s -> 0:s 1124.61/291.70 false :: true:false 1124.61/291.70 le :: 0:s -> 0:s -> true:false 1124.61/291.70 app :: nil:add -> nil:add -> nil:add 1124.61/291.70 nil :: nil:add 1124.61/291.70 add :: 0:s -> nil:add -> nil:add 1124.61/291.70 min :: nil:add -> 0:s 1124.61/291.70 if_min :: true:false -> nil:add -> 0:s 1124.61/291.70 rm :: 0:s -> nil:add -> nil:add 1124.61/291.70 if_rm :: true:false -> 0:s -> nil:add -> nil:add 1124.61/291.70 minsort :: nil:add -> nil:add -> nil:add 1124.61/291.70 if_minsort :: true:false -> nil:add -> nil:add -> nil:add 1124.61/291.70 1124.61/291.70 Rewrite Strategy: INNERMOST 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (5) CompletionProof (UPPER BOUND(ID)) 1124.61/291.70 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 1124.61/291.70 1124.61/291.70 min(v0) -> null_min [0] 1124.61/291.70 if_min(v0, v1) -> null_if_min [0] 1124.61/291.70 if_rm(v0, v1, v2) -> null_if_rm [0] 1124.61/291.70 minsort(v0, v1) -> null_minsort [0] 1124.61/291.70 if_minsort(v0, v1, v2) -> null_if_minsort [0] 1124.61/291.70 eq(v0, v1) -> null_eq [0] 1124.61/291.70 le(v0, v1) -> null_le [0] 1124.61/291.70 app(v0, v1) -> null_app [0] 1124.61/291.70 rm(v0, v1) -> null_rm [0] 1124.61/291.70 1124.61/291.70 And the following fresh constants: null_min, null_if_min, null_if_rm, null_minsort, null_if_minsort, null_eq, null_le, null_app, null_rm 1124.61/291.70 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (6) 1124.61/291.70 Obligation: 1124.61/291.70 Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: 1124.61/291.70 1124.61/291.70 Runtime Complexity Weighted TRS with Types. 1124.61/291.70 The TRS R consists of the following rules: 1124.61/291.70 1124.61/291.70 eq(0, 0) -> true [1] 1124.61/291.70 eq(0, s(x)) -> false [1] 1124.61/291.70 eq(s(x), 0) -> false [1] 1124.61/291.70 eq(s(x), s(y)) -> eq(x, y) [1] 1124.61/291.70 le(0, y) -> true [1] 1124.61/291.70 le(s(x), 0) -> false [1] 1124.61/291.70 le(s(x), s(y)) -> le(x, y) [1] 1124.61/291.70 app(nil, y) -> y [1] 1124.61/291.70 app(add(n, x), y) -> add(n, app(x, y)) [1] 1124.61/291.70 min(add(n, nil)) -> n [1] 1124.61/291.70 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) [1] 1124.61/291.70 if_min(true, add(n, add(m, x))) -> min(add(n, x)) [1] 1124.61/291.70 if_min(false, add(n, add(m, x))) -> min(add(m, x)) [1] 1124.61/291.70 rm(n, nil) -> nil [1] 1124.61/291.70 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) [1] 1124.61/291.70 if_rm(true, n, add(m, x)) -> rm(n, x) [1] 1124.61/291.70 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) [1] 1124.61/291.70 minsort(nil, nil) -> nil [1] 1124.61/291.70 minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) [1] 1124.61/291.70 if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) [1] 1124.61/291.70 if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) [1] 1124.61/291.70 min(v0) -> null_min [0] 1124.61/291.70 if_min(v0, v1) -> null_if_min [0] 1124.61/291.70 if_rm(v0, v1, v2) -> null_if_rm [0] 1124.61/291.70 minsort(v0, v1) -> null_minsort [0] 1124.61/291.70 if_minsort(v0, v1, v2) -> null_if_minsort [0] 1124.61/291.70 eq(v0, v1) -> null_eq [0] 1124.61/291.70 le(v0, v1) -> null_le [0] 1124.61/291.70 app(v0, v1) -> null_app [0] 1124.61/291.70 rm(v0, v1) -> null_rm [0] 1124.61/291.70 1124.61/291.70 The TRS has the following type information: 1124.61/291.70 eq :: 0:s:null_min:null_if_min -> 0:s:null_min:null_if_min -> true:false:null_eq:null_le 1124.61/291.70 0 :: 0:s:null_min:null_if_min 1124.61/291.70 true :: true:false:null_eq:null_le 1124.61/291.70 s :: 0:s:null_min:null_if_min -> 0:s:null_min:null_if_min 1124.61/291.70 false :: true:false:null_eq:null_le 1124.61/291.70 le :: 0:s:null_min:null_if_min -> 0:s:null_min:null_if_min -> true:false:null_eq:null_le 1124.61/291.70 app :: nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 nil :: nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 add :: 0:s:null_min:null_if_min -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 min :: nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> 0:s:null_min:null_if_min 1124.61/291.70 if_min :: true:false:null_eq:null_le -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> 0:s:null_min:null_if_min 1124.61/291.70 rm :: 0:s:null_min:null_if_min -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 if_rm :: true:false:null_eq:null_le -> 0:s:null_min:null_if_min -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 minsort :: nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 if_minsort :: true:false:null_eq:null_le -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm -> nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 null_min :: 0:s:null_min:null_if_min 1124.61/291.70 null_if_min :: 0:s:null_min:null_if_min 1124.61/291.70 null_if_rm :: nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 null_minsort :: nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 null_if_minsort :: nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 null_eq :: true:false:null_eq:null_le 1124.61/291.70 null_le :: true:false:null_eq:null_le 1124.61/291.70 null_app :: nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 null_rm :: nil:add:null_if_rm:null_minsort:null_if_minsort:null_app:null_rm 1124.61/291.70 1124.61/291.70 Rewrite Strategy: INNERMOST 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (7) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) 1124.61/291.70 Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. 1124.61/291.70 The constant constructors are abstracted as follows: 1124.61/291.70 1124.61/291.70 0 => 0 1124.61/291.70 true => 2 1124.61/291.70 false => 1 1124.61/291.70 nil => 0 1124.61/291.70 null_min => 0 1124.61/291.70 null_if_min => 0 1124.61/291.70 null_if_rm => 0 1124.61/291.70 null_minsort => 0 1124.61/291.70 null_if_minsort => 0 1124.61/291.70 null_eq => 0 1124.61/291.70 null_le => 0 1124.61/291.70 null_app => 0 1124.61/291.70 null_rm => 0 1124.61/291.70 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (8) 1124.61/291.70 Obligation: 1124.61/291.70 Complexity RNTS consisting of the following rules: 1124.61/291.70 1124.61/291.70 app(z, z') -{ 1 }-> y :|: y >= 0, z = 0, z' = y 1124.61/291.70 app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1124.61/291.70 app(z, z') -{ 1 }-> 1 + n + app(x, y) :|: n >= 0, x >= 0, y >= 0, z = 1 + n + x, z' = y 1124.61/291.70 eq(z, z') -{ 1 }-> eq(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x 1124.61/291.70 eq(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 1124.61/291.70 eq(z, z') -{ 1 }-> 1 :|: z' = 1 + x, x >= 0, z = 0 1124.61/291.70 eq(z, z') -{ 1 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 1124.61/291.70 eq(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1124.61/291.70 if_min(z, z') -{ 1 }-> min(1 + m + x) :|: n >= 0, z = 1, x >= 0, z' = 1 + n + (1 + m + x), m >= 0 1124.61/291.70 if_min(z, z') -{ 1 }-> min(1 + n + x) :|: z = 2, n >= 0, x >= 0, z' = 1 + n + (1 + m + x), m >= 0 1124.61/291.70 if_min(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1124.61/291.70 if_minsort(z, z', z'') -{ 1 }-> minsort(x, 1 + n + y) :|: n >= 0, z'' = y, z = 1, z' = 1 + n + x, x >= 0, y >= 0 1124.61/291.70 if_minsort(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 1124.61/291.70 if_minsort(z, z', z'') -{ 1 }-> 1 + n + minsort(app(rm(n, x), y), 0) :|: z = 2, n >= 0, z'' = y, z' = 1 + n + x, x >= 0, y >= 0 1124.61/291.70 if_rm(z, z', z'') -{ 1 }-> rm(n, x) :|: z = 2, n >= 0, z'' = 1 + m + x, x >= 0, z' = n, m >= 0 1124.61/291.70 if_rm(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 1124.61/291.70 if_rm(z, z', z'') -{ 1 }-> 1 + m + rm(n, x) :|: n >= 0, z = 1, z'' = 1 + m + x, x >= 0, z' = n, m >= 0 1124.61/291.70 le(z, z') -{ 1 }-> le(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x 1124.61/291.70 le(z, z') -{ 1 }-> 2 :|: y >= 0, z = 0, z' = y 1124.61/291.70 le(z, z') -{ 1 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 1124.61/291.70 le(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1124.61/291.70 min(z) -{ 1 }-> n :|: z = 1 + n + 0, n >= 0 1124.61/291.70 min(z) -{ 1 }-> if_min(le(n, m), 1 + n + (1 + m + x)) :|: n >= 0, x >= 0, z = 1 + n + (1 + m + x), m >= 0 1124.61/291.70 min(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 1124.61/291.70 minsort(z, z') -{ 1 }-> if_minsort(eq(n, min(1 + n + x)), 1 + n + x, y) :|: n >= 0, x >= 0, y >= 0, z = 1 + n + x, z' = y 1124.61/291.70 minsort(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0 1124.61/291.70 minsort(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1124.61/291.70 rm(z, z') -{ 1 }-> if_rm(eq(n, m), n, 1 + m + x) :|: n >= 0, z' = 1 + m + x, z = n, x >= 0, m >= 0 1124.61/291.70 rm(z, z') -{ 1 }-> 0 :|: n >= 0, z = n, z' = 0 1124.61/291.70 rm(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 1124.61/291.70 1124.61/291.70 Only complete derivations are relevant for the runtime complexity. 1124.61/291.70 1124.61/291.70 ---------------------------------------- 1124.61/291.70 1124.61/291.70 (9) CompleteCoflocoProof (FINISHED) 1124.61/291.70 Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: 1124.61/291.70 1124.61/291.70 eq(start(V1, V, V29),0,[eq(V1, V, Out)],[V1 >= 0,V >= 0]). 1124.61/291.70 eq(start(V1, V, V29),0,[le(V1, V, Out)],[V1 >= 0,V >= 0]). 1124.61/291.70 eq(start(V1, V, V29),0,[app(V1, V, Out)],[V1 >= 0,V >= 0]). 1124.61/291.70 eq(start(V1, V, V29),0,[min(V1, Out)],[V1 >= 0]). 1124.61/291.70 eq(start(V1, V, V29),0,[fun(V1, V, Out)],[V1 >= 0,V >= 0]). 1124.61/291.70 eq(start(V1, V, V29),0,[rm(V1, V, Out)],[V1 >= 0,V >= 0]). 1124.61/291.70 eq(start(V1, V, V29),0,[fun1(V1, V, V29, Out)],[V1 >= 0,V >= 0,V29 >= 0]). 1124.61/291.70 eq(start(V1, V, V29),0,[minsort(V1, V, Out)],[V1 >= 0,V >= 0]). 1124.61/291.70 eq(start(V1, V, V29),0,[fun2(V1, V, V29, Out)],[V1 >= 0,V >= 0,V29 >= 0]). 1124.61/291.70 eq(eq(V1, V, Out),1,[],[Out = 2,V1 = 0,V = 0]). 1124.61/291.70 eq(eq(V1, V, Out),1,[],[Out = 1,V = 1 + V2,V2 >= 0,V1 = 0]). 1124.61/291.70 eq(eq(V1, V, Out),1,[],[Out = 1,V3 >= 0,V1 = 1 + V3,V = 0]). 1124.61/291.70 eq(eq(V1, V, Out),1,[eq(V4, V5, Ret)],[Out = Ret,V = 1 + V5,V4 >= 0,V5 >= 0,V1 = 1 + V4]). 1124.61/291.70 eq(le(V1, V, Out),1,[],[Out = 2,V6 >= 0,V1 = 0,V = V6]). 1124.61/291.70 eq(le(V1, V, Out),1,[],[Out = 1,V7 >= 0,V1 = 1 + V7,V = 0]). 1124.61/291.70 eq(le(V1, V, Out),1,[le(V8, V9, Ret1)],[Out = Ret1,V = 1 + V9,V8 >= 0,V9 >= 0,V1 = 1 + V8]). 1124.61/291.70 eq(app(V1, V, Out),1,[],[Out = V10,V10 >= 0,V1 = 0,V = V10]). 1124.61/291.70 eq(app(V1, V, Out),1,[app(V12, V11, Ret11)],[Out = 1 + Ret11 + V13,V13 >= 0,V12 >= 0,V11 >= 0,V1 = 1 + V12 + V13,V = V11]). 1124.61/291.70 eq(min(V1, Out),1,[],[Out = V14,V1 = 1 + V14,V14 >= 0]). 1124.61/291.70 eq(min(V1, Out),1,[le(V17, V16, Ret0),fun(Ret0, 1 + V17 + (1 + V16 + V15), Ret2)],[Out = Ret2,V17 >= 0,V15 >= 0,V1 = 2 + V15 + V16 + V17,V16 >= 0]). 1124.61/291.70 eq(fun(V1, V, Out),1,[min(1 + V20 + V18, Ret3)],[Out = Ret3,V1 = 2,V20 >= 0,V18 >= 0,V = 2 + V18 + V19 + V20,V19 >= 0]). 1124.61/291.70 eq(fun(V1, V, Out),1,[min(1 + V22 + V21, Ret4)],[Out = Ret4,V23 >= 0,V1 = 1,V21 >= 0,V = 2 + V21 + V22 + V23,V22 >= 0]). 1124.61/291.70 eq(rm(V1, V, Out),1,[],[Out = 0,V24 >= 0,V1 = V24,V = 0]). 1124.61/291.70 eq(rm(V1, V, Out),1,[eq(V26, V27, Ret01),fun1(Ret01, V26, 1 + V27 + V25, Ret5)],[Out = Ret5,V26 >= 0,V = 1 + V25 + V27,V1 = V26,V25 >= 0,V27 >= 0]). 1124.61/291.70 eq(fun1(V1, V, V29, Out),1,[rm(V28, V30, Ret6)],[Out = Ret6,V1 = 2,V28 >= 0,V29 = 1 + V30 + V31,V30 >= 0,V = V28,V31 >= 0]). 1124.61/291.70 eq(fun1(V1, V, V29, Out),1,[rm(V32, V33, Ret12)],[Out = 1 + Ret12 + V34,V32 >= 0,V1 = 1,V29 = 1 + V33 + V34,V33 >= 0,V = V32,V34 >= 0]). 1124.61/291.70 eq(minsort(V1, V, Out),1,[],[Out = 0,V1 = 0,V = 0]). 1124.61/291.70 eq(minsort(V1, V, Out),1,[min(1 + V37 + V36, Ret011),eq(V37, Ret011, Ret02),fun2(Ret02, 1 + V37 + V36, V35, Ret7)],[Out = Ret7,V37 >= 0,V36 >= 0,V35 >= 0,V1 = 1 + V36 + V37,V = V35]). 1124.61/291.70 eq(fun2(V1, V, V29, Out),1,[rm(V38, V39, Ret100),app(Ret100, V40, Ret10),minsort(Ret10, 0, Ret13)],[Out = 1 + Ret13 + V38,V1 = 2,V38 >= 0,V29 = V40,V = 1 + V38 + V39,V39 >= 0,V40 >= 0]). 1124.61/291.70 eq(fun2(V1, V, V29, Out),1,[minsort(V42, 1 + V41 + V43, Ret8)],[Out = Ret8,V41 >= 0,V29 = V43,V1 = 1,V = 1 + V41 + V42,V42 >= 0,V43 >= 0]). 1124.61/291.70 eq(min(V1, Out),0,[],[Out = 0,V44 >= 0,V1 = V44]). 1124.61/291.70 eq(fun(V1, V, Out),0,[],[Out = 0,V46 >= 0,V45 >= 0,V1 = V46,V = V45]). 1124.61/291.70 eq(fun1(V1, V, V29, Out),0,[],[Out = 0,V48 >= 0,V29 = V49,V47 >= 0,V1 = V48,V = V47,V49 >= 0]). 1124.61/291.70 eq(minsort(V1, V, Out),0,[],[Out = 0,V50 >= 0,V51 >= 0,V1 = V50,V = V51]). 1124.61/291.70 eq(fun2(V1, V, V29, Out),0,[],[Out = 0,V52 >= 0,V29 = V53,V54 >= 0,V1 = V52,V = V54,V53 >= 0]). 1124.61/291.70 eq(eq(V1, V, Out),0,[],[Out = 0,V56 >= 0,V55 >= 0,V1 = V56,V = V55]). 1124.61/291.70 eq(le(V1, V, Out),0,[],[Out = 0,V58 >= 0,V57 >= 0,V1 = V58,V = V57]). 1124.61/291.70 eq(app(V1, V, Out),0,[],[Out = 0,V59 >= 0,V60 >= 0,V1 = V59,V = V60]). 1124.61/291.70 eq(rm(V1, V, Out),0,[],[Out = 0,V61 >= 0,V62 >= 0,V1 = V61,V = V62]). 1124.61/291.70 input_output_vars(eq(V1,V,Out),[V1,V],[Out]). 1124.61/291.70 input_output_vars(le(V1,V,Out),[V1,V],[Out]). 1124.61/291.70 input_output_vars(app(V1,V,Out),[V1,V],[Out]). 1124.61/291.70 input_output_vars(min(V1,Out),[V1],[Out]). 1124.61/291.70 input_output_vars(fun(V1,V,Out),[V1,V],[Out]). 1124.61/291.70 input_output_vars(rm(V1,V,Out),[V1,V],[Out]). 1124.61/291.70 input_output_vars(fun1(V1,V,V29,Out),[V1,V,V29],[Out]). 1124.61/291.70 input_output_vars(minsort(V1,V,Out),[V1,V],[Out]). 1124.61/291.70 input_output_vars(fun2(V1,V,V29,Out),[V1,V,V29],[Out]). 1124.61/291.70 1124.61/291.70 1124.61/291.70 CoFloCo proof output: 1124.61/291.70 Preprocessing Cost Relations 1124.61/291.70 ===================================== 1124.61/291.70 1124.61/291.70 #### Computed strongly connected components 1124.61/291.70 0. recursive : [app/3] 1124.61/291.70 1. recursive : [eq/3] 1124.61/291.70 2. recursive : [le/3] 1124.61/291.70 3. recursive : [fun/3,min/2] 1124.61/291.70 4. recursive : [fun1/4,rm/3] 1124.61/291.70 5. recursive : [fun2/4,minsort/3] 1124.61/291.70 6. non_recursive : [start/3] 1124.61/291.70 1124.61/291.70 #### Obtained direct recursion through partial evaluation 1124.61/291.70 0. SCC is partially evaluated into app/3 1124.61/291.70 1. SCC is partially evaluated into eq/3 1124.61/291.70 2. SCC is partially evaluated into le/3 1124.61/291.70 3. SCC is partially evaluated into min/2 1124.61/291.70 4. SCC is partially evaluated into rm/3 1124.61/291.70 5. SCC is partially evaluated into minsort/3 1124.61/291.70 6. SCC is partially evaluated into start/3 1124.61/291.70 1124.61/291.70 Control-Flow Refinement of Cost Relations 1124.61/291.70 ===================================== 1124.61/291.70 1124.61/291.70 ### Specialization of cost equations app/3 1124.61/291.70 * CE 26 is refined into CE [41] 1124.61/291.70 * CE 24 is refined into CE [42] 1124.61/291.70 * CE 25 is refined into CE [43] 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Cost equations --> "Loop" of app/3 1124.61/291.70 * CEs [43] --> Loop 28 1124.61/291.70 * CEs [41] --> Loop 29 1124.61/291.70 * CEs [42] --> Loop 30 1124.61/291.70 1124.61/291.70 ### Ranking functions of CR app(V1,V,Out) 1124.61/291.70 * RF of phase [28]: [V1] 1124.61/291.70 1124.61/291.70 #### Partial ranking functions of CR app(V1,V,Out) 1124.61/291.70 * Partial RF of phase [28]: 1124.61/291.70 - RF of loop [28:1]: 1124.61/291.70 V1 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Specialization of cost equations eq/3 1124.61/291.70 * CE 36 is refined into CE [44] 1124.61/291.70 * CE 34 is refined into CE [45] 1124.61/291.70 * CE 33 is refined into CE [46] 1124.61/291.70 * CE 32 is refined into CE [47] 1124.61/291.70 * CE 35 is refined into CE [48] 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Cost equations --> "Loop" of eq/3 1124.61/291.70 * CEs [48] --> Loop 31 1124.61/291.70 * CEs [44] --> Loop 32 1124.61/291.70 * CEs [45] --> Loop 33 1124.61/291.70 * CEs [46] --> Loop 34 1124.61/291.70 * CEs [47] --> Loop 35 1124.61/291.70 1124.61/291.70 ### Ranking functions of CR eq(V1,V,Out) 1124.61/291.70 * RF of phase [31]: [V,V1] 1124.61/291.70 1124.61/291.70 #### Partial ranking functions of CR eq(V1,V,Out) 1124.61/291.70 * Partial RF of phase [31]: 1124.61/291.70 - RF of loop [31:1]: 1124.61/291.70 V 1124.61/291.70 V1 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Specialization of cost equations le/3 1124.61/291.70 * CE 40 is refined into CE [49] 1124.61/291.70 * CE 38 is refined into CE [50] 1124.61/291.70 * CE 37 is refined into CE [51] 1124.61/291.70 * CE 39 is refined into CE [52] 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Cost equations --> "Loop" of le/3 1124.61/291.70 * CEs [52] --> Loop 36 1124.61/291.70 * CEs [49] --> Loop 37 1124.61/291.70 * CEs [50] --> Loop 38 1124.61/291.70 * CEs [51] --> Loop 39 1124.61/291.70 1124.61/291.70 ### Ranking functions of CR le(V1,V,Out) 1124.61/291.70 * RF of phase [36]: [V,V1] 1124.61/291.70 1124.61/291.70 #### Partial ranking functions of CR le(V1,V,Out) 1124.61/291.70 * Partial RF of phase [36]: 1124.61/291.70 - RF of loop [36:1]: 1124.61/291.70 V 1124.61/291.70 V1 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Specialization of cost equations min/2 1124.61/291.70 * CE 30 is refined into CE [53] 1124.61/291.70 * CE 27 is refined into CE [54,55,56,57,58] 1124.61/291.70 * CE 31 is refined into CE [59] 1124.61/291.70 * CE 28 is refined into CE [60,61] 1124.61/291.70 * CE 29 is refined into CE [62,63] 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Cost equations --> "Loop" of min/2 1124.61/291.70 * CEs [60,61,62,63] --> Loop 40 1124.61/291.70 * CEs [53] --> Loop 41 1124.61/291.70 * CEs [54,55,56,57,58,59] --> Loop 42 1124.61/291.70 1124.61/291.70 ### Ranking functions of CR min(V1,Out) 1124.61/291.70 * RF of phase [40]: [V1-1] 1124.61/291.70 1124.61/291.70 #### Partial ranking functions of CR min(V1,Out) 1124.61/291.70 * Partial RF of phase [40]: 1124.61/291.70 - RF of loop [40:1]: 1124.61/291.70 V1-1 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Specialization of cost equations rm/3 1124.61/291.70 * CE 19 is refined into CE [64,65,66,67,68,69,70] 1124.61/291.70 * CE 22 is refined into CE [71] 1124.61/291.70 * CE 23 is refined into CE [72] 1124.61/291.70 * CE 20 is refined into CE [73,74,75,76] 1124.61/291.70 * CE 21 is refined into CE [77,78] 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Cost equations --> "Loop" of rm/3 1124.61/291.70 * CEs [74,75,76] --> Loop 43 1124.61/291.70 * CEs [78] --> Loop 44 1124.61/291.70 * CEs [73] --> Loop 45 1124.61/291.70 * CEs [77] --> Loop 46 1124.61/291.70 * CEs [71] --> Loop 47 1124.61/291.70 * CEs [64,65,66,67,68,69,70,72] --> Loop 48 1124.61/291.70 1124.61/291.70 ### Ranking functions of CR rm(V1,V,Out) 1124.61/291.70 * RF of phase [43,44]: [V] 1124.61/291.70 * RF of phase [45,46]: [V] 1124.61/291.70 1124.61/291.70 #### Partial ranking functions of CR rm(V1,V,Out) 1124.61/291.70 * Partial RF of phase [43,44]: 1124.61/291.70 - RF of loop [43:1]: 1124.61/291.70 V 1124.61/291.70 - RF of loop [44:1]: 1124.61/291.70 V-1 1124.61/291.70 -V1+V 1124.61/291.70 * Partial RF of phase [45,46]: 1124.61/291.70 - RF of loop [45:1]: 1124.61/291.70 V-1 1124.61/291.70 - RF of loop [46:1]: 1124.61/291.70 V 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Specialization of cost equations minsort/3 1124.61/291.70 * CE 14 is refined into CE [79,80,81,82,83,84,85,86,87,88,89,90,91,92,93] 1124.61/291.70 * CE 17 is refined into CE [94] 1124.61/291.70 * CE 18 is refined into CE [95] 1124.61/291.70 * CE 15 is refined into CE [96,97,98,99,100,101,102] 1124.61/291.70 * CE 16 is refined into CE [103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144] 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Cost equations --> "Loop" of minsort/3 1124.61/291.70 * CEs [96,97,98,99,100,101,102] --> Loop 49 1124.61/291.70 * CEs [111,123,133,143] --> Loop 50 1124.61/291.70 * CEs [112,124,134,144] --> Loop 51 1124.61/291.70 * CEs [105,117,127,137] --> Loop 52 1124.61/291.70 * CEs [106,118,128,138] --> Loop 53 1124.61/291.70 * CEs [103,115,119,125,129,135,139] --> Loop 54 1124.61/291.70 * CEs [104,116,120,126,130,136,140] --> Loop 55 1124.61/291.70 * CEs [107,109,113,121,131,141] --> Loop 56 1124.61/291.70 * CEs [108,110,114,122,132,142] --> Loop 57 1124.61/291.70 * CEs [82] --> Loop 58 1124.61/291.70 * CEs [79,80,81,83,84,85,86,87,88,89,90,91,92,93,94,95] --> Loop 59 1124.61/291.70 1124.61/291.70 ### Ranking functions of CR minsort(V1,V,Out) 1124.61/291.70 1124.61/291.70 #### Partial ranking functions of CR minsort(V1,V,Out) 1124.61/291.70 * Partial RF of phase [49,50,51,52,53,54,56]: 1124.61/291.70 - RF of loop [49:1,53:1]: 1124.61/291.70 V1-1 depends on loops [50:1,52:1,54:1,56:1] 1124.61/291.70 - RF of loop [50:1]: 1124.61/291.70 V1/2+V/2-1 1124.61/291.70 - RF of loop [51:1]: 1124.61/291.70 V1/2-1 depends on loops [50:1,52:1,54:1,56:1] 1124.61/291.70 - RF of loop [52:1,54:1]: 1124.61/291.70 V1+V-1 1124.61/291.70 - RF of loop [56:1]: 1124.61/291.70 V1+V 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Specialization of cost equations start/3 1124.61/291.70 * CE 7 is refined into CE [145,146,147] 1124.61/291.70 * CE 3 is refined into CE [148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164] 1124.61/291.70 * CE 5 is refined into CE [165,166,167] 1124.61/291.70 * CE 6 is refined into CE [168,169,170] 1124.61/291.70 * CE 2 is refined into CE [171,172] 1124.61/291.70 * CE 1 is refined into CE [173] 1124.61/291.70 * CE 4 is refined into CE [174,175,176] 1124.61/291.70 * CE 8 is refined into CE [177,178,179,180,181,182,183] 1124.61/291.70 * CE 9 is refined into CE [184,185,186,187,188] 1124.61/291.70 * CE 10 is refined into CE [189,190,191,192] 1124.61/291.70 * CE 11 is refined into CE [193,194,195] 1124.61/291.70 * CE 12 is refined into CE [196,197,198] 1124.61/291.70 * CE 13 is refined into CE [199,200] 1124.61/291.70 1124.61/291.70 1124.61/291.70 ### Cost equations --> "Loop" of start/3 1124.61/291.70 * CEs [183] --> Loop 60 1124.61/291.70 * CEs [179,185] --> Loop 61 1124.61/291.70 * CEs [145,146,147] --> Loop 62 1124.61/291.70 * CEs [148,150,151,152,153,154,155,157,158,160,161,162,163,164] --> Loop 63 1124.61/291.70 * CEs [149,156,159,165,166,167] --> Loop 64 1124.61/291.70 * CEs [168,169,170] --> Loop 65 1124.61/291.70 * CEs [171,172] --> Loop 66 1124.61/291.70 * CEs [174,175,176] --> Loop 67 1124.61/291.70 * CEs [173,177,178,180,181,182,184,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200] --> Loop 68 1124.61/291.71 1124.61/291.71 ### Ranking functions of CR start(V1,V,V29) 1124.61/291.71 1124.61/291.71 #### Partial ranking functions of CR start(V1,V,V29) 1124.61/291.71 1124.61/291.71 1124.61/291.71 Computing Bounds 1124.61/291.71 ===================================== 1124.61/291.71 1124.61/291.71 #### Cost of chains of app(V1,V,Out): 1124.61/291.71 * Chain [[28],30]: 1*it(28)+1 1124.61/291.71 Such that:it(28) =< -V+Out 1124.61/291.71 1124.61/291.71 with precondition: [V+V1=Out,V1>=1,V>=0] 1124.61/291.71 1124.61/291.71 * Chain [[28],29]: 1*it(28)+0 1124.61/291.71 Such that:it(28) =< Out 1124.61/291.71 1124.61/291.71 with precondition: [V>=0,Out>=1,V1>=Out] 1124.61/291.71 1124.61/291.71 * Chain [30]: 1 1124.61/291.71 with precondition: [V1=0,V=Out,V>=0] 1124.61/291.71 1124.61/291.71 * Chain [29]: 0 1124.61/291.71 with precondition: [Out=0,V1>=0,V>=0] 1124.61/291.71 1124.61/291.71 1124.61/291.71 #### Cost of chains of eq(V1,V,Out): 1124.61/291.71 * Chain [[31],35]: 1*it(31)+1 1124.61/291.71 Such that:it(31) =< V1 1124.61/291.71 1124.61/291.71 with precondition: [Out=2,V1=V,V1>=1] 1124.61/291.71 1124.61/291.71 * Chain [[31],34]: 1*it(31)+1 1124.61/291.71 Such that:it(31) =< V1 1124.61/291.71 1124.61/291.71 with precondition: [Out=1,V1>=1,V>=V1+1] 1124.61/291.71 1124.61/291.71 * Chain [[31],33]: 1*it(31)+1 1124.61/291.71 Such that:it(31) =< V 1124.61/291.71 1124.61/291.71 with precondition: [Out=1,V>=1,V1>=V+1] 1124.61/291.71 1124.61/291.71 * Chain [[31],32]: 1*it(31)+0 1124.61/291.71 Such that:it(31) =< V 1124.61/291.71 1124.61/291.71 with precondition: [Out=0,V1>=1,V>=1] 1124.61/291.71 1124.61/291.71 * Chain [35]: 1 1124.61/291.71 with precondition: [V1=0,V=0,Out=2] 1124.61/291.71 1124.61/291.71 * Chain [34]: 1 1124.61/291.71 with precondition: [V1=0,Out=1,V>=1] 1124.61/291.71 1124.61/291.71 * Chain [33]: 1 1124.61/291.71 with precondition: [V=0,Out=1,V1>=1] 1124.61/291.71 1124.61/291.71 * Chain [32]: 0 1124.61/291.71 with precondition: [Out=0,V1>=0,V>=0] 1124.61/291.71 1124.61/291.71 1124.61/291.71 #### Cost of chains of le(V1,V,Out): 1124.61/291.71 * Chain [[36],39]: 1*it(36)+1 1124.61/291.71 Such that:it(36) =< V1 1124.61/291.71 1124.61/291.71 with precondition: [Out=2,V1>=1,V>=V1] 1124.61/291.71 1124.61/291.71 * Chain [[36],38]: 1*it(36)+1 1124.61/291.71 Such that:it(36) =< V 1124.61/291.71 1124.61/291.71 with precondition: [Out=1,V>=1,V1>=V+1] 1124.61/291.71 1124.61/291.71 * Chain [[36],37]: 1*it(36)+0 1124.61/291.71 Such that:it(36) =< V 1124.61/291.71 1124.61/291.71 with precondition: [Out=0,V1>=1,V>=1] 1124.61/291.71 1124.61/291.71 * Chain [39]: 1 1124.61/291.71 with precondition: [V1=0,Out=2,V>=0] 1124.61/291.71 1124.61/291.71 * Chain [38]: 1 1124.61/291.71 with precondition: [V=0,Out=1,V1>=1] 1124.61/291.71 1124.61/291.71 * Chain [37]: 0 1124.61/291.71 with precondition: [Out=0,V1>=0,V>=0] 1124.61/291.71 1124.61/291.71 1124.61/291.71 #### Cost of chains of min(V1,Out): 1124.61/291.71 * Chain [[40],42]: 6*it(40)+2*s(10)+2 1124.61/291.71 Such that:aux(3) =< V1/2 1124.61/291.71 aux(4) =< V1 1124.61/291.71 it(40) =< aux(4) 1124.61/291.71 s(11) =< it(40)*aux(3) 1124.61/291.71 s(10) =< s(11) 1124.61/291.71 1124.61/291.71 with precondition: [Out=0,V1>=2] 1124.61/291.71 1124.61/291.71 * Chain [[40],41]: 3*it(40)+2*s(10)+1 1124.61/291.71 Such that:it(40) =< V1-Out 1124.61/291.71 aux(3) =< V1/2 1124.61/291.71 s(11) =< it(40)*aux(3) 1124.61/291.71 s(10) =< s(11) 1124.61/291.71 1124.61/291.71 with precondition: [Out>=0,V1>=Out+2] 1124.61/291.71 1124.61/291.71 * Chain [42]: 1*s(3)+2*s(4)+2 1124.61/291.71 Such that:s(3) =< V1 1124.61/291.71 aux(1) =< V1/2 1124.61/291.71 s(4) =< aux(1) 1124.61/291.71 1124.61/291.71 with precondition: [Out=0,V1>=0] 1124.61/291.71 1124.61/291.71 * Chain [41]: 1 1124.61/291.71 with precondition: [V1=Out+1,V1>=1] 1124.61/291.71 1124.61/291.71 1124.61/291.71 #### Cost of chains of rm(V1,V,Out): 1124.61/291.71 * Chain [[45,46],48]: 8*it(45)+2 1124.61/291.71 Such that:aux(11) =< V 1124.61/291.71 it(45) =< aux(11) 1124.61/291.71 1124.61/291.71 with precondition: [V1=0,Out>=0,V>=Out,2*V>=Out+2] 1124.61/291.71 1124.61/291.71 * Chain [[45,46],47]: 6*it(45)+1 1124.61/291.71 Such that:aux(12) =< V 1124.61/291.71 it(45) =< aux(12) 1124.61/291.71 1124.61/291.71 with precondition: [V1=0,Out>=0,V>=Out,2*V>=Out+2] 1124.61/291.71 1124.61/291.71 * Chain [[43,44],48]: 5*it(43)+3*it(44)+2*s(21)+1*s(30)+1*s(31)+1*s(32)+2 1124.61/291.71 Such that:it(44) =< -V1+V 1124.61/291.71 aux(18) =< V1 1124.61/291.71 aux(19) =< V 1124.61/291.71 it(44) =< aux(19) 1124.61/291.71 s(21) =< aux(18) 1124.61/291.71 it(43) =< aux(19) 1124.61/291.71 aux(15) =< aux(18) 1124.61/291.71 s(30) =< it(43)*aux(18) 1124.61/291.71 s(31) =< it(43)*aux(19) 1124.61/291.71 s(32) =< it(44)*aux(15) 1124.61/291.71 1124.61/291.71 with precondition: [V1>=1,Out>=0,V>=Out,Out+V>=2] 1124.61/291.71 1124.61/291.71 * Chain [[43,44],47]: 3*it(43)+3*it(44)+1*s(30)+1*s(31)+1*s(32)+1 1124.61/291.71 Such that:it(44) =< -V1+V 1124.61/291.71 aux(14) =< V1 1124.61/291.71 aux(20) =< V 1124.61/291.71 it(44) =< aux(20) 1124.61/291.71 it(43) =< aux(20) 1124.61/291.71 aux(15) =< aux(14) 1124.61/291.71 s(30) =< it(43)*aux(14) 1124.61/291.71 s(31) =< it(43)*aux(20) 1124.61/291.71 s(32) =< it(44)*aux(15) 1124.61/291.71 1124.61/291.71 with precondition: [V1>=1,Out>=0,V>=Out,Out+V>=2] 1124.61/291.71 1124.61/291.71 * Chain [48]: 2*s(20)+2*s(21)+2 1124.61/291.71 Such that:aux(7) =< V1 1124.61/291.71 aux(8) =< V 1124.61/291.71 s(21) =< aux(7) 1124.61/291.71 s(20) =< aux(8) 1124.61/291.71 1124.61/291.71 with precondition: [Out=0,V1>=0,V>=0] 1124.61/291.71 1124.61/291.71 * Chain [47]: 1 1124.61/291.71 with precondition: [V=0,Out=0,V1>=0] 1124.61/291.71 1124.61/291.71 1124.61/291.71 #### Cost of chains of minsort(V1,V,Out): 1124.61/291.71 * Chain [[49,50,51,52,53,54,56],59]: 5*it(49)+8*it(50)+14*it(51)+260*it(52)+20*s(63)+22*s(493)+2*s(494)+10*s(495)+79*s(503)+2*s(504)+6*s(505)+16*s(506)+8*s(507)+4*s(508)+150*s(513)+4*s(514)+12*s(515)+16*s(516)+8*s(517)+4*s(518)+71*s(523)+2*s(524)+6*s(525)+4*s(526)+4*s(534)+2*s(540)+18*s(541)+4*s(546)+16*s(548)+8*s(549)+4 1124.61/291.71 Such that:it(50) =< V1/2+V/2 1124.61/291.71 aux(178) =< V1 1124.61/291.71 aux(179) =< V1+V 1124.61/291.71 it(52) =< aux(179) 1124.61/291.71 s(62) =< it(52)*aux(179) 1124.61/291.71 s(63) =< s(62) 1124.61/291.71 it(51) =< aux(179) 1124.61/291.71 it(50) =< aux(179) 1124.61/291.71 s(551) =< aux(179) 1124.61/291.71 aux(140) =< aux(179)+1 1124.61/291.71 aux(92) =< aux(179) 1124.61/291.71 aux(135) =< aux(179)-1 1124.61/291.71 aux(97) =< aux(179)-2 1124.61/291.71 s(138) =< aux(179)*(1/2) 1124.61/291.71 s(551) =< aux(179)*(1/2) 1124.61/291.71 s(543) =< aux(179)*(1/2) 1124.61/291.71 aux(82) =< it(50)*aux(179) 1124.61/291.71 aux(83) =< it(52)*aux(140) 1124.61/291.71 aux(84) =< it(52)*aux(92) 1124.61/291.71 s(530) =< it(52)*aux(135) 1124.61/291.71 s(512) =< it(50)*aux(97) 1124.61/291.71 aux(96) =< it(50)*aux(92) 1124.61/291.71 s(528) =< aux(84)*(1/2) 1124.61/291.71 s(510) =< aux(96)*(1/2) 1124.61/291.71 it(49) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(178) 1124.61/291.71 it(51) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(178) 1124.61/291.71 s(538) =< it(51)*aux(135) 1124.61/291.71 aux(131) =< it(51)*aux(92) 1124.61/291.71 s(522) =< it(51)*aux(97) 1124.61/291.71 aux(94) =< it(49)*aux(92) 1124.61/291.71 s(520) =< aux(131)*(1/2) 1124.61/291.71 s(499) =< aux(94)*(1/2) 1124.61/291.71 s(284) =< aux(92) 1124.61/291.71 s(548) =< it(52)*aux(92) 1124.61/291.71 s(549) =< it(52)*s(284) 1124.61/291.71 s(546) =< s(551) 1124.61/291.71 s(542) =< it(52)*s(138) 1124.61/291.71 s(541) =< s(542) 1124.61/291.71 s(540) =< s(543) 1124.61/291.71 s(534) =< s(538) 1124.61/291.71 s(513) =< aux(131) 1124.61/291.71 s(514) =< s(520) 1124.61/291.71 s(519) =< s(513)*s(138) 1124.61/291.71 s(515) =< s(519) 1124.61/291.71 s(526) =< s(530) 1124.61/291.71 s(523) =< aux(84) 1124.61/291.71 s(524) =< s(528) 1124.61/291.71 s(527) =< s(523)*s(138) 1124.61/291.71 s(525) =< s(527) 1124.61/291.71 s(518) =< s(522) 1124.61/291.71 s(516) =< s(513)*aux(92) 1124.61/291.71 s(517) =< s(513)*s(284) 1124.61/291.71 s(508) =< s(512) 1124.61/291.71 s(503) =< aux(96) 1124.61/291.71 s(506) =< s(503)*aux(179) 1124.61/291.71 s(507) =< s(503)*aux(92) 1124.61/291.71 s(504) =< s(510) 1124.61/291.71 s(509) =< s(503)*s(138) 1124.61/291.71 s(505) =< s(509) 1124.61/291.71 s(493) =< aux(94) 1124.61/291.71 s(498) =< s(493)*s(138) 1124.61/291.71 s(495) =< s(498) 1124.61/291.71 s(494) =< s(499) 1124.61/291.71 1124.61/291.71 with precondition: [V1>=1,V>=0,Out>=0,Out+V1>=2,V+V1>=Out] 1124.61/291.71 1124.61/291.71 * Chain [[49,50,51,52,53,54,56],58]: 5*it(49)+8*it(50)+7*it(51)+197*it(52)+7*it(53)+8*it(54)+22*s(493)+2*s(494)+10*s(495)+79*s(503)+2*s(504)+6*s(505)+16*s(506)+8*s(507)+4*s(508)+79*s(513)+2*s(514)+6*s(515)+16*s(516)+8*s(517)+4*s(518)+71*s(523)+2*s(524)+6*s(525)+4*s(526)+71*s(531)+2*s(532)+6*s(533)+4*s(534)+2*s(540)+18*s(541)+4*s(546)+16*s(548)+8*s(549)+3 1124.61/291.71 Such that:aux(180) =< V1 1124.61/291.71 aux(181) =< V1+V 1124.61/291.71 aux(182) =< V1/2+V/2 1124.61/291.71 it(50) =< aux(182) 1124.61/291.71 it(52) =< aux(181) 1124.61/291.71 it(53) =< aux(181) 1124.61/291.71 it(54) =< aux(181) 1124.61/291.71 it(51) =< aux(182) 1124.61/291.71 it(54) =< aux(182) 1124.61/291.71 s(551) =< aux(182) 1124.61/291.71 aux(140) =< aux(181)+1 1124.61/291.71 aux(92) =< aux(181) 1124.61/291.71 aux(135) =< aux(181)-1 1124.61/291.71 aux(97) =< aux(181)-2 1124.61/291.71 s(138) =< aux(181)*(1/2) 1124.61/291.71 s(551) =< aux(181)*(1/2) 1124.61/291.71 s(543) =< aux(181)*(1/2) 1124.61/291.71 aux(82) =< it(50)*aux(181) 1124.61/291.71 aux(83) =< it(52)*aux(140) 1124.61/291.71 aux(84) =< it(54)*aux(92) 1124.61/291.71 s(530) =< it(52)*aux(135) 1124.61/291.71 aux(134) =< it(52)*aux(92) 1124.61/291.71 s(512) =< it(50)*aux(97) 1124.61/291.71 aux(96) =< it(50)*aux(92) 1124.61/291.71 s(528) =< aux(134)*(1/2) 1124.61/291.71 s(510) =< aux(96)*(1/2) 1124.61/291.71 it(49) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(180) 1124.61/291.71 it(51) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(180) 1124.61/291.71 it(53) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(180) 1124.61/291.71 s(538) =< it(53)*aux(135) 1124.61/291.71 aux(151) =< it(53)*aux(92) 1124.61/291.71 s(522) =< it(51)*aux(97) 1124.61/291.71 aux(131) =< it(51)*aux(92) 1124.61/291.71 aux(94) =< it(49)*aux(92) 1124.61/291.71 s(536) =< aux(151)*(1/2) 1124.61/291.71 s(520) =< aux(131)*(1/2) 1124.61/291.71 s(499) =< aux(94)*(1/2) 1124.61/291.71 s(284) =< aux(92) 1124.61/291.71 s(548) =< it(52)*aux(92) 1124.61/291.71 s(549) =< it(52)*s(284) 1124.61/291.71 s(546) =< s(551) 1124.61/291.71 s(542) =< it(52)*s(138) 1124.61/291.71 s(541) =< s(542) 1124.61/291.71 s(540) =< s(543) 1124.61/291.71 s(534) =< s(538) 1124.61/291.71 s(531) =< aux(151) 1124.61/291.71 s(532) =< s(536) 1124.61/291.71 s(535) =< s(531)*s(138) 1124.61/291.71 s(533) =< s(535) 1124.61/291.71 s(526) =< s(530) 1124.61/291.71 s(523) =< aux(134) 1124.61/291.71 s(524) =< s(528) 1124.61/291.71 s(527) =< s(523)*s(138) 1124.61/291.71 s(525) =< s(527) 1124.61/291.71 s(518) =< s(522) 1124.61/291.71 s(513) =< aux(131) 1124.61/291.71 s(516) =< s(513)*aux(92) 1124.61/291.71 s(517) =< s(513)*s(284) 1124.61/291.71 s(514) =< s(520) 1124.61/291.71 s(519) =< s(513)*s(138) 1124.61/291.71 s(515) =< s(519) 1124.61/291.71 s(508) =< s(512) 1124.61/291.71 s(503) =< aux(96) 1124.61/291.71 s(506) =< s(503)*aux(181) 1124.61/291.71 s(507) =< s(503)*aux(92) 1124.61/291.71 s(504) =< s(510) 1124.61/291.71 s(509) =< s(503)*s(138) 1124.61/291.71 s(505) =< s(509) 1124.61/291.71 s(493) =< aux(94) 1124.61/291.71 s(498) =< s(493)*s(138) 1124.61/291.71 s(495) =< s(498) 1124.61/291.71 s(494) =< s(499) 1124.61/291.71 1124.61/291.71 with precondition: [V1>=1,V>=0,Out>=0,V+V1>=2,Out+V1>=2,V+V1>=Out+1] 1124.61/291.71 1124.61/291.71 * Chain [[49,50,51,52,53,54,56],57,59]: 5*it(49)+12*it(50)+7*it(51)+287*it(52)+7*it(53)+8*it(54)+22*s(493)+2*s(494)+10*s(495)+79*s(503)+2*s(504)+6*s(505)+16*s(506)+8*s(507)+4*s(508)+79*s(513)+2*s(514)+6*s(515)+16*s(516)+8*s(517)+4*s(518)+71*s(523)+2*s(524)+6*s(525)+4*s(526)+71*s(531)+2*s(532)+6*s(533)+4*s(534)+2*s(540)+18*s(541)+4*s(546)+16*s(548)+8*s(549)+8*s(558)+16*s(575)+8*s(577)+11 1124.61/291.71 Such that:aux(192) =< V1 1124.61/291.71 aux(193) =< V1+V 1124.61/291.71 aux(194) =< V1/2+V/2 1124.61/291.71 it(50) =< aux(194) 1124.61/291.71 it(52) =< aux(193) 1124.61/291.71 s(574) =< aux(193) 1124.61/291.71 s(575) =< it(52)*aux(193) 1124.61/291.71 s(577) =< it(52)*s(574) 1124.61/291.71 s(557) =< it(52)*aux(194) 1124.61/291.71 s(558) =< s(557) 1124.61/291.71 it(53) =< aux(193) 1124.61/291.71 it(54) =< aux(193) 1124.61/291.71 it(51) =< aux(194) 1124.61/291.71 it(54) =< aux(194) 1124.61/291.71 s(551) =< aux(194) 1124.61/291.71 aux(140) =< aux(193)+1 1124.61/291.71 aux(92) =< aux(193) 1124.61/291.71 aux(135) =< aux(193)-1 1124.61/291.71 aux(97) =< aux(193)-2 1124.61/291.71 s(138) =< aux(193)*(1/2) 1124.61/291.71 s(551) =< aux(193)*(1/2) 1124.61/291.71 s(543) =< aux(193)*(1/2) 1124.61/291.71 aux(82) =< it(50)*aux(193) 1124.61/291.71 aux(83) =< it(52)*aux(140) 1124.61/291.71 aux(84) =< it(54)*aux(92) 1124.61/291.71 s(530) =< it(52)*aux(135) 1124.61/291.71 aux(134) =< it(52)*aux(92) 1124.61/291.71 s(512) =< it(50)*aux(97) 1124.61/291.71 aux(96) =< it(50)*aux(92) 1124.61/291.71 s(528) =< aux(134)*(1/2) 1124.61/291.71 s(510) =< aux(96)*(1/2) 1124.61/291.71 it(49) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(192) 1124.61/291.71 it(51) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(192) 1124.61/291.71 it(53) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(192) 1124.61/291.71 s(538) =< it(53)*aux(135) 1124.61/291.71 aux(151) =< it(53)*aux(92) 1124.61/291.71 s(522) =< it(51)*aux(97) 1124.61/291.71 aux(131) =< it(51)*aux(92) 1124.61/291.71 aux(94) =< it(49)*aux(92) 1124.61/291.71 s(536) =< aux(151)*(1/2) 1124.61/291.71 s(520) =< aux(131)*(1/2) 1124.61/291.71 s(499) =< aux(94)*(1/2) 1124.61/291.71 s(284) =< aux(92) 1124.61/291.71 s(548) =< it(52)*aux(92) 1124.61/291.71 s(549) =< it(52)*s(284) 1124.61/291.71 s(546) =< s(551) 1124.61/291.71 s(542) =< it(52)*s(138) 1124.61/291.71 s(541) =< s(542) 1124.61/291.71 s(540) =< s(543) 1124.61/291.71 s(534) =< s(538) 1124.61/291.71 s(531) =< aux(151) 1124.61/291.71 s(532) =< s(536) 1124.61/291.71 s(535) =< s(531)*s(138) 1124.61/291.71 s(533) =< s(535) 1124.61/291.71 s(526) =< s(530) 1124.61/291.71 s(523) =< aux(134) 1124.61/291.71 s(524) =< s(528) 1124.61/291.71 s(527) =< s(523)*s(138) 1124.61/291.71 s(525) =< s(527) 1124.61/291.71 s(518) =< s(522) 1124.61/291.71 s(513) =< aux(131) 1124.61/291.71 s(516) =< s(513)*aux(92) 1124.61/291.71 s(517) =< s(513)*s(284) 1124.61/291.71 s(514) =< s(520) 1124.61/291.71 s(519) =< s(513)*s(138) 1124.61/291.71 s(515) =< s(519) 1124.61/291.71 s(508) =< s(512) 1124.61/291.71 s(503) =< aux(96) 1124.61/291.71 s(506) =< s(503)*aux(193) 1124.61/291.71 s(507) =< s(503)*aux(92) 1124.61/291.71 s(504) =< s(510) 1124.61/291.71 s(509) =< s(503)*s(138) 1124.61/291.71 s(505) =< s(509) 1124.61/291.71 s(493) =< aux(94) 1124.61/291.71 s(498) =< s(493)*s(138) 1124.61/291.71 s(495) =< s(498) 1124.61/291.71 s(494) =< s(499) 1124.61/291.71 1124.61/291.71 with precondition: [V1>=1,V>=0,Out>=1,V+V1>=2,Out+V1>=3,V+V1>=Out] 1124.61/291.71 1124.61/291.71 * Chain [[49,50,51,52,53,54,56],55,59]: 5*it(49)+10*it(50)+7*it(51)+288*it(52)+7*it(53)+8*it(54)+22*s(493)+2*s(494)+10*s(495)+79*s(503)+2*s(504)+6*s(505)+16*s(506)+8*s(507)+4*s(508)+79*s(513)+2*s(514)+6*s(515)+16*s(516)+8*s(517)+4*s(518)+71*s(523)+2*s(524)+6*s(525)+4*s(526)+71*s(531)+2*s(532)+6*s(533)+4*s(534)+2*s(540)+18*s(541)+4*s(546)+16*s(548)+8*s(549)+10*s(628)+11 1124.61/291.71 Such that:aux(205) =< V1 1124.61/291.71 aux(206) =< V1+V 1124.61/291.71 aux(207) =< V1/2+V/2 1124.61/291.71 it(50) =< aux(207) 1124.61/291.71 it(52) =< aux(206) 1124.61/291.71 s(627) =< it(52)*aux(207) 1124.61/291.71 s(628) =< s(627) 1124.61/291.71 it(53) =< aux(206) 1124.61/291.71 it(54) =< aux(206) 1124.61/291.71 it(51) =< aux(207) 1124.61/291.71 it(54) =< aux(207) 1124.61/291.71 s(551) =< aux(207) 1124.61/291.71 aux(140) =< aux(206)+1 1124.61/291.71 aux(92) =< aux(206) 1124.61/291.71 aux(135) =< aux(206)-1 1124.61/291.71 aux(97) =< aux(206)-2 1124.61/291.71 s(138) =< aux(206)*(1/2) 1124.61/291.71 s(551) =< aux(206)*(1/2) 1124.61/291.71 s(543) =< aux(206)*(1/2) 1124.61/291.71 aux(82) =< it(50)*aux(206) 1124.61/291.71 aux(83) =< it(52)*aux(140) 1124.61/291.71 aux(84) =< it(54)*aux(92) 1124.61/291.71 s(530) =< it(52)*aux(135) 1124.61/291.71 aux(134) =< it(52)*aux(92) 1124.61/291.71 s(512) =< it(50)*aux(97) 1124.61/291.71 aux(96) =< it(50)*aux(92) 1124.61/291.71 s(528) =< aux(134)*(1/2) 1124.61/291.71 s(510) =< aux(96)*(1/2) 1124.61/291.71 it(49) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(205) 1124.61/291.71 it(51) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(205) 1124.61/291.71 it(53) =< aux(83)+aux(84)+aux(83)+aux(82)+aux(205) 1124.61/291.71 s(538) =< it(53)*aux(135) 1124.61/291.71 aux(151) =< it(53)*aux(92) 1124.61/291.71 s(522) =< it(51)*aux(97) 1124.61/291.71 aux(131) =< it(51)*aux(92) 1124.61/291.71 aux(94) =< it(49)*aux(92) 1124.61/291.71 s(536) =< aux(151)*(1/2) 1124.61/291.71 s(520) =< aux(131)*(1/2) 1124.61/291.71 s(499) =< aux(94)*(1/2) 1124.61/291.71 s(284) =< aux(92) 1124.61/291.71 s(548) =< it(52)*aux(92) 1124.61/291.71 s(549) =< it(52)*s(284) 1124.61/291.71 s(546) =< s(551) 1124.61/291.71 s(542) =< it(52)*s(138) 1124.61/291.71 s(541) =< s(542) 1124.61/291.71 s(540) =< s(543) 1124.61/291.71 s(534) =< s(538) 1124.61/291.71 s(531) =< aux(151) 1124.61/291.71 s(532) =< s(536) 1124.61/291.71 s(535) =< s(531)*s(138) 1124.61/291.71 s(533) =< s(535) 1124.61/291.71 s(526) =< s(530) 1124.61/291.71 s(523) =< aux(134) 1124.61/291.71 s(524) =< s(528) 1124.61/291.71 s(527) =< s(523)*s(138) 1124.61/291.71 s(525) =< s(527) 1124.61/291.71 s(518) =< s(522) 1124.61/291.71 s(513) =< aux(131) 1124.61/291.71 s(516) =< s(513)*aux(92) 1124.61/291.71 s(517) =< s(513)*s(284) 1124.61/291.71 s(514) =< s(520) 1124.61/291.71 s(519) =< s(513)*s(138) 1124.61/291.71 s(515) =< s(519) 1124.61/291.71 s(508) =< s(512) 1124.61/291.71 s(503) =< aux(96) 1124.61/291.71 s(506) =< s(503)*aux(206) 1124.61/291.71 s(507) =< s(503)*aux(92) 1124.61/291.71 s(504) =< s(510) 1124.61/291.71 s(509) =< s(503)*s(138) 1124.61/291.71 s(505) =< s(509) 1124.61/291.71 s(493) =< aux(94) 1124.61/291.71 s(498) =< s(493)*s(138) 1124.61/291.71 s(495) =< s(498) 1124.61/291.71 s(494) =< s(499) 1124.61/291.71 1124.61/291.71 with precondition: [V1>=1,V>=0,Out>=1,V+V1>=3,V1+2*Out>=5,V+V1>=Out] 1124.61/291.71 1124.61/291.71 * Chain [59]: 49*s(60)+6*s(61)+20*s(63)+4 1124.61/291.71 Such that:aux(29) =< V1 1124.61/291.71 aux(30) =< V1/2 1124.61/291.71 s(60) =< aux(29) 1124.61/291.71 s(61) =< aux(30) 1124.61/291.71 s(62) =< s(60)*aux(30) 1124.61/291.71 s(63) =< s(62) 1124.61/291.71 1124.61/291.71 with precondition: [Out=0,V1>=0,V>=0] 1124.61/291.71 1124.61/291.71 * Chain [58]: 3 1124.61/291.71 with precondition: [V1=1,Out=0,V>=0] 1124.61/291.71 1124.61/291.71 * Chain [57,59]: 90*s(555)+4*s(556)+8*s(558)+16*s(575)+8*s(577)+11 1124.61/291.71 Such that:aux(189) =< V1 1124.61/291.71 aux(190) =< V1/2 1124.61/291.71 s(555) =< aux(189) 1124.61/291.71 s(574) =< aux(189) 1124.61/291.71 s(575) =< s(555)*aux(189) 1124.61/291.71 s(577) =< s(555)*s(574) 1124.61/291.71 s(556) =< aux(190) 1124.61/291.71 s(557) =< s(555)*aux(190) 1124.61/291.71 s(558) =< s(557) 1124.61/291.71 1124.61/291.71 with precondition: [V>=0,Out>=1,V1>=Out] 1124.61/291.71 1124.61/291.71 * Chain [55,59]: 91*s(625)+2*s(626)+10*s(628)+11 1124.61/291.71 Such that:aux(202) =< V1 1124.61/291.71 aux(203) =< V1/2 1124.61/291.71 s(625) =< aux(202) 1124.61/291.71 s(626) =< aux(203) 1124.61/291.71 s(627) =< s(625)*aux(203) 1124.61/291.71 s(628) =< s(627) 1124.61/291.71 1124.61/291.71 with precondition: [V1>=2,V>=0,Out>=1,V1>=Out] 1124.61/291.71 1124.61/291.71 1124.61/291.71 #### Cost of chains of start(V1,V,V29): 1124.61/291.71 * Chain [68]: 28*s(961)+248*s(962)+14*s(972)+42*s(974)+6*s(988)+2*s(991)+2*s(992)+2*s(993)+32*s(1005)+16*s(1011)+8*s(1012)+30*s(1013)+1032*s(1014)+18*s(1016)+21*s(1017)+21*s(1018)+15*s(1035)+72*s(1045)+32*s(1046)+12*s(1047)+72*s(1049)+8*s(1050)+12*s(1051)+213*s(1052)+6*s(1053)+18*s(1055)+16*s(1056)+284*s(1057)+8*s(1058)+24*s(1060)+12*s(1061)+237*s(1062)+48*s(1063)+24*s(1064)+6*s(1065)+18*s(1067)+12*s(1068)+237*s(1069)+48*s(1070)+24*s(1071)+6*s(1072)+18*s(1074)+66*s(1075)+30*s(1077)+6*s(1078)+16*s(1079)+20*s(1125)+14*s(1126)+5*s(1131)+4*s(1138)+4*s(1139)+150*s(1140)+4*s(1141)+12*s(1143)+4*s(1144)+16*s(1145)+8*s(1146)+4*s(1147)+79*s(1148)+16*s(1149)+8*s(1150)+2*s(1151)+6*s(1153)+22*s(1154)+10*s(1156)+2*s(1157)+11 1124.61/291.71 Such that:s(985) =< -V1+V 1124.61/291.71 s(1002) =< V1+V 1124.61/291.71 s(1004) =< V1/2+V/2 1124.61/291.71 aux(212) =< V1 1124.61/291.71 aux(213) =< V1/2 1124.61/291.71 aux(214) =< V 1124.61/291.71 s(962) =< aux(212) 1124.61/291.71 s(961) =< aux(214) 1124.61/291.71 s(988) =< s(985) 1124.61/291.71 s(988) =< aux(214) 1124.61/291.71 s(990) =< aux(212) 1124.61/291.71 s(991) =< s(961)*aux(212) 1124.61/291.71 s(992) =< s(961)*aux(214) 1124.61/291.71 s(993) =< s(988)*s(990) 1124.61/291.71 s(972) =< aux(213) 1124.61/291.71 s(973) =< s(962)*aux(213) 1124.61/291.71 s(974) =< s(973) 1124.61/291.71 s(1005) =< s(1004) 1124.61/291.71 s(1011) =< s(962)*aux(212) 1124.61/291.71 s(1012) =< s(962)*s(990) 1124.61/291.71 s(1013) =< s(1004) 1124.61/291.71 s(1014) =< s(1002) 1124.61/291.71 s(1015) =< s(1014)*s(1004) 1124.61/291.71 s(1016) =< s(1015) 1124.61/291.71 s(1017) =< s(1002) 1124.61/291.71 s(1005) =< s(1002) 1124.61/291.71 s(1018) =< s(1004) 1124.61/291.71 s(1019) =< s(1004) 1124.61/291.71 s(1020) =< s(1002)+1 1124.61/291.71 s(1021) =< s(1002) 1124.61/291.71 s(1022) =< s(1002)-1 1124.61/291.71 s(1023) =< s(1002)-2 1124.61/291.71 s(1024) =< s(1002)*(1/2) 1124.61/291.71 s(1019) =< s(1002)*(1/2) 1124.61/291.71 s(1025) =< s(1002)*(1/2) 1124.61/291.71 s(1026) =< s(1013)*s(1002) 1124.61/291.71 s(1027) =< s(1014)*s(1020) 1124.61/291.71 s(1028) =< s(1005)*s(1021) 1124.61/291.71 s(1029) =< s(1014)*s(1022) 1124.61/291.71 s(1030) =< s(1014)*s(1021) 1124.61/291.71 s(1031) =< s(1013)*s(1023) 1124.61/291.71 s(1032) =< s(1013)*s(1021) 1124.61/291.71 s(1033) =< s(1030)*(1/2) 1124.61/291.71 s(1034) =< s(1032)*(1/2) 1124.61/291.71 s(1035) =< s(1027)+s(1028)+s(1027)+s(1026)+aux(212) 1124.61/291.71 s(1018) =< s(1027)+s(1028)+s(1027)+s(1026)+aux(212) 1124.61/291.71 s(1017) =< s(1027)+s(1028)+s(1027)+s(1026)+aux(212) 1124.61/291.71 s(1036) =< s(1017)*s(1022) 1124.61/291.71 s(1037) =< s(1017)*s(1021) 1124.61/291.71 s(1038) =< s(1018)*s(1023) 1124.61/291.71 s(1039) =< s(1018)*s(1021) 1124.61/291.71 s(1040) =< s(1035)*s(1021) 1124.61/291.71 s(1041) =< s(1037)*(1/2) 1124.61/291.71 s(1042) =< s(1039)*(1/2) 1124.61/291.71 s(1043) =< s(1040)*(1/2) 1124.61/291.71 s(1044) =< s(1021) 1124.61/291.71 s(1045) =< s(1014)*s(1021) 1124.61/291.71 s(1046) =< s(1014)*s(1044) 1124.61/291.71 s(1047) =< s(1019) 1124.61/291.71 s(1048) =< s(1014)*s(1024) 1124.61/291.71 s(1049) =< s(1048) 1124.61/291.71 s(1050) =< s(1025) 1124.61/291.71 s(1051) =< s(1036) 1124.61/291.71 s(1052) =< s(1037) 1124.61/291.71 s(1053) =< s(1041) 1124.61/291.71 s(1054) =< s(1052)*s(1024) 1124.61/291.71 s(1055) =< s(1054) 1124.61/291.71 s(1056) =< s(1029) 1124.61/291.71 s(1057) =< s(1030) 1124.61/291.71 s(1058) =< s(1033) 1124.61/291.71 s(1059) =< s(1057)*s(1024) 1124.61/291.71 s(1060) =< s(1059) 1124.61/291.71 s(1061) =< s(1038) 1124.61/291.71 s(1062) =< s(1039) 1124.61/291.71 s(1063) =< s(1062)*s(1021) 1124.61/291.71 s(1064) =< s(1062)*s(1044) 1124.61/291.71 s(1065) =< s(1042) 1124.61/291.71 s(1066) =< s(1062)*s(1024) 1124.61/291.71 s(1067) =< s(1066) 1124.61/291.71 s(1068) =< s(1031) 1124.61/291.71 s(1069) =< s(1032) 1124.61/291.71 s(1070) =< s(1069)*s(1002) 1124.61/291.71 s(1071) =< s(1069)*s(1021) 1124.61/291.71 s(1072) =< s(1034) 1124.61/291.71 s(1073) =< s(1069)*s(1024) 1124.61/291.71 s(1074) =< s(1073) 1124.61/291.71 s(1075) =< s(1040) 1124.61/291.71 s(1076) =< s(1075)*s(1024) 1124.61/291.71 s(1077) =< s(1076) 1124.61/291.71 s(1078) =< s(1043) 1124.61/291.71 s(1079) =< s(1014)*s(1002) 1124.61/291.71 s(1124) =< s(1014)*s(1002) 1124.61/291.71 s(1125) =< s(1124) 1124.61/291.71 s(1126) =< s(1002) 1124.61/291.71 s(1127) =< s(1002) 1124.61/291.71 s(1127) =< s(1002)*(1/2) 1124.61/291.71 s(1128) =< s(1005)*s(1002) 1124.61/291.71 s(1129) =< s(1005)*s(1023) 1124.61/291.71 s(1130) =< s(1028)*(1/2) 1124.61/291.71 s(1131) =< s(1027)+s(1030)+s(1027)+s(1128)+aux(212) 1124.61/291.71 s(1126) =< s(1027)+s(1030)+s(1027)+s(1128)+aux(212) 1124.61/291.71 s(1132) =< s(1126)*s(1022) 1124.61/291.71 s(1133) =< s(1126)*s(1021) 1124.61/291.71 s(1134) =< s(1126)*s(1023) 1124.61/291.71 s(1135) =< s(1131)*s(1021) 1124.61/291.71 s(1136) =< s(1133)*(1/2) 1124.61/291.71 s(1137) =< s(1135)*(1/2) 1124.61/291.71 s(1138) =< s(1127) 1124.61/291.71 s(1139) =< s(1132) 1124.61/291.71 s(1140) =< s(1133) 1124.61/291.71 s(1141) =< s(1136) 1124.61/291.71 s(1142) =< s(1140)*s(1024) 1124.61/291.71 s(1143) =< s(1142) 1124.61/291.71 s(1144) =< s(1134) 1124.61/291.71 s(1145) =< s(1140)*s(1021) 1124.61/291.71 s(1146) =< s(1140)*s(1044) 1124.61/291.71 s(1147) =< s(1129) 1124.61/291.71 s(1148) =< s(1028) 1124.61/291.71 s(1149) =< s(1148)*s(1002) 1124.61/291.71 s(1150) =< s(1148)*s(1021) 1124.61/291.71 s(1151) =< s(1130) 1124.61/291.71 s(1152) =< s(1148)*s(1024) 1124.61/291.71 s(1153) =< s(1152) 1124.61/291.71 s(1154) =< s(1135) 1124.61/291.71 s(1155) =< s(1154)*s(1024) 1124.61/291.71 s(1156) =< s(1155) 1124.61/291.71 s(1157) =< s(1137) 1124.61/291.71 1124.61/291.71 with precondition: [V1>=0] 1124.61/291.71 1124.61/291.71 * Chain [67]: 24*s(1159)+4*s(1162)+6*s(1167)+2*s(1170)+2*s(1171)+2*s(1172)+3 1124.61/291.71 Such that:s(1164) =< -V+V29 1124.61/291.71 aux(215) =< V 1124.61/291.71 aux(216) =< V29 1124.61/291.71 s(1167) =< s(1164) 1124.61/291.71 s(1167) =< aux(216) 1124.61/291.71 s(1159) =< aux(216) 1124.61/291.71 s(1169) =< aux(215) 1124.61/291.71 s(1170) =< s(1159)*aux(215) 1124.61/291.71 s(1171) =< s(1159)*aux(216) 1124.61/291.71 s(1172) =< s(1167)*s(1169) 1124.61/291.71 s(1162) =< aux(215) 1124.61/291.71 1124.61/291.71 with precondition: [V1=1,V>=0,V29>=1] 1124.61/291.71 1124.61/291.71 * Chain [66]: 230*s(1176)+12*s(1177)+38*s(1179)+32*s(1184)+16*s(1190)+8*s(1191)+30*s(1192)+1032*s(1193)+18*s(1195)+21*s(1196)+21*s(1197)+15*s(1214)+72*s(1224)+32*s(1225)+12*s(1226)+72*s(1228)+8*s(1229)+12*s(1230)+213*s(1231)+6*s(1232)+18*s(1234)+16*s(1235)+284*s(1236)+8*s(1237)+24*s(1239)+12*s(1240)+237*s(1241)+48*s(1242)+24*s(1243)+6*s(1244)+18*s(1246)+12*s(1247)+237*s(1248)+48*s(1249)+24*s(1250)+6*s(1251)+18*s(1253)+66*s(1254)+30*s(1256)+6*s(1257)+16*s(1258)+20*s(1304)+14*s(1305)+5*s(1310)+4*s(1317)+4*s(1318)+150*s(1319)+4*s(1320)+12*s(1322)+4*s(1323)+16*s(1324)+8*s(1325)+4*s(1326)+79*s(1327)+16*s(1328)+8*s(1329)+2*s(1330)+6*s(1332)+22*s(1333)+10*s(1335)+2*s(1336)+12 1124.61/291.71 Such that:s(1181) =< V+V29 1124.61/291.71 s(1183) =< V/2+V29/2 1124.61/291.71 aux(217) =< V 1124.61/291.71 aux(218) =< V/2 1124.61/291.71 s(1176) =< aux(217) 1124.61/291.71 s(1177) =< aux(218) 1124.61/291.71 s(1178) =< s(1176)*aux(218) 1124.61/291.71 s(1179) =< s(1178) 1124.61/291.71 s(1184) =< s(1183) 1124.61/291.71 s(1189) =< aux(217) 1124.61/291.71 s(1190) =< s(1176)*aux(217) 1124.61/291.71 s(1191) =< s(1176)*s(1189) 1124.61/291.71 s(1192) =< s(1183) 1124.61/291.71 s(1193) =< s(1181) 1124.61/291.71 s(1194) =< s(1193)*s(1183) 1124.61/291.71 s(1195) =< s(1194) 1124.61/291.71 s(1196) =< s(1181) 1124.61/291.71 s(1184) =< s(1181) 1124.61/291.71 s(1197) =< s(1183) 1124.61/291.71 s(1198) =< s(1183) 1124.61/291.71 s(1199) =< s(1181)+1 1124.61/291.71 s(1200) =< s(1181) 1124.61/291.71 s(1201) =< s(1181)-1 1124.61/291.71 s(1202) =< s(1181)-2 1124.61/291.71 s(1203) =< s(1181)*(1/2) 1124.61/291.71 s(1198) =< s(1181)*(1/2) 1124.61/291.71 s(1204) =< s(1181)*(1/2) 1124.61/291.71 s(1205) =< s(1192)*s(1181) 1124.61/291.71 s(1206) =< s(1193)*s(1199) 1124.61/291.71 s(1207) =< s(1184)*s(1200) 1124.61/291.71 s(1208) =< s(1193)*s(1201) 1124.61/291.71 s(1209) =< s(1193)*s(1200) 1124.61/291.71 s(1210) =< s(1192)*s(1202) 1124.61/291.71 s(1211) =< s(1192)*s(1200) 1124.61/291.71 s(1212) =< s(1209)*(1/2) 1124.61/291.71 s(1213) =< s(1211)*(1/2) 1124.61/291.71 s(1214) =< s(1206)+s(1207)+s(1206)+s(1205)+aux(217) 1124.61/291.71 s(1197) =< s(1206)+s(1207)+s(1206)+s(1205)+aux(217) 1124.61/291.71 s(1196) =< s(1206)+s(1207)+s(1206)+s(1205)+aux(217) 1124.61/291.71 s(1215) =< s(1196)*s(1201) 1124.61/291.71 s(1216) =< s(1196)*s(1200) 1124.61/291.71 s(1217) =< s(1197)*s(1202) 1124.61/291.71 s(1218) =< s(1197)*s(1200) 1124.61/291.71 s(1219) =< s(1214)*s(1200) 1124.61/291.71 s(1220) =< s(1216)*(1/2) 1124.61/291.71 s(1221) =< s(1218)*(1/2) 1124.61/291.71 s(1222) =< s(1219)*(1/2) 1124.61/291.71 s(1223) =< s(1200) 1124.61/291.71 s(1224) =< s(1193)*s(1200) 1124.61/291.71 s(1225) =< s(1193)*s(1223) 1124.61/291.71 s(1226) =< s(1198) 1124.61/291.71 s(1227) =< s(1193)*s(1203) 1124.61/291.71 s(1228) =< s(1227) 1124.61/291.71 s(1229) =< s(1204) 1124.61/291.71 s(1230) =< s(1215) 1124.61/291.71 s(1231) =< s(1216) 1124.61/291.71 s(1232) =< s(1220) 1124.61/291.71 s(1233) =< s(1231)*s(1203) 1124.61/291.71 s(1234) =< s(1233) 1124.61/291.71 s(1235) =< s(1208) 1124.61/291.71 s(1236) =< s(1209) 1124.61/291.71 s(1237) =< s(1212) 1124.61/291.71 s(1238) =< s(1236)*s(1203) 1124.61/291.71 s(1239) =< s(1238) 1124.61/291.71 s(1240) =< s(1217) 1124.61/291.71 s(1241) =< s(1218) 1124.61/291.71 s(1242) =< s(1241)*s(1200) 1124.61/291.71 s(1243) =< s(1241)*s(1223) 1124.61/291.71 s(1244) =< s(1221) 1124.61/291.71 s(1245) =< s(1241)*s(1203) 1124.61/291.71 s(1246) =< s(1245) 1124.61/291.71 s(1247) =< s(1210) 1124.61/291.71 s(1248) =< s(1211) 1124.61/291.71 s(1249) =< s(1248)*s(1181) 1124.61/291.71 s(1250) =< s(1248)*s(1200) 1124.61/291.71 s(1251) =< s(1213) 1124.61/291.71 s(1252) =< s(1248)*s(1203) 1124.61/291.71 s(1253) =< s(1252) 1124.61/291.71 s(1254) =< s(1219) 1124.61/291.71 s(1255) =< s(1254)*s(1203) 1124.61/291.71 s(1256) =< s(1255) 1124.61/291.71 s(1257) =< s(1222) 1124.61/291.71 s(1258) =< s(1193)*s(1181) 1124.61/291.71 s(1303) =< s(1193)*s(1181) 1124.61/291.71 s(1304) =< s(1303) 1124.61/291.71 s(1305) =< s(1181) 1124.61/291.71 s(1306) =< s(1181) 1124.61/291.71 s(1306) =< s(1181)*(1/2) 1124.61/291.71 s(1307) =< s(1184)*s(1181) 1124.61/291.71 s(1308) =< s(1184)*s(1202) 1124.61/291.71 s(1309) =< s(1207)*(1/2) 1124.61/291.71 s(1310) =< s(1206)+s(1209)+s(1206)+s(1307)+aux(217) 1124.61/291.71 s(1305) =< s(1206)+s(1209)+s(1206)+s(1307)+aux(217) 1124.61/291.71 s(1311) =< s(1305)*s(1201) 1124.61/291.71 s(1312) =< s(1305)*s(1200) 1124.61/291.71 s(1313) =< s(1305)*s(1202) 1124.61/291.71 s(1314) =< s(1310)*s(1200) 1124.61/291.71 s(1315) =< s(1312)*(1/2) 1124.61/291.71 s(1316) =< s(1314)*(1/2) 1124.61/291.71 s(1317) =< s(1306) 1124.61/291.71 s(1318) =< s(1311) 1124.61/291.71 s(1319) =< s(1312) 1124.61/291.71 s(1320) =< s(1315) 1124.61/291.71 s(1321) =< s(1319)*s(1203) 1124.61/291.71 s(1322) =< s(1321) 1124.61/291.71 s(1323) =< s(1313) 1124.61/291.71 s(1324) =< s(1319)*s(1200) 1124.61/291.71 s(1325) =< s(1319)*s(1223) 1124.61/291.71 s(1326) =< s(1308) 1124.61/291.71 s(1327) =< s(1207) 1124.61/291.71 s(1328) =< s(1327)*s(1181) 1124.61/291.71 s(1329) =< s(1327)*s(1200) 1124.61/291.71 s(1330) =< s(1309) 1124.61/291.71 s(1331) =< s(1327)*s(1203) 1124.61/291.71 s(1332) =< s(1331) 1124.61/291.71 s(1333) =< s(1314) 1124.61/291.71 s(1334) =< s(1333)*s(1203) 1124.61/291.71 s(1335) =< s(1334) 1124.61/291.71 s(1336) =< s(1316) 1124.61/291.71 1124.61/291.71 with precondition: [V1=1,V>=1,V29>=0] 1124.61/291.71 1124.61/291.71 * Chain [65]: 10*s(1339)+2*s(1340)+4*s(1342)+3 1124.61/291.71 Such that:aux(219) =< V 1124.61/291.71 aux(220) =< V/2 1124.61/291.71 s(1339) =< aux(219) 1124.61/291.71 s(1340) =< aux(220) 1124.61/291.71 s(1341) =< s(1339)*aux(220) 1124.61/291.71 s(1342) =< s(1341) 1124.61/291.71 1124.61/291.71 with precondition: [V1=1,V>=2] 1124.61/291.71 1124.61/291.71 * Chain [64]: 38*s(1348)+96*s(1353)+3663*s(1354)+108*s(1355)+108*s(1357)+98*s(1359)+240*s(1360)+63*s(1365)+63*s(1366)+45*s(1383)+96*s(1394)+36*s(1395)+216*s(1397)+24*s(1398)+36*s(1399)+639*s(1400)+18*s(1401)+54*s(1403)+48*s(1404)+852*s(1405)+24*s(1406)+72*s(1408)+36*s(1409)+711*s(1410)+144*s(1411)+72*s(1412)+18*s(1413)+54*s(1415)+36*s(1416)+711*s(1417)+144*s(1418)+72*s(1419)+18*s(1420)+54*s(1422)+198*s(1423)+90*s(1425)+18*s(1426)+60*s(1473)+42*s(1474)+15*s(1479)+12*s(1486)+12*s(1487)+450*s(1488)+12*s(1489)+36*s(1491)+12*s(1492)+48*s(1493)+24*s(1494)+12*s(1495)+237*s(1496)+48*s(1497)+24*s(1498)+6*s(1499)+18*s(1501)+66*s(1502)+30*s(1504)+6*s(1505)+4*s(1673)+2*s(1675)+6*s(1843)+2*s(1846)+2*s(1848)+15 1124.61/291.71 Such that:s(1840) =< -V+V29 1124.61/291.71 aux(229) =< V 1124.61/291.71 aux(230) =< V29 1124.61/291.71 aux(231) =< V29/2 1124.61/291.71 s(1843) =< s(1840) 1124.61/291.71 s(1843) =< aux(230) 1124.61/291.71 s(1354) =< aux(230) 1124.61/291.71 s(1672) =< aux(229) 1124.61/291.71 s(1846) =< s(1354)*aux(229) 1124.61/291.71 s(1359) =< s(1354)*aux(230) 1124.61/291.71 s(1848) =< s(1843)*s(1672) 1124.61/291.71 s(1348) =< aux(229) 1124.61/291.71 s(1353) =< aux(231) 1124.61/291.71 s(1355) =< aux(231) 1124.61/291.71 s(1356) =< s(1354)*aux(231) 1124.61/291.71 s(1357) =< s(1356) 1124.61/291.71 s(1358) =< aux(230) 1124.61/291.71 s(1360) =< s(1354)*s(1358) 1124.61/291.71 s(1365) =< aux(230) 1124.61/291.71 s(1353) =< aux(230) 1124.61/291.71 s(1366) =< aux(231) 1124.61/291.71 s(1367) =< aux(231) 1124.61/291.71 s(1368) =< aux(230)+1 1124.61/291.71 s(1370) =< aux(230)-1 1124.61/291.71 s(1371) =< aux(230)-2 1124.61/291.71 s(1372) =< aux(230)*(1/2) 1124.61/291.71 s(1367) =< aux(230)*(1/2) 1124.61/291.71 s(1373) =< aux(230)*(1/2) 1124.61/291.71 s(1374) =< s(1355)*aux(230) 1124.61/291.71 s(1375) =< s(1354)*s(1368) 1124.61/291.71 s(1376) =< s(1353)*s(1358) 1124.61/291.71 s(1377) =< s(1354)*s(1370) 1124.61/291.71 s(1378) =< s(1354)*s(1358) 1124.61/291.71 s(1379) =< s(1355)*s(1371) 1124.61/291.71 s(1380) =< s(1355)*s(1358) 1124.61/291.71 s(1381) =< s(1378)*(1/2) 1124.61/291.71 s(1382) =< s(1380)*(1/2) 1124.61/291.71 s(1383) =< s(1375)+s(1376)+s(1375)+s(1374)+aux(230) 1124.61/291.71 s(1366) =< s(1375)+s(1376)+s(1375)+s(1374)+aux(230) 1124.61/291.71 s(1365) =< s(1375)+s(1376)+s(1375)+s(1374)+aux(230) 1124.61/291.71 s(1384) =< s(1365)*s(1370) 1124.61/291.71 s(1385) =< s(1365)*s(1358) 1124.61/291.71 s(1386) =< s(1366)*s(1371) 1124.61/291.71 s(1387) =< s(1366)*s(1358) 1124.61/291.71 s(1388) =< s(1383)*s(1358) 1124.61/291.71 s(1389) =< s(1385)*(1/2) 1124.61/291.71 s(1390) =< s(1387)*(1/2) 1124.61/291.71 s(1391) =< s(1388)*(1/2) 1124.61/291.71 s(1392) =< s(1358) 1124.61/291.71 s(1394) =< s(1354)*s(1392) 1124.61/291.71 s(1395) =< s(1367) 1124.61/291.71 s(1396) =< s(1354)*s(1372) 1124.61/291.71 s(1397) =< s(1396) 1124.61/291.71 s(1398) =< s(1373) 1124.61/291.71 s(1399) =< s(1384) 1124.61/291.71 s(1400) =< s(1385) 1124.61/291.71 s(1401) =< s(1389) 1124.61/291.71 s(1402) =< s(1400)*s(1372) 1124.61/291.71 s(1403) =< s(1402) 1124.61/291.71 s(1404) =< s(1377) 1124.61/291.71 s(1405) =< s(1378) 1124.61/291.71 s(1406) =< s(1381) 1124.61/291.71 s(1407) =< s(1405)*s(1372) 1124.61/291.71 s(1408) =< s(1407) 1124.61/291.71 s(1409) =< s(1386) 1124.61/291.71 s(1410) =< s(1387) 1124.61/291.71 s(1411) =< s(1410)*s(1358) 1124.61/291.71 s(1412) =< s(1410)*s(1392) 1124.61/291.71 s(1413) =< s(1390) 1124.61/291.71 s(1414) =< s(1410)*s(1372) 1124.61/291.71 s(1415) =< s(1414) 1124.61/291.71 s(1416) =< s(1379) 1124.61/291.71 s(1417) =< s(1380) 1124.61/291.71 s(1418) =< s(1417)*aux(230) 1124.61/291.71 s(1419) =< s(1417)*s(1358) 1124.61/291.71 s(1420) =< s(1382) 1124.61/291.71 s(1421) =< s(1417)*s(1372) 1124.61/291.71 s(1422) =< s(1421) 1124.61/291.71 s(1423) =< s(1388) 1124.61/291.71 s(1424) =< s(1423)*s(1372) 1124.61/291.71 s(1425) =< s(1424) 1124.61/291.71 s(1426) =< s(1391) 1124.61/291.71 s(1472) =< s(1354)*aux(230) 1124.61/291.71 s(1473) =< s(1472) 1124.61/291.71 s(1474) =< aux(230) 1124.61/291.71 s(1475) =< aux(230) 1124.61/291.71 s(1475) =< aux(230)*(1/2) 1124.61/291.71 s(1476) =< s(1353)*aux(230) 1124.61/291.71 s(1477) =< s(1353)*s(1371) 1124.61/291.71 s(1478) =< s(1376)*(1/2) 1124.61/291.71 s(1479) =< s(1375)+s(1378)+s(1375)+s(1476)+aux(230) 1124.61/291.71 s(1474) =< s(1375)+s(1378)+s(1375)+s(1476)+aux(230) 1124.61/291.71 s(1480) =< s(1474)*s(1370) 1124.61/291.71 s(1481) =< s(1474)*s(1358) 1124.61/291.71 s(1482) =< s(1474)*s(1371) 1124.61/291.71 s(1483) =< s(1479)*s(1358) 1124.61/291.71 s(1484) =< s(1481)*(1/2) 1124.61/291.71 s(1485) =< s(1483)*(1/2) 1124.61/291.71 s(1486) =< s(1475) 1124.61/291.71 s(1487) =< s(1480) 1124.61/291.71 s(1488) =< s(1481) 1124.61/291.71 s(1489) =< s(1484) 1124.61/291.71 s(1490) =< s(1488)*s(1372) 1124.61/291.71 s(1491) =< s(1490) 1124.61/291.71 s(1492) =< s(1482) 1124.61/291.71 s(1493) =< s(1488)*s(1358) 1124.61/291.71 s(1494) =< s(1488)*s(1392) 1124.61/291.71 s(1495) =< s(1477) 1124.61/291.71 s(1496) =< s(1376) 1124.61/291.71 s(1497) =< s(1496)*aux(230) 1124.61/291.71 s(1498) =< s(1496)*s(1358) 1124.61/291.71 s(1499) =< s(1478) 1124.61/291.71 s(1500) =< s(1496)*s(1372) 1124.61/291.71 s(1501) =< s(1500) 1124.61/291.71 s(1502) =< s(1483) 1124.61/291.71 s(1503) =< s(1502)*s(1372) 1124.61/291.71 s(1504) =< s(1503) 1124.61/291.71 s(1505) =< s(1485) 1124.61/291.71 s(1673) =< s(1348)*aux(229) 1124.61/291.71 s(1675) =< s(1348)*s(1672) 1124.61/291.71 1124.61/291.71 with precondition: [V1=2,V>=0,V29>=1] 1124.61/291.71 1124.61/291.71 * Chain [63]: 2789*s(1851)+147*s(1854)+18*s(1855)+60*s(1857)+1389*s(1871)+6*s(1872)+20*s(1874)+1*s(1877)+32*s(1882)+1213*s(1883)+36*s(1884)+36*s(1886)+32*s(1888)+80*s(1889)+21*s(1894)+21*s(1895)+15*s(1912)+32*s(1923)+12*s(1924)+72*s(1926)+8*s(1927)+12*s(1928)+213*s(1929)+6*s(1930)+18*s(1932)+16*s(1933)+284*s(1934)+8*s(1935)+24*s(1937)+12*s(1938)+237*s(1939)+48*s(1940)+24*s(1941)+6*s(1942)+18*s(1944)+12*s(1945)+237*s(1946)+48*s(1947)+24*s(1948)+6*s(1949)+18*s(1951)+66*s(1952)+30*s(1954)+6*s(1955)+20*s(2002)+14*s(2003)+5*s(2008)+4*s(2015)+4*s(2016)+150*s(2017)+4*s(2018)+12*s(2020)+4*s(2021)+16*s(2022)+8*s(2023)+4*s(2024)+79*s(2025)+16*s(2026)+8*s(2027)+2*s(2028)+6*s(2030)+22*s(2031)+10*s(2033)+2*s(2034)+42*s(2041)+56*s(2043)+32*s(2051)+84*s(2057)+168*s(2058)+21*s(2063)+21*s(2064)+15*s(2081)+64*s(2092)+12*s(2093)+144*s(2095)+16*s(2096)+12*s(2097)+213*s(2098)+6*s(2099)+18*s(2101)+32*s(2102)+884*s(2103)+8*s(2104)+24*s(2106)+12*s(2107)+237*s(2108)+48*s(2109)+24*s(2110)+6*s(2111)+18*s(2113)+12*s(2114)+237*s(2115)+48*s(2116)+24*s(2117)+6*s(2118)+18*s(2120)+66*s(2121)+30*s(2123)+6*s(2124)+96*s(2171)+14*s(2172)+5*s(2177)+20*s(2184)+4*s(2185)+150*s(2186)+4*s(2187)+12*s(2189)+4*s(2190)+16*s(2191)+8*s(2192)+4*s(2193)+79*s(2194)+16*s(2195)+8*s(2196)+2*s(2197)+6*s(2199)+22*s(2200)+10*s(2202)+2*s(2203)+4*s(2262)+4*s(2264)+76*s(2272)+32*s(2294)+80*s(2295)+56*s(2300)+20*s(2318)+32*s(2329)+16*s(2330)+72*s(2332)+8*s(2333)+16*s(2334)+600*s(2335)+16*s(2336)+48*s(2338)+16*s(2339)+600*s(2340)+16*s(2341)+48*s(2343)+16*s(2344)+64*s(2346)+32*s(2347)+16*s(2351)+64*s(2353)+32*s(2354)+88*s(2358)+40*s(2360)+8*s(2361)+56*s(2485)+20*s(2503)+16*s(2519)+600*s(2520)+16*s(2521)+48*s(2523)+16*s(2526)+48*s(2528)+16*s(2529)+64*s(2531)+32*s(2532)+16*s(2536)+64*s(2538)+32*s(2539)+88*s(2543)+40*s(2545)+8*s(2546)+15 1124.61/291.71 Such that:aux(234) =< V+V29/2 1124.61/291.71 s(1877) =< 2*V 1124.61/291.71 aux(235) =< 2*V+V29 1124.61/291.71 s(1870) =< V/2+V29/2 1124.61/291.71 aux(251) =< V 1124.61/291.71 aux(252) =< V+V29 1124.61/291.71 aux(253) =< V/2 1124.61/291.71 aux(254) =< V29 1124.61/291.71 aux(255) =< V29/2 1124.61/291.71 s(1851) =< aux(251) 1124.61/291.71 s(2051) =< aux(253) 1124.61/291.71 s(2041) =< aux(253) 1124.61/291.71 s(2042) =< s(1851)*aux(253) 1124.61/291.71 s(2043) =< s(2042) 1124.61/291.71 s(2056) =< aux(251) 1124.61/291.71 s(2057) =< s(1851)*aux(251) 1124.61/291.71 s(2058) =< s(1851)*s(2056) 1124.61/291.71 s(2063) =< aux(251) 1124.61/291.71 s(2051) =< aux(251) 1124.61/291.71 s(2064) =< aux(253) 1124.61/291.71 s(2065) =< aux(253) 1124.61/291.71 s(2066) =< aux(251)+1 1124.61/291.71 s(2068) =< aux(251)-1 1124.61/291.71 s(2069) =< aux(251)-2 1124.61/291.71 s(2070) =< aux(251)*(1/2) 1124.61/291.71 s(2065) =< aux(251)*(1/2) 1124.61/291.71 s(2071) =< aux(251)*(1/2) 1124.61/291.71 s(2072) =< s(2041)*aux(251) 1124.61/291.71 s(2073) =< s(1851)*s(2066) 1124.61/291.71 s(2074) =< s(2051)*s(2056) 1124.61/291.71 s(2075) =< s(1851)*s(2068) 1124.61/291.71 s(2076) =< s(1851)*s(2056) 1124.61/291.71 s(2077) =< s(2041)*s(2069) 1124.61/291.71 s(2078) =< s(2041)*s(2056) 1124.61/291.71 s(2079) =< s(2076)*(1/2) 1124.61/291.71 s(2080) =< s(2078)*(1/2) 1124.61/291.71 s(2081) =< s(2073)+s(2074)+s(2073)+s(2072)+aux(251) 1124.61/291.71 s(2064) =< s(2073)+s(2074)+s(2073)+s(2072)+aux(251) 1124.61/291.71 s(2063) =< s(2073)+s(2074)+s(2073)+s(2072)+aux(251) 1124.61/291.71 s(2082) =< s(2063)*s(2068) 1124.61/291.71 s(2083) =< s(2063)*s(2056) 1124.61/291.71 s(2084) =< s(2064)*s(2069) 1124.61/291.71 s(2085) =< s(2064)*s(2056) 1124.61/291.71 s(2086) =< s(2081)*s(2056) 1124.61/291.71 s(2087) =< s(2083)*(1/2) 1124.61/291.71 s(2088) =< s(2085)*(1/2) 1124.61/291.71 s(2089) =< s(2086)*(1/2) 1124.61/291.71 s(2090) =< s(2056) 1124.61/291.71 s(2092) =< s(1851)*s(2090) 1124.61/291.71 s(2093) =< s(2065) 1124.61/291.71 s(2094) =< s(1851)*s(2070) 1124.61/291.71 s(2095) =< s(2094) 1124.61/291.71 s(2096) =< s(2071) 1124.61/291.71 s(2097) =< s(2082) 1124.61/291.71 s(2098) =< s(2083) 1124.61/291.71 s(2099) =< s(2087) 1124.61/291.71 s(2100) =< s(2098)*s(2070) 1124.61/291.71 s(2101) =< s(2100) 1124.61/291.71 s(2102) =< s(2075) 1124.61/291.71 s(2103) =< s(2076) 1124.61/291.71 s(2104) =< s(2079) 1124.61/291.71 s(2105) =< s(2103)*s(2070) 1124.61/291.71 s(2106) =< s(2105) 1124.61/291.71 s(2107) =< s(2084) 1124.61/291.71 s(2108) =< s(2085) 1124.61/291.71 s(2109) =< s(2108)*s(2056) 1124.61/291.71 s(2110) =< s(2108)*s(2090) 1124.61/291.71 s(2111) =< s(2088) 1124.61/291.71 s(2112) =< s(2108)*s(2070) 1124.61/291.71 s(2113) =< s(2112) 1124.61/291.71 s(2114) =< s(2077) 1124.61/291.71 s(2115) =< s(2078) 1124.61/291.71 s(2116) =< s(2115)*aux(251) 1124.61/291.71 s(2117) =< s(2115)*s(2056) 1124.61/291.71 s(2118) =< s(2080) 1124.61/291.71 s(2119) =< s(2115)*s(2070) 1124.61/291.71 s(2120) =< s(2119) 1124.61/291.71 s(2121) =< s(2086) 1124.61/291.71 s(2122) =< s(2121)*s(2070) 1124.61/291.71 s(2123) =< s(2122) 1124.61/291.71 s(2124) =< s(2089) 1124.61/291.71 s(2170) =< s(1851)*aux(251) 1124.61/291.71 s(2171) =< s(2170) 1124.61/291.71 s(2172) =< aux(251) 1124.61/291.71 s(2173) =< aux(251) 1124.61/291.71 s(2173) =< aux(251)*(1/2) 1124.61/291.71 s(2174) =< s(2051)*aux(251) 1124.61/291.71 s(2175) =< s(2051)*s(2069) 1124.61/291.71 s(2176) =< s(2074)*(1/2) 1124.61/291.71 s(2177) =< s(2073)+s(2076)+s(2073)+s(2174)+aux(251) 1124.61/291.71 s(2172) =< s(2073)+s(2076)+s(2073)+s(2174)+aux(251) 1124.61/291.71 s(2178) =< s(2172)*s(2068) 1124.61/291.71 s(2179) =< s(2172)*s(2056) 1124.61/291.71 s(2180) =< s(2172)*s(2069) 1124.61/291.71 s(2181) =< s(2177)*s(2056) 1124.61/291.71 s(2182) =< s(2179)*(1/2) 1124.61/291.71 s(2183) =< s(2181)*(1/2) 1124.61/291.71 s(2184) =< s(2173) 1124.61/291.71 s(2185) =< s(2178) 1124.61/291.71 s(2186) =< s(2179) 1124.61/291.71 s(2187) =< s(2182) 1124.61/291.71 s(2188) =< s(2186)*s(2070) 1124.61/291.71 s(2189) =< s(2188) 1124.61/291.71 s(2190) =< s(2180) 1124.61/291.71 s(2191) =< s(2186)*s(2056) 1124.61/291.71 s(2192) =< s(2186)*s(2090) 1124.61/291.71 s(2193) =< s(2175) 1124.61/291.71 s(2194) =< s(2074) 1124.61/291.71 s(2195) =< s(2194)*aux(251) 1124.61/291.71 s(2196) =< s(2194)*s(2056) 1124.61/291.71 s(2197) =< s(2176) 1124.61/291.71 s(2198) =< s(2194)*s(2070) 1124.61/291.71 s(2199) =< s(2198) 1124.61/291.71 s(2200) =< s(2181) 1124.61/291.71 s(2201) =< s(2200)*s(2070) 1124.61/291.71 s(2202) =< s(2201) 1124.61/291.71 s(2203) =< s(2183) 1124.61/291.71 s(1871) =< aux(252) 1124.61/291.71 s(2271) =< s(1871)*aux(252) 1124.61/291.71 s(2272) =< s(2271) 1124.61/291.71 s(2261) =< aux(252) 1124.61/291.71 s(2262) =< s(1851)*aux(252) 1124.61/291.71 s(2264) =< s(1851)*s(2261) 1124.61/291.71 s(2294) =< s(1871)*aux(252) 1124.61/291.71 s(2295) =< s(1871)*s(2261) 1124.61/291.71 s(2300) =< aux(252) 1124.61/291.71 s(2302) =< aux(252) 1124.61/291.71 s(2303) =< aux(252)+1 1124.61/291.71 s(2305) =< aux(252)-1 1124.61/291.71 s(2306) =< aux(252)-2 1124.61/291.71 s(2307) =< aux(252)*(1/2) 1124.61/291.71 s(2302) =< aux(252)*(1/2) 1124.61/291.71 s(2308) =< aux(252)*(1/2) 1124.61/291.71 s(2310) =< s(1871)*s(2303) 1124.61/291.71 s(2311) =< s(1871)*s(2261) 1124.61/291.71 s(2312) =< s(1871)*s(2305) 1124.61/291.71 s(2314) =< s(1871)*s(2306) 1124.61/291.71 s(2316) =< s(2311)*(1/2) 1124.61/291.71 s(2318) =< s(2310)+s(2311)+s(2310)+s(2271)+aux(252) 1124.61/291.71 s(2300) =< s(2310)+s(2311)+s(2310)+s(2271)+aux(252) 1124.61/291.71 s(2319) =< s(2300)*s(2305) 1124.61/291.71 s(2320) =< s(2300)*s(2261) 1124.61/291.71 s(2321) =< s(2300)*s(2306) 1124.61/291.71 s(2323) =< s(2318)*s(2261) 1124.61/291.71 s(2324) =< s(2320)*(1/2) 1124.61/291.71 s(2326) =< s(2323)*(1/2) 1124.61/291.71 s(2327) =< s(2261) 1124.61/291.71 s(2329) =< s(1871)*s(2327) 1124.61/291.71 s(2330) =< s(2302) 1124.61/291.71 s(2331) =< s(1871)*s(2307) 1124.61/291.71 s(2332) =< s(2331) 1124.61/291.71 s(2333) =< s(2308) 1124.61/291.71 s(2334) =< s(2319) 1124.61/291.71 s(2335) =< s(2320) 1124.61/291.71 s(2336) =< s(2324) 1124.61/291.71 s(2337) =< s(2335)*s(2307) 1124.61/291.71 s(2338) =< s(2337) 1124.61/291.71 s(2339) =< s(2312) 1124.61/291.71 s(2340) =< s(2311) 1124.61/291.71 s(2341) =< s(2316) 1124.61/291.71 s(2342) =< s(2340)*s(2307) 1124.61/291.71 s(2343) =< s(2342) 1124.61/291.71 s(2344) =< s(2321) 1124.61/291.71 s(2346) =< s(2335)*s(2261) 1124.61/291.71 s(2347) =< s(2335)*s(2327) 1124.61/291.71 s(2351) =< s(2314) 1124.61/291.71 s(2353) =< s(2340)*aux(252) 1124.61/291.71 s(2354) =< s(2340)*s(2261) 1124.61/291.71 s(2358) =< s(2323) 1124.61/291.71 s(2359) =< s(2358)*s(2307) 1124.61/291.71 s(2360) =< s(2359) 1124.61/291.71 s(2361) =< s(2326) 1124.61/291.71 s(2485) =< aux(251) 1124.61/291.71 s(2499) =< s(1851)*s(2069) 1124.61/291.71 s(2501) =< s(2076)*(1/2) 1124.61/291.71 s(2503) =< s(2073)+s(2076)+s(2073)+s(2170)+aux(251) 1124.61/291.71 s(2485) =< s(2073)+s(2076)+s(2073)+s(2170)+aux(251) 1124.61/291.71 s(2504) =< s(2485)*s(2068) 1124.61/291.71 s(2505) =< s(2485)*s(2056) 1124.61/291.71 s(2506) =< s(2485)*s(2069) 1124.61/291.71 s(2508) =< s(2503)*s(2056) 1124.61/291.71 s(2509) =< s(2505)*(1/2) 1124.61/291.71 s(2511) =< s(2508)*(1/2) 1124.61/291.71 s(2519) =< s(2504) 1124.61/291.71 s(2520) =< s(2505) 1124.61/291.71 s(2521) =< s(2509) 1124.61/291.71 s(2522) =< s(2520)*s(2070) 1124.61/291.71 s(2523) =< s(2522) 1124.61/291.71 s(2526) =< s(2501) 1124.61/291.71 s(2527) =< s(2103)*s(2070) 1124.61/291.71 s(2528) =< s(2527) 1124.61/291.71 s(2529) =< s(2506) 1124.61/291.71 s(2531) =< s(2520)*s(2056) 1124.61/291.71 s(2532) =< s(2520)*s(2090) 1124.61/291.71 s(2536) =< s(2499) 1124.61/291.71 s(2538) =< s(2103)*aux(251) 1124.61/291.71 s(2539) =< s(2103)*s(2056) 1124.61/291.71 s(2543) =< s(2508) 1124.61/291.71 s(2544) =< s(2543)*s(2070) 1124.61/291.71 s(2545) =< s(2544) 1124.61/291.71 s(2546) =< s(2511) 1124.61/291.71 s(1854) =< aux(254) 1124.61/291.71 s(1855) =< aux(255) 1124.61/291.71 s(1856) =< s(1854)*aux(255) 1124.61/291.71 s(1857) =< s(1856) 1124.61/291.71 s(1882) =< aux(234) 1124.61/291.71 s(1883) =< aux(235) 1124.61/291.71 s(1884) =< aux(234) 1124.61/291.71 s(1885) =< s(1883)*aux(234) 1124.61/291.71 s(1886) =< s(1885) 1124.61/291.71 s(1887) =< aux(235) 1124.61/291.71 s(1888) =< s(1883)*aux(235) 1124.61/291.71 s(1889) =< s(1883)*s(1887) 1124.61/291.71 s(1894) =< aux(235) 1124.61/291.71 s(1882) =< aux(235) 1124.61/291.71 s(1895) =< aux(234) 1124.61/291.71 s(1896) =< aux(234) 1124.61/291.71 s(1897) =< aux(235)+1 1124.61/291.71 s(1899) =< aux(235)-1 1124.61/291.71 s(1900) =< aux(235)-2 1124.61/291.71 s(1901) =< aux(235)*(1/2) 1124.61/291.71 s(1896) =< aux(235)*(1/2) 1124.61/291.71 s(1902) =< aux(235)*(1/2) 1124.61/291.71 s(1903) =< s(1884)*aux(235) 1124.61/291.71 s(1904) =< s(1883)*s(1897) 1124.61/291.71 s(1905) =< s(1882)*s(1887) 1124.61/291.71 s(1906) =< s(1883)*s(1899) 1124.61/291.71 s(1907) =< s(1883)*s(1887) 1124.61/291.71 s(1908) =< s(1884)*s(1900) 1124.61/291.71 s(1909) =< s(1884)*s(1887) 1124.61/291.71 s(1910) =< s(1907)*(1/2) 1124.61/291.71 s(1911) =< s(1909)*(1/2) 1124.61/291.71 s(1912) =< s(1904)+s(1905)+s(1904)+s(1903)+aux(235) 1124.61/291.71 s(1895) =< s(1904)+s(1905)+s(1904)+s(1903)+aux(235) 1124.61/291.71 s(1894) =< s(1904)+s(1905)+s(1904)+s(1903)+aux(235) 1124.61/291.71 s(1913) =< s(1894)*s(1899) 1124.61/291.71 s(1914) =< s(1894)*s(1887) 1124.61/291.71 s(1915) =< s(1895)*s(1900) 1124.61/291.71 s(1916) =< s(1895)*s(1887) 1124.61/291.71 s(1917) =< s(1912)*s(1887) 1124.61/291.71 s(1918) =< s(1914)*(1/2) 1124.61/291.71 s(1919) =< s(1916)*(1/2) 1124.61/291.71 s(1920) =< s(1917)*(1/2) 1124.61/291.71 s(1921) =< s(1887) 1124.61/291.71 s(1923) =< s(1883)*s(1921) 1124.61/291.71 s(1924) =< s(1896) 1124.61/291.71 s(1925) =< s(1883)*s(1901) 1124.61/291.71 s(1926) =< s(1925) 1124.61/291.71 s(1927) =< s(1902) 1124.61/291.71 s(1928) =< s(1913) 1124.61/291.71 s(1929) =< s(1914) 1124.61/291.71 s(1930) =< s(1918) 1124.61/291.71 s(1931) =< s(1929)*s(1901) 1124.61/291.71 s(1932) =< s(1931) 1124.61/291.71 s(1933) =< s(1906) 1124.61/291.71 s(1934) =< s(1907) 1124.61/291.71 s(1935) =< s(1910) 1124.61/291.71 s(1936) =< s(1934)*s(1901) 1124.61/291.71 s(1937) =< s(1936) 1124.61/291.71 s(1938) =< s(1915) 1124.61/291.71 s(1939) =< s(1916) 1124.61/291.71 s(1940) =< s(1939)*s(1887) 1124.61/291.71 s(1941) =< s(1939)*s(1921) 1124.61/291.71 s(1942) =< s(1919) 1124.61/291.71 s(1943) =< s(1939)*s(1901) 1124.61/291.71 s(1944) =< s(1943) 1124.61/291.71 s(1945) =< s(1908) 1124.61/291.71 s(1946) =< s(1909) 1124.61/291.71 s(1947) =< s(1946)*aux(235) 1124.61/291.71 s(1948) =< s(1946)*s(1887) 1124.61/291.71 s(1949) =< s(1911) 1124.61/291.71 s(1950) =< s(1946)*s(1901) 1124.61/291.71 s(1951) =< s(1950) 1124.61/291.71 s(1952) =< s(1917) 1124.61/291.71 s(1953) =< s(1952)*s(1901) 1124.61/291.71 s(1954) =< s(1953) 1124.61/291.71 s(1955) =< s(1920) 1124.61/291.71 s(2001) =< s(1883)*aux(235) 1124.61/291.71 s(2002) =< s(2001) 1124.61/291.71 s(2003) =< aux(235) 1124.61/291.71 s(2004) =< aux(235) 1124.61/291.71 s(2004) =< aux(235)*(1/2) 1124.61/291.71 s(2005) =< s(1882)*aux(235) 1124.61/291.71 s(2006) =< s(1882)*s(1900) 1124.61/291.71 s(2007) =< s(1905)*(1/2) 1124.61/291.71 s(2008) =< s(1904)+s(1907)+s(1904)+s(2005)+aux(235) 1124.61/291.71 s(2003) =< s(1904)+s(1907)+s(1904)+s(2005)+aux(235) 1124.61/291.71 s(2009) =< s(2003)*s(1899) 1124.61/291.71 s(2010) =< s(2003)*s(1887) 1124.61/291.71 s(2011) =< s(2003)*s(1900) 1124.61/291.71 s(2012) =< s(2008)*s(1887) 1124.61/291.71 s(2013) =< s(2010)*(1/2) 1124.61/291.71 s(2014) =< s(2012)*(1/2) 1124.61/291.71 s(2015) =< s(2004) 1124.61/291.71 s(2016) =< s(2009) 1124.61/291.71 s(2017) =< s(2010) 1124.61/291.71 s(2018) =< s(2013) 1124.61/291.71 s(2019) =< s(2017)*s(1901) 1124.61/291.71 s(2020) =< s(2019) 1124.61/291.71 s(2021) =< s(2011) 1124.61/291.71 s(2022) =< s(2017)*s(1887) 1124.61/291.71 s(2023) =< s(2017)*s(1921) 1124.61/291.71 s(2024) =< s(2006) 1124.61/291.71 s(2025) =< s(1905) 1124.61/291.71 s(2026) =< s(2025)*aux(235) 1124.61/291.71 s(2027) =< s(2025)*s(1887) 1124.61/291.71 s(2028) =< s(2007) 1124.61/291.71 s(2029) =< s(2025)*s(1901) 1124.61/291.71 s(2030) =< s(2029) 1124.61/291.71 s(2031) =< s(2012) 1124.61/291.71 s(2032) =< s(2031)*s(1901) 1124.61/291.71 s(2033) =< s(2032) 1124.61/291.71 s(2034) =< s(2014) 1124.61/291.71 s(1872) =< s(1870) 1124.61/291.71 s(1873) =< s(1871)*s(1870) 1124.61/291.71 s(1874) =< s(1873) 1124.61/291.71 1124.61/291.71 with precondition: [V1=2,V>=1,V29>=0] 1124.61/291.71 1124.61/291.71 * Chain [62]: 10*s(2628)+2*s(2629)+4*s(2631)+3 1124.61/291.71 Such that:aux(256) =< V 1124.61/291.71 aux(257) =< V/2 1124.61/291.71 s(2628) =< aux(256) 1124.61/291.71 s(2629) =< aux(257) 1124.61/291.71 s(2630) =< s(2628)*aux(257) 1124.61/291.71 s(2631) =< s(2630) 1124.61/291.71 1124.61/291.71 with precondition: [V1=2,V>=2] 1124.61/291.71 1124.61/291.71 * Chain [61]: 1 1124.61/291.71 with precondition: [V=0,V1>=1] 1124.61/291.71 1124.61/291.71 * Chain [60]: 1*s(2636)+1 1124.61/291.71 Such that:s(2636) =< V 1124.61/291.71 1124.61/291.71 with precondition: [V1=V,V1>=1] 1124.61/291.71 1124.61/291.71 1124.61/291.71 Closed-form bounds of start(V1,V,V29): 1124.61/291.71 ------------------------------------- 1124.61/291.71 * Chain [68] with precondition: [V1>=0] 1124.61/291.71 - Upper bound: 268*V1+11+24*V1*V1+2*V1*nat(V)+92*V1*nat(V1+V)+20*V1*nat(V1+V)*nat(V1+V)+2*V1*nat(-V1+V)+V1/2*(42*V1)+nat(V)*28+nat(V)*2*nat(V)+nat(nat(V1+V)+ -2)*4*nat(V1+V)+nat(nat(V1+V)+ -2)*28*nat(V1/2+V/2)+nat(nat(V1+V)+ -1)*32*nat(V1+V)+nat(V1+V)*1115+nat(V1+V)*1061*nat(V1+V)+nat(V1+V)*298*nat(V1+V)*nat(V1+V)+nat(V1+V)*45*nat(V1+V)*nat(V1+V)*nat(V1+V)+nat(V1+V)*35*nat(V1+V)*nat(V1+V)*nat(V1/2+V/2)+nat(V1+V)*350*nat(V1+V)*nat(V1/2+V/2)+nat(V1+V)*613*nat(V1/2+V/2)+nat(-V1+V)*6+nat(V1/2+V/2)*95+7*V1 1124.61/291.71 - Complexity: n^4 1124.61/291.71 * Chain [67] with precondition: [V1=1,V>=0,V29>=1] 1124.61/291.71 - Upper bound: 4*V+3+2*V*V29+2*V*nat(-V+V29)+24*V29+2*V29*V29+nat(-V+V29)*6 1124.61/291.71 - Complexity: n^2 1124.61/291.71 * Chain [66] with precondition: [V1=1,V>=1,V29>=0] 1124.61/291.71 - Upper bound: 250*V+12+24*V*V+(V+V29)*(92*V)+(V+V29)*((V+V29)*(20*V))+V/2*(38*V)+(V+V29)*(nat(V+V29-2)*4)+(V/2+V29/2)*(nat(V+V29-2)*28)+(32*V+32*V29-32)*(V+V29)+(1115*V+1115*V29)+(1061*V+1061*V29)*(V+V29)+(V+V29)*((298*V+298*V29)*(V+V29))+(V+V29)*((V+V29)*((45*V+45*V29)*(V+V29)))+(V/2+V29/2)*((V+V29)*((35*V+35*V29)*(V+V29)))+(V/2+V29/2)*((350*V+350*V29)*(V+V29))+(V/2+V29/2)*(613*V+613*V29)+(95/2*V+95/2*V29)+6*V 1124.61/291.71 - Complexity: n^4 1124.61/291.71 * Chain [65] with precondition: [V1=1,V>=2] 1124.61/291.71 - Upper bound: 10*V+3+V/2*(4*V)+V 1124.61/291.71 - Complexity: n^2 1124.61/291.71 * Chain [64] with precondition: [V1=2,V>=0,V29>=1] 1124.61/291.71 - Upper bound: 38*V+15+6*V*V+2*V*V29+2*V*nat(-V+V29)+3972*V29+3533*V29*V29+954*V29*V29*V29+135*V29*V29*V29*V29+V29/2*(105*V29*V29*V29)+V29/2*(1050*V29*V29)+12*V29*nat(V29-2)+(V29-1)*(96*V29)+V29/2*(1893*V29)+V29/2*(nat(V29-2)*84)+nat(-V+V29)*6+303/2*V29 1124.61/291.71 - Complexity: n^4 1124.61/291.71 * Chain [63] with precondition: [V1=2,V>=1,V29>=0] 1124.61/291.71 - Upper bound: 3028*V+15+3033*V*V+986*V*V*V+125*V*V*V*V+V/2*(35*V*V*V)+V/2*(350*V*V)+36*V*nat(V-2)+(V-1)*(64*V)+(V+V29)*(8*V)+V/2*(651*V)+147*V29+V29/2*(60*V29)+V/2*(nat(V-2)*28)+(V+V29)*(nat(V+V29-2)*32)+(56*V+28*V29-56)*(V+V29/2)+(8*V+4*V29-8)*(2*V+V29)+(32*V+32*V29-32)*(V+V29)+(64*V+32*V29-32)*(2*V+V29)+2*V+(1525*V+1525*V29)+(1828*V+1828*V29)*(V+V29)+(V+V29)*((668*V+668*V29)*(V+V29))+(V+V29)*((V+V29)*((80*V+80*V29)*(V+V29)))+(V/2+V29/2)*(20*V+20*V29)+(101*V+101/2*V29)+(631*V+631/2*V29)*(2*V+V29)+(2*V+V29)*((350*V+175*V29)*(2*V+V29))+(2*V+V29)*((2*V+V29)*((35*V+35/2*V29)*(2*V+V29)))+(2632*V+1316*V29)+(2354*V+1177*V29)*(2*V+V29)+(2*V+V29)*((636*V+318*V29)*(2*V+V29))+(2*V+V29)*((2*V+V29)*((90*V+45*V29)*(2*V+V29)))+(3*V+3*V29)+107/2*V+9*V29 1124.61/291.71 - Complexity: n^4 1124.61/291.71 * Chain [62] with precondition: [V1=2,V>=2] 1124.61/291.71 - Upper bound: 10*V+3+V/2*(4*V)+V 1124.61/291.71 - Complexity: n^2 1124.61/291.71 * Chain [61] with precondition: [V=0,V1>=1] 1124.61/291.71 - Upper bound: 1 1124.61/291.71 - Complexity: constant 1124.61/291.71 * Chain [60] with precondition: [V1=V,V1>=1] 1124.61/291.71 - Upper bound: V+1 1124.61/291.71 - Complexity: n 1124.61/291.71 1124.61/291.71 ### Maximum cost of start(V1,V,V29): nat(V)*3+2+max([nat(V)*6+max([nat(V)*4*nat(V/2)+nat(V/2)*2,nat(V)*18+8+nat(V)*2*nat(V)+max([nat(V)*10+1+nat(V)*4*nat(V)+max([nat(V)*18*nat(V)+nat(V)*212+nat(V)*8*nat(V+V29)+nat(V)*38*nat(V/2)+nat(nat(V+V29)+ -2)*4*nat(V+V29)+nat(nat(V+V29)+ -1)*32*nat(V+V29)+nat(V+V29)*1115+nat(V+V29)*1061*nat(V+V29)+nat(V+V29)*298*nat(V+V29)*nat(V+V29)+nat(V+V29)*45*nat(V+V29)*nat(V+V29)*nat(V+V29)+nat(V+V29)*20*nat(V/2+V29/2)+nat(V/2+V29/2)*6+nat(V/2)*12+max([nat(V)*20*nat(V+V29)*nat(V+V29)+nat(V)*84*nat(V+V29)+nat(nat(V+V29)+ -2)*28*nat(V/2+V29/2)+nat(V+V29)*35*nat(V+V29)*nat(V+V29)*nat(V/2+V29/2)+nat(V+V29)*350*nat(V+V29)*nat(V/2+V29/2)+nat(V+V29)*593*nat(V/2+V29/2)+nat(V/2+V29/2)*89,nat(V)*2778+3+nat(V)*3009*nat(V)+nat(V)*986*nat(V)*nat(V)+nat(V)*125*nat(V)*nat(V)*nat(V)+nat(V)*35*nat(V)*nat(V)*nat(V/2)+nat(V)*350*nat(V)*nat(V/2)+nat(V)*36*nat(nat(V)+ -2)+nat(V)*64*nat(nat(V)+ -1)+nat(V)*613*nat(V/2)+nat(V29)*147+nat(V29)*60*nat(V29/2)+nat(nat(V)+ -2)*28*nat(V/2)+nat(nat(V+V29)+ -2)*28*nat(V+V29)+nat(nat(2*V+V29)+ -2)*28*nat(V+V29/2)+nat(nat(2*V+V29)+ -2)*4*nat(2*V+V29)+nat(nat(2*V+V29)+ -1)*32*nat(2*V+V29)+nat(2*V)+nat(V+V29)*410+nat(V+V29)*767*nat(V+V29)+nat(V+V29)*370*nat(V+V29)*nat(V+V29)+nat(V+V29)*35*nat(V+V29)*nat(V+V29)*nat(V+V29)+nat(V+V29/2)*101+nat(V+V29/2)*631*nat(2*V+V29)+nat(V+V29/2)*350*nat(2*V+V29)*nat(2*V+V29)+nat(V+V29/2)*35*nat(2*V+V29)*nat(2*V+V29)*nat(2*V+V29)+nat(2*V+V29)*1316+nat(2*V+V29)*1177*nat(2*V+V29)+nat(2*V+V29)*318*nat(2*V+V29)*nat(2*V+V29)+nat(2*V+V29)*45*nat(2*V+V29)*nat(2*V+V29)*nat(2*V+V29)+nat(V/2)*95+nat(V29/2)*18]),nat(V)*2*nat(V29)+3+nat(V)*2*nat(-V+V29)+nat(V29)*3972+nat(V29)*3533*nat(V29)+nat(V29)*954*nat(V29)*nat(V29)+nat(V29)*135*nat(V29)*nat(V29)*nat(V29)+nat(V29)*105*nat(V29)*nat(V29)*nat(V29/2)+nat(V29)*1050*nat(V29)*nat(V29/2)+nat(V29)*12*nat(nat(V29)+ -2)+nat(V29)*96*nat(nat(V29)+ -1)+nat(V29)*1893*nat(V29/2)+nat(nat(V29)+ -2)*84*nat(V29/2)+nat(-V+V29)*6+nat(V29/2)*303]),24*V1*V1+268*V1+2*V1*nat(V)+92*V1*nat(V1+V)+20*V1*nat(V1+V)*nat(V1+V)+2*V1*nat(-V1+V)+V1/2*(42*V1)+nat(nat(V1+V)+ -2)*4*nat(V1+V)+nat(nat(V1+V)+ -2)*28*nat(V1/2+V/2)+nat(nat(V1+V)+ -1)*32*nat(V1+V)+nat(V1+V)*1115+nat(V1+V)*1061*nat(V1+V)+nat(V1+V)*298*nat(V1+V)*nat(V1+V)+nat(V1+V)*45*nat(V1+V)*nat(V1+V)*nat(V1+V)+nat(V1+V)*35*nat(V1+V)*nat(V1+V)*nat(V1/2+V/2)+nat(V1+V)*350*nat(V1+V)*nat(V1/2+V/2)+nat(V1+V)*613*nat(V1/2+V/2)+nat(-V1+V)*6+nat(V1/2+V/2)*95+7*V1])]),nat(V)*2*nat(-V+V29)+nat(V)*2*nat(V29)+nat(V29)*24+nat(V29)*2*nat(V29)+nat(-V+V29)*6])+nat(V)+1 1124.61/291.71 Asymptotic class: n^4 1124.61/291.71 * Total analysis performed in 7615 ms. 1124.61/291.71 1124.61/291.71 1124.61/291.71 ---------------------------------------- 1124.61/291.71 1124.61/291.71 (10) 1124.61/291.71 BOUNDS(1, n^4) 1124.61/291.71 1124.61/291.71 ---------------------------------------- 1124.61/291.71 1124.61/291.71 (11) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1124.61/291.71 Transformed a relative TRS into a decreasing-loop problem. 1124.61/291.71 ---------------------------------------- 1124.61/291.71 1124.61/291.71 (12) 1124.61/291.71 Obligation: 1124.61/291.71 Analyzing the following TRS for decreasing loops: 1124.61/291.71 1124.61/291.71 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^4). 1124.61/291.71 1124.61/291.71 1124.61/291.71 The TRS R consists of the following rules: 1124.61/291.71 1124.61/291.71 eq(0, 0) -> true 1124.61/291.71 eq(0, s(x)) -> false 1124.61/291.71 eq(s(x), 0) -> false 1124.61/291.71 eq(s(x), s(y)) -> eq(x, y) 1124.61/291.71 le(0, y) -> true 1124.61/291.71 le(s(x), 0) -> false 1124.61/291.71 le(s(x), s(y)) -> le(x, y) 1124.61/291.71 app(nil, y) -> y 1124.61/291.71 app(add(n, x), y) -> add(n, app(x, y)) 1124.61/291.71 min(add(n, nil)) -> n 1124.61/291.71 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 1124.61/291.71 if_min(true, add(n, add(m, x))) -> min(add(n, x)) 1124.61/291.71 if_min(false, add(n, add(m, x))) -> min(add(m, x)) 1124.61/291.71 rm(n, nil) -> nil 1124.61/291.71 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 1124.61/291.71 if_rm(true, n, add(m, x)) -> rm(n, x) 1124.61/291.71 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) 1124.61/291.71 minsort(nil, nil) -> nil 1124.61/291.71 minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) 1124.61/291.71 if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) 1124.61/291.71 if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) 1124.61/291.71 1124.61/291.71 S is empty. 1124.61/291.71 Rewrite Strategy: INNERMOST 1124.61/291.71 ---------------------------------------- 1124.61/291.71 1124.61/291.71 (13) DecreasingLoopProof (LOWER BOUND(ID)) 1124.61/291.71 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1124.61/291.71 1124.61/291.71 The rewrite sequence 1124.61/291.71 1124.61/291.71 le(s(x), s(y)) ->^+ le(x, y) 1124.61/291.71 1124.61/291.71 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1124.61/291.71 1124.61/291.71 The pumping substitution is [x / s(x), y / s(y)]. 1124.61/291.71 1124.61/291.71 The result substitution is [ ]. 1124.61/291.71 1124.61/291.71 1124.61/291.71 1124.61/291.71 1124.61/291.71 ---------------------------------------- 1124.61/291.71 1124.61/291.71 (14) 1124.61/291.71 Complex Obligation (BEST) 1124.61/291.71 1124.61/291.71 ---------------------------------------- 1124.61/291.71 1124.61/291.71 (15) 1124.61/291.71 Obligation: 1124.61/291.71 Proved the lower bound n^1 for the following obligation: 1124.61/291.71 1124.61/291.71 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^4). 1124.61/291.71 1124.61/291.71 1124.61/291.71 The TRS R consists of the following rules: 1124.61/291.71 1124.61/291.71 eq(0, 0) -> true 1124.61/291.71 eq(0, s(x)) -> false 1124.61/291.71 eq(s(x), 0) -> false 1124.61/291.71 eq(s(x), s(y)) -> eq(x, y) 1124.61/291.71 le(0, y) -> true 1124.61/291.71 le(s(x), 0) -> false 1124.61/291.71 le(s(x), s(y)) -> le(x, y) 1124.61/291.71 app(nil, y) -> y 1124.61/291.71 app(add(n, x), y) -> add(n, app(x, y)) 1124.61/291.71 min(add(n, nil)) -> n 1124.61/291.71 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 1124.61/291.71 if_min(true, add(n, add(m, x))) -> min(add(n, x)) 1124.61/291.71 if_min(false, add(n, add(m, x))) -> min(add(m, x)) 1124.61/291.71 rm(n, nil) -> nil 1124.61/291.71 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 1124.61/291.71 if_rm(true, n, add(m, x)) -> rm(n, x) 1124.61/291.71 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) 1124.61/291.71 minsort(nil, nil) -> nil 1124.61/291.71 minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) 1124.61/291.71 if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) 1124.61/291.71 if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) 1124.61/291.71 1124.61/291.71 S is empty. 1124.61/291.71 Rewrite Strategy: INNERMOST 1124.61/291.71 ---------------------------------------- 1124.61/291.71 1124.61/291.71 (16) LowerBoundPropagationProof (FINISHED) 1124.61/291.71 Propagated lower bound. 1124.61/291.71 ---------------------------------------- 1124.61/291.71 1124.61/291.71 (17) 1124.61/291.71 BOUNDS(n^1, INF) 1124.61/291.71 1124.61/291.71 ---------------------------------------- 1124.61/291.71 1124.61/291.71 (18) 1124.61/291.71 Obligation: 1124.61/291.71 Analyzing the following TRS for decreasing loops: 1124.61/291.71 1124.61/291.71 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^4). 1124.61/291.71 1124.61/291.71 1124.61/291.71 The TRS R consists of the following rules: 1124.61/291.71 1124.61/291.71 eq(0, 0) -> true 1124.61/291.71 eq(0, s(x)) -> false 1124.61/291.71 eq(s(x), 0) -> false 1124.61/291.71 eq(s(x), s(y)) -> eq(x, y) 1124.61/291.71 le(0, y) -> true 1124.61/291.71 le(s(x), 0) -> false 1124.61/291.71 le(s(x), s(y)) -> le(x, y) 1124.61/291.71 app(nil, y) -> y 1124.61/291.71 app(add(n, x), y) -> add(n, app(x, y)) 1124.61/291.71 min(add(n, nil)) -> n 1124.61/291.71 min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 1124.61/291.71 if_min(true, add(n, add(m, x))) -> min(add(n, x)) 1124.61/291.71 if_min(false, add(n, add(m, x))) -> min(add(m, x)) 1124.61/291.71 rm(n, nil) -> nil 1124.61/291.71 rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 1124.61/291.71 if_rm(true, n, add(m, x)) -> rm(n, x) 1124.61/291.71 if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) 1124.61/291.71 minsort(nil, nil) -> nil 1124.61/291.71 minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) 1124.61/291.71 if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) 1124.61/291.71 if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) 1124.61/291.71 1124.61/291.71 S is empty. 1124.61/291.71 Rewrite Strategy: INNERMOST 1124.92/291.77 EOF