WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 365 ms] (4) CpxRelTRS (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxWeightedTrs (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedTrs (11) CompletionProof [UPPER BOUND(ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) CompleteCoflocoProof [FINISHED, 6332 ms] (16) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(g(i(a, b, b'), c), d) -> if(e, f(.(b, c), d'), f(.(b', c), d')) f(g(h(a, b), c), d) -> if(e, f(.(b, g(h(a, b), c)), d), f(c, d')) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(i(x_1, x_2, x_3)) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(a) -> a encArg(b) -> b encArg(b') -> b' encArg(c) -> c encArg(d) -> d encArg(if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(e) -> e encArg(.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) encArg(d') -> d' encArg(h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_i(x_1, x_2, x_3) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) encode_a -> a encode_b -> b encode_b' -> b' encode_c -> c encode_d -> d encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_e -> e encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) encode_d' -> d' encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(g(i(a, b, b'), c), d) -> if(e, f(.(b, c), d'), f(.(b', c), d')) f(g(h(a, b), c), d) -> if(e, f(.(b, g(h(a, b), c)), d), f(c, d')) The (relative) TRS S consists of the following rules: encArg(g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(i(x_1, x_2, x_3)) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(a) -> a encArg(b) -> b encArg(b') -> b' encArg(c) -> c encArg(d) -> d encArg(if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(e) -> e encArg(.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) encArg(d') -> d' encArg(h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_i(x_1, x_2, x_3) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) encode_a -> a encode_b -> b encode_b' -> b' encode_c -> c encode_d -> d encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_e -> e encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) encode_d' -> d' encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) Rewrite Strategy: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(g(i(a, b, b'), c), d) -> if(e, f(.(b, c), d'), f(.(b', c), d')) f(g(h(a, b), c), d) -> if(e, f(.(b, g(h(a, b), c)), d), f(c, d')) The (relative) TRS S consists of the following rules: encArg(g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(i(x_1, x_2, x_3)) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(a) -> a encArg(b) -> b encArg(b') -> b' encArg(c) -> c encArg(d) -> d encArg(if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(e) -> e encArg(.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) encArg(d') -> d' encArg(h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_i(x_1, x_2, x_3) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) encode_a -> a encode_b -> b encode_b' -> b' encode_c -> c encode_d -> d encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_e -> e encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) encode_d' -> d' encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) Rewrite Strategy: FULL ---------------------------------------- (5) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS is a non-duplicating overlay system, we have rc = irc. ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(g(i(a, b, b'), c), d) -> if(e, f(.(b, c), d'), f(.(b', c), d')) f(g(h(a, b), c), d) -> if(e, f(.(b, g(h(a, b), c)), d), f(c, d')) The (relative) TRS S consists of the following rules: encArg(g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(i(x_1, x_2, x_3)) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(a) -> a encArg(b) -> b encArg(b') -> b' encArg(c) -> c encArg(d) -> d encArg(if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(e) -> e encArg(.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) encArg(d') -> d' encArg(h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_i(x_1, x_2, x_3) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) encode_a -> a encode_b -> b encode_b' -> b' encode_c -> c encode_d -> d encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_e -> e encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) encode_d' -> d' encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) Rewrite Strategy: INNERMOST ---------------------------------------- (7) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: f(g(i(a, b, b'), c), d) -> if(e, f(.(b, c), d'), f(.(b', c), d')) [1] f(g(h(a, b), c), d) -> if(e, f(.(b, g(h(a, b), c)), d), f(c, d')) [1] encArg(g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0] encArg(i(x_1, x_2, x_3)) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(a) -> a [0] encArg(b) -> b [0] encArg(b') -> b' [0] encArg(c) -> c [0] encArg(d) -> d [0] encArg(if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(e) -> e [0] encArg(.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) [0] encArg(d') -> d' [0] encArg(h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0] encode_i(x_1, x_2, x_3) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_a -> a [0] encode_b -> b [0] encode_b' -> b' [0] encode_c -> c [0] encode_d -> d [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_e -> e [0] encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) [0] encode_d' -> d' [0] encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: f(g(i(a, b, b'), c), d) -> if(e, f(.(b, c), d'), f(.(b', c), d')) [1] f(g(h(a, b), c), d) -> if(e, f(.(b, g(h(a, b), c)), d), f(c, d')) [1] encArg(g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0] encArg(i(x_1, x_2, x_3)) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(a) -> a [0] encArg(b) -> b [0] encArg(b') -> b' [0] encArg(c) -> c [0] encArg(d) -> d [0] encArg(if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(e) -> e [0] encArg(.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) [0] encArg(d') -> d' [0] encArg(h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0] encode_i(x_1, x_2, x_3) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_a -> a [0] encode_b -> b [0] encode_b' -> b' [0] encode_c -> c [0] encode_d -> d [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_e -> e [0] encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) [0] encode_d' -> d' [0] encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) [0] The TRS has the following type information: f :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f g :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f i :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f a :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f b :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f b' :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f c :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f d :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f if :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f e :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f . :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f d' :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f h :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f encArg :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f cons_f :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_f :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_g :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_i :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_a :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_b :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_b' :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_c :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_d :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_if :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_e :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_. :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_d' :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f encode_h :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f Rewrite Strategy: INNERMOST ---------------------------------------- (11) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_g(v0, v1) -> null_encode_g [0] encode_i(v0, v1, v2) -> null_encode_i [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] encode_b' -> null_encode_b' [0] encode_c -> null_encode_c [0] encode_d -> null_encode_d [0] encode_if(v0, v1, v2) -> null_encode_if [0] encode_e -> null_encode_e [0] encode_.(v0, v1) -> null_encode_. [0] encode_d' -> null_encode_d' [0] encode_h(v0, v1) -> null_encode_h [0] f(v0, v1) -> null_f [0] And the following fresh constants: null_encArg, null_encode_f, null_encode_g, null_encode_i, null_encode_a, null_encode_b, null_encode_b', null_encode_c, null_encode_d, null_encode_if, null_encode_e, null_encode_., null_encode_d', null_encode_h, null_f ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: f(g(i(a, b, b'), c), d) -> if(e, f(.(b, c), d'), f(.(b', c), d')) [1] f(g(h(a, b), c), d) -> if(e, f(.(b, g(h(a, b), c)), d), f(c, d')) [1] encArg(g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0] encArg(i(x_1, x_2, x_3)) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(a) -> a [0] encArg(b) -> b [0] encArg(b') -> b' [0] encArg(c) -> c [0] encArg(d) -> d [0] encArg(if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encArg(e) -> e [0] encArg(.(x_1, x_2)) -> .(encArg(x_1), encArg(x_2)) [0] encArg(d') -> d' [0] encArg(h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0] encode_i(x_1, x_2, x_3) -> i(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_a -> a [0] encode_b -> b [0] encode_b' -> b' [0] encode_c -> c [0] encode_d -> d [0] encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) [0] encode_e -> e [0] encode_.(x_1, x_2) -> .(encArg(x_1), encArg(x_2)) [0] encode_d' -> d' [0] encode_h(x_1, x_2) -> h(encArg(x_1), encArg(x_2)) [0] encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_g(v0, v1) -> null_encode_g [0] encode_i(v0, v1, v2) -> null_encode_i [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] encode_b' -> null_encode_b' [0] encode_c -> null_encode_c [0] encode_d -> null_encode_d [0] encode_if(v0, v1, v2) -> null_encode_if [0] encode_e -> null_encode_e [0] encode_.(v0, v1) -> null_encode_. [0] encode_d' -> null_encode_d' [0] encode_h(v0, v1) -> null_encode_h [0] f(v0, v1) -> null_f [0] The TRS has the following type information: f :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f g :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f i :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f a :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f b :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f b' :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f c :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f d :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f if :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f e :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f . :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f d' :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f h :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encArg :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f cons_f :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_f :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_g :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_i :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_a :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_b :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_b' :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_c :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_d :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_if :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_e :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_. :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_d' :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f encode_h :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f -> a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encArg :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_f :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_g :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_i :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_a :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_b :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_b' :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_c :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_d :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_if :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_e :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_. :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_d' :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_encode_h :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f null_f :: a:b:b':i:c:g:d:e:.:d':if:h:cons_f:null_encArg:null_encode_f:null_encode_g:null_encode_i:null_encode_a:null_encode_b:null_encode_b':null_encode_c:null_encode_d:null_encode_if:null_encode_e:null_encode_.:null_encode_d':null_encode_h:null_f Rewrite Strategy: INNERMOST ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: a => 0 b => 1 b' => 2 c => 3 d => 4 e => 6 d' => 5 null_encArg => 0 null_encode_f => 0 null_encode_g => 0 null_encode_i => 0 null_encode_a => 0 null_encode_b => 0 null_encode_b' => 0 null_encode_c => 0 null_encode_d => 0 null_encode_if => 0 null_encode_e => 0 null_encode_. => 0 null_encode_d' => 0 null_encode_h => 0 null_f => 0 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 6 :|: z = 6 encArg(z) -{ 0 }-> 5 :|: z = 5 encArg(z) -{ 0 }-> 4 :|: z = 4 encArg(z) -{ 0 }-> 3 :|: z = 3 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) + encArg(x_3) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0 encode_.(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_.(z, z') -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_a -{ 0 }-> 0 :|: encode_b -{ 0 }-> 1 :|: encode_b -{ 0 }-> 0 :|: encode_b' -{ 0 }-> 2 :|: encode_b' -{ 0 }-> 0 :|: encode_c -{ 0 }-> 3 :|: encode_c -{ 0 }-> 0 :|: encode_d -{ 0 }-> 4 :|: encode_d -{ 0 }-> 0 :|: encode_d' -{ 0 }-> 5 :|: encode_d' -{ 0 }-> 0 :|: encode_e -{ 0 }-> 6 :|: encode_e -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_g(z, z') -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_h(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_h(z, z') -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_i(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_i(z, z', z'') -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) + encArg(x_3) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 encode_if(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 encode_if(z, z', z'') -{ 0 }-> 1 + encArg(x_1) + encArg(x_2) + encArg(x_3) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3 f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 f(z, z') -{ 1 }-> 1 + 6 + f(1 + 1 + 3, 5) + f(1 + 2 + 3, 5) :|: z = 1 + (1 + 0 + 1 + 2) + 3, z' = 4 f(z, z') -{ 1 }-> 1 + 6 + f(1 + 1 + (1 + (1 + 0 + 1) + 3), 4) + f(3, 5) :|: z' = 4, z = 1 + (1 + 0 + 1) + 3 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (15) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V1, V, V13),0,[f(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V13),0,[encArg(V1, Out)],[V1 >= 0]). eq(start(V1, V, V13),0,[fun(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V13),0,[fun1(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V13),0,[fun2(V1, V, V13, Out)],[V1 >= 0,V >= 0,V13 >= 0]). eq(start(V1, V, V13),0,[fun3(Out)],[]). eq(start(V1, V, V13),0,[fun4(Out)],[]). eq(start(V1, V, V13),0,[fun5(Out)],[]). eq(start(V1, V, V13),0,[fun6(Out)],[]). eq(start(V1, V, V13),0,[fun7(Out)],[]). eq(start(V1, V, V13),0,[fun8(V1, V, V13, Out)],[V1 >= 0,V >= 0,V13 >= 0]). eq(start(V1, V, V13),0,[fun9(Out)],[]). eq(start(V1, V, V13),0,[fun10(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V13),0,[fun11(Out)],[]). eq(start(V1, V, V13),0,[fun12(V1, V, Out)],[V1 >= 0,V >= 0]). eq(f(V1, V, Out),1,[f(1 + 1 + 3, 5, Ret01),f(1 + 2 + 3, 5, Ret1)],[Out = 7 + Ret01 + Ret1,V1 = 8,V = 4]). eq(f(V1, V, Out),1,[f(1 + 1 + (1 + (1 + 0 + 1) + 3), 4, Ret011),f(3, 5, Ret11)],[Out = 7 + Ret011 + Ret11,V = 4,V1 = 6]). eq(encArg(V1, Out),0,[encArg(V3, Ret012),encArg(V2, Ret12)],[Out = 1 + Ret012 + Ret12,V3 >= 0,V1 = 1 + V2 + V3,V2 >= 0]). eq(encArg(V1, Out),0,[encArg(V5, Ret001),encArg(V6, Ret013),encArg(V4, Ret13)],[Out = 1 + Ret001 + Ret013 + Ret13,V5 >= 0,V1 = 1 + V4 + V5 + V6,V4 >= 0,V6 >= 0]). eq(encArg(V1, Out),0,[],[Out = 0,V1 = 0]). eq(encArg(V1, Out),0,[],[Out = 1,V1 = 1]). eq(encArg(V1, Out),0,[],[Out = 2,V1 = 2]). eq(encArg(V1, Out),0,[],[Out = 3,V1 = 3]). eq(encArg(V1, Out),0,[],[Out = 4,V1 = 4]). eq(encArg(V1, Out),0,[],[Out = 6,V1 = 6]). eq(encArg(V1, Out),0,[],[Out = 5,V1 = 5]). eq(encArg(V1, Out),0,[encArg(V8, Ret0),encArg(V7, Ret14),f(Ret0, Ret14, Ret)],[Out = Ret,V8 >= 0,V1 = 1 + V7 + V8,V7 >= 0]). eq(fun(V1, V, Out),0,[encArg(V10, Ret02),encArg(V9, Ret15),f(Ret02, Ret15, Ret2)],[Out = Ret2,V10 >= 0,V9 >= 0,V1 = V10,V = V9]). eq(fun1(V1, V, Out),0,[encArg(V12, Ret014),encArg(V11, Ret16)],[Out = 1 + Ret014 + Ret16,V12 >= 0,V11 >= 0,V1 = V12,V = V11]). eq(fun2(V1, V, V13, Out),0,[encArg(V15, Ret0011),encArg(V16, Ret015),encArg(V14, Ret17)],[Out = 1 + Ret0011 + Ret015 + Ret17,V15 >= 0,V14 >= 0,V16 >= 0,V1 = V15,V = V16,V13 = V14]). eq(fun3(Out),0,[],[Out = 0]). eq(fun4(Out),0,[],[Out = 1]). eq(fun5(Out),0,[],[Out = 2]). eq(fun6(Out),0,[],[Out = 3]). eq(fun7(Out),0,[],[Out = 4]). eq(fun8(V1, V, V13, Out),0,[encArg(V19, Ret0012),encArg(V18, Ret016),encArg(V17, Ret18)],[Out = 1 + Ret0012 + Ret016 + Ret18,V19 >= 0,V17 >= 0,V18 >= 0,V1 = V19,V = V18,V13 = V17]). eq(fun9(Out),0,[],[Out = 6]). eq(fun10(V1, V, Out),0,[encArg(V21, Ret017),encArg(V20, Ret19)],[Out = 1 + Ret017 + Ret19,V21 >= 0,V20 >= 0,V1 = V21,V = V20]). eq(fun11(Out),0,[],[Out = 5]). eq(fun12(V1, V, Out),0,[encArg(V23, Ret018),encArg(V22, Ret110)],[Out = 1 + Ret018 + Ret110,V23 >= 0,V22 >= 0,V1 = V23,V = V22]). eq(encArg(V1, Out),0,[],[Out = 0,V24 >= 0,V1 = V24]). eq(fun(V1, V, Out),0,[],[Out = 0,V26 >= 0,V25 >= 0,V1 = V26,V = V25]). eq(fun1(V1, V, Out),0,[],[Out = 0,V28 >= 0,V27 >= 0,V1 = V28,V = V27]). eq(fun2(V1, V, V13, Out),0,[],[Out = 0,V29 >= 0,V13 = V31,V30 >= 0,V1 = V29,V = V30,V31 >= 0]). eq(fun4(Out),0,[],[Out = 0]). eq(fun5(Out),0,[],[Out = 0]). eq(fun6(Out),0,[],[Out = 0]). eq(fun7(Out),0,[],[Out = 0]). eq(fun8(V1, V, V13, Out),0,[],[Out = 0,V32 >= 0,V13 = V33,V34 >= 0,V1 = V32,V = V34,V33 >= 0]). eq(fun9(Out),0,[],[Out = 0]). eq(fun10(V1, V, Out),0,[],[Out = 0,V36 >= 0,V35 >= 0,V1 = V36,V = V35]). eq(fun11(Out),0,[],[Out = 0]). eq(fun12(V1, V, Out),0,[],[Out = 0,V38 >= 0,V37 >= 0,V1 = V38,V = V37]). eq(f(V1, V, Out),0,[],[Out = 0,V39 >= 0,V40 >= 0,V1 = V39,V = V40]). input_output_vars(f(V1,V,Out),[V1,V],[Out]). input_output_vars(encArg(V1,Out),[V1],[Out]). input_output_vars(fun(V1,V,Out),[V1,V],[Out]). input_output_vars(fun1(V1,V,Out),[V1,V],[Out]). input_output_vars(fun2(V1,V,V13,Out),[V1,V,V13],[Out]). input_output_vars(fun3(Out),[],[Out]). input_output_vars(fun4(Out),[],[Out]). input_output_vars(fun5(Out),[],[Out]). input_output_vars(fun6(Out),[],[Out]). input_output_vars(fun7(Out),[],[Out]). input_output_vars(fun8(V1,V,V13,Out),[V1,V,V13],[Out]). input_output_vars(fun9(Out),[],[Out]). input_output_vars(fun10(V1,V,Out),[V1,V],[Out]). input_output_vars(fun11(Out),[],[Out]). input_output_vars(fun12(V1,V,Out),[V1,V],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive [multiple] : [f/3] 1. recursive [non_tail,multiple] : [encArg/2] 2. non_recursive : [fun/3] 3. non_recursive : [fun1/3] 4. non_recursive : [fun10/3] 5. non_recursive : [fun11/1] 6. non_recursive : [fun12/3] 7. non_recursive : [fun2/4] 8. non_recursive : [fun3/1] 9. non_recursive : [fun4/1] 10. non_recursive : [fun5/1] 11. non_recursive : [fun6/1] 12. non_recursive : [fun7/1] 13. non_recursive : [fun8/4] 14. non_recursive : [fun9/1] 15. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into f/3 1. SCC is partially evaluated into encArg/2 2. SCC is partially evaluated into fun/3 3. SCC is partially evaluated into fun1/3 4. SCC is partially evaluated into fun10/3 5. SCC is partially evaluated into fun11/1 6. SCC is partially evaluated into fun12/3 7. SCC is partially evaluated into fun2/4 8. SCC is completely evaluated into other SCCs 9. SCC is partially evaluated into fun4/1 10. SCC is partially evaluated into fun5/1 11. SCC is partially evaluated into fun6/1 12. SCC is partially evaluated into fun7/1 13. SCC is partially evaluated into fun8/4 14. SCC is partially evaluated into fun9/1 15. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations f/3 * CE 18 is refined into CE [53] * CE 16 is refined into CE [54] * CE 17 is refined into CE [55] ### Cost equations --> "Loop" of f/3 * CEs [54] --> Loop 32 * CEs [55] --> Loop 33 * CEs [53] --> Loop 34 ### Ranking functions of CR f(V1,V,Out) #### Partial ranking functions of CR f(V1,V,Out) ### Specialization of cost equations encArg/2 * CE 21 is refined into CE [56] * CE 26 is refined into CE [57] * CE 27 is refined into CE [58] * CE 25 is refined into CE [59] * CE 24 is refined into CE [60] * CE 23 is refined into CE [61] * CE 22 is refined into CE [62] * CE 19 is refined into CE [63] * CE 28 is refined into CE [64,65,66] * CE 20 is refined into CE [67] ### Cost equations --> "Loop" of encArg/2 * CEs [67] --> Loop 35 * CEs [63] --> Loop 36 * CEs [64] --> Loop 37 * CEs [65] --> Loop 38 * CEs [66] --> Loop 39 * CEs [56] --> Loop 40 * CEs [57] --> Loop 41 * CEs [58] --> Loop 42 * CEs [59] --> Loop 43 * CEs [60] --> Loop 44 * CEs [61] --> Loop 45 * CEs [62] --> Loop 46 ### Ranking functions of CR encArg(V1,Out) * RF of phase [35,36,37,38,39]: [V1] #### Partial ranking functions of CR encArg(V1,Out) * Partial RF of phase [35,36,37,38,39]: - RF of loop [35:1,35:2,35:3,36:1,36:2,37:1,37:2,38:1,38:2,39:1,39:2]: V1 ### Specialization of cost equations fun/3 * CE 29 is refined into CE [68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122] * CE 30 is refined into CE [123] ### Cost equations --> "Loop" of fun/3 * CEs [69] --> Loop 47 * CEs [73,74] --> Loop 48 * CEs [71,117] --> Loop 49 * CEs [114] --> Loop 50 * CEs [113] --> Loop 51 * CEs [68,107,111] --> Loop 52 * CEs [112] --> Loop 53 * CEs [110] --> Loop 54 * CEs [108,109,115] --> Loop 55 * CEs [105] --> Loop 56 * CEs [104] --> Loop 57 * CEs [103] --> Loop 58 * CEs [102] --> Loop 59 * CEs [100,101,106] --> Loop 60 * CEs [98] --> Loop 61 * CEs [97] --> Loop 62 * CEs [96] --> Loop 63 * CEs [95] --> Loop 64 * CEs [93,94,99] --> Loop 65 * CEs [91] --> Loop 66 * CEs [90] --> Loop 67 * CEs [89] --> Loop 68 * CEs [88] --> Loop 69 * CEs [86,87,92] --> Loop 70 * CEs [77,84,121] --> Loop 71 * CEs [76,83,120] --> Loop 72 * CEs [75,82,119] --> Loop 73 * CEs [72,81,118] --> Loop 74 * CEs [70,78,79,80,85,116,122,123] --> Loop 75 ### Ranking functions of CR fun(V1,V,Out) #### Partial ranking functions of CR fun(V1,V,Out) ### Specialization of cost equations fun1/3 * CE 31 is refined into CE [124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172] * CE 32 is refined into CE [173] ### Cost equations --> "Loop" of fun1/3 * CEs [172] --> Loop 76 * CEs [173] --> Loop 77 * CEs [171] --> Loop 78 * CEs [170] --> Loop 79 * CEs [169] --> Loop 80 * CEs [168] --> Loop 81 * CEs [125] --> Loop 82 * CEs [167] --> Loop 83 * CEs [165] --> Loop 84 * CEs [164] --> Loop 85 * CEs [163] --> Loop 86 * CEs [162] --> Loop 87 * CEs [161] --> Loop 88 * CEs [159,160] --> Loop 89 * CEs [158] --> Loop 90 * CEs [157] --> Loop 91 * CEs [156] --> Loop 92 * CEs [155] --> Loop 93 * CEs [154] --> Loop 94 * CEs [152,153] --> Loop 95 * CEs [151] --> Loop 96 * CEs [150] --> Loop 97 * CEs [149] --> Loop 98 * CEs [148] --> Loop 99 * CEs [147] --> Loop 100 * CEs [145,146] --> Loop 101 * CEs [144] --> Loop 102 * CEs [143] --> Loop 103 * CEs [142] --> Loop 104 * CEs [141] --> Loop 105 * CEs [140] --> Loop 106 * CEs [138,139] --> Loop 107 * CEs [137] --> Loop 108 * CEs [129,136] --> Loop 109 * CEs [128,135] --> Loop 110 * CEs [127,134] --> Loop 111 * CEs [126,130,133] --> Loop 112 * CEs [124,131,132,166] --> Loop 113 ### Ranking functions of CR fun1(V1,V,Out) #### Partial ranking functions of CR fun1(V1,V,Out) ### Specialization of cost equations fun10/3 * CE 47 is refined into CE [174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222] * CE 48 is refined into CE [223] ### Cost equations --> "Loop" of fun10/3 * CEs [222] --> Loop 114 * CEs [223] --> Loop 115 * CEs [221] --> Loop 116 * CEs [220] --> Loop 117 * CEs [219] --> Loop 118 * CEs [218] --> Loop 119 * CEs [175] --> Loop 120 * CEs [217] --> Loop 121 * CEs [215] --> Loop 122 * CEs [214] --> Loop 123 * CEs [213] --> Loop 124 * CEs [212] --> Loop 125 * CEs [211] --> Loop 126 * CEs [209,210] --> Loop 127 * CEs [208] --> Loop 128 * CEs [207] --> Loop 129 * CEs [206] --> Loop 130 * CEs [205] --> Loop 131 * CEs [204] --> Loop 132 * CEs [202,203] --> Loop 133 * CEs [201] --> Loop 134 * CEs [200] --> Loop 135 * CEs [199] --> Loop 136 * CEs [198] --> Loop 137 * CEs [197] --> Loop 138 * CEs [195,196] --> Loop 139 * CEs [194] --> Loop 140 * CEs [193] --> Loop 141 * CEs [192] --> Loop 142 * CEs [191] --> Loop 143 * CEs [190] --> Loop 144 * CEs [188,189] --> Loop 145 * CEs [187] --> Loop 146 * CEs [179,186] --> Loop 147 * CEs [178,185] --> Loop 148 * CEs [177,184] --> Loop 149 * CEs [176,180,183] --> Loop 150 * CEs [174,181,182,216] --> Loop 151 ### Ranking functions of CR fun10(V1,V,Out) #### Partial ranking functions of CR fun10(V1,V,Out) ### Specialization of cost equations fun11/1 * CE 49 is refined into CE [224] * CE 50 is refined into CE [225] ### Cost equations --> "Loop" of fun11/1 * CEs [224] --> Loop 152 * CEs [225] --> Loop 153 ### Ranking functions of CR fun11(Out) #### Partial ranking functions of CR fun11(Out) ### Specialization of cost equations fun12/3 * CE 51 is refined into CE [226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274] * CE 52 is refined into CE [275] ### Cost equations --> "Loop" of fun12/3 * CEs [274] --> Loop 154 * CEs [275] --> Loop 155 * CEs [273] --> Loop 156 * CEs [272] --> Loop 157 * CEs [271] --> Loop 158 * CEs [270] --> Loop 159 * CEs [227] --> Loop 160 * CEs [269] --> Loop 161 * CEs [267] --> Loop 162 * CEs [266] --> Loop 163 * CEs [265] --> Loop 164 * CEs [264] --> Loop 165 * CEs [263] --> Loop 166 * CEs [261,262] --> Loop 167 * CEs [260] --> Loop 168 * CEs [259] --> Loop 169 * CEs [258] --> Loop 170 * CEs [257] --> Loop 171 * CEs [256] --> Loop 172 * CEs [254,255] --> Loop 173 * CEs [253] --> Loop 174 * CEs [252] --> Loop 175 * CEs [251] --> Loop 176 * CEs [250] --> Loop 177 * CEs [249] --> Loop 178 * CEs [247,248] --> Loop 179 * CEs [246] --> Loop 180 * CEs [245] --> Loop 181 * CEs [244] --> Loop 182 * CEs [243] --> Loop 183 * CEs [242] --> Loop 184 * CEs [240,241] --> Loop 185 * CEs [239] --> Loop 186 * CEs [231,238] --> Loop 187 * CEs [230,237] --> Loop 188 * CEs [229,236] --> Loop 189 * CEs [228,232,235] --> Loop 190 * CEs [226,233,234,268] --> Loop 191 ### Ranking functions of CR fun12(V1,V,Out) #### Partial ranking functions of CR fun12(V1,V,Out) ### Specialization of cost equations fun2/4 * CE 33 is refined into CE [276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618] * CE 34 is refined into CE [619] ### Cost equations --> "Loop" of fun2/4 * CEs [618] --> Loop 192 * CEs [619] --> Loop 193 * CEs [617] --> Loop 194 * CEs [616] --> Loop 195 * CEs [615] --> Loop 196 * CEs [614] --> Loop 197 * CEs [613] --> Loop 198 * CEs [611] --> Loop 199 * CEs [610] --> Loop 200 * CEs [609] --> Loop 201 * CEs [608] --> Loop 202 * CEs [607] --> Loop 203 * CEs [312] --> Loop 204 * CEs [606] --> Loop 205 * CEs [604] --> Loop 206 * CEs [603] --> Loop 207 * CEs [602] --> Loop 208 * CEs [601] --> Loop 209 * CEs [600] --> Loop 210 * CEs [305] --> Loop 211 * CEs [599] --> Loop 212 * CEs [597] --> Loop 213 * CEs [596] --> Loop 214 * CEs [595] --> Loop 215 * CEs [594] --> Loop 216 * CEs [593] --> Loop 217 * CEs [298] --> Loop 218 * CEs [592] --> Loop 219 * CEs [590] --> Loop 220 * CEs [589] --> Loop 221 * CEs [588] --> Loop 222 * CEs [587] --> Loop 223 * CEs [586] --> Loop 224 * CEs [291] --> Loop 225 * CEs [585] --> Loop 226 * CEs [583] --> Loop 227 * CEs [288] --> Loop 228 * CEs [582] --> Loop 229 * CEs [287] --> Loop 230 * CEs [581] --> Loop 231 * CEs [286] --> Loop 232 * CEs [580] --> Loop 233 * CEs [285] --> Loop 234 * CEs [579] --> Loop 235 * CEs [284] --> Loop 236 * CEs [577,578] --> Loop 237 * CEs [569] --> Loop 238 * CEs [568] --> Loop 239 * CEs [567] --> Loop 240 * CEs [566] --> Loop 241 * CEs [565] --> Loop 242 * CEs [522] --> Loop 243 * CEs [564] --> Loop 244 * CEs [562] --> Loop 245 * CEs [561] --> Loop 246 * CEs [560] --> Loop 247 * CEs [559] --> Loop 248 * CEs [558] --> Loop 249 * CEs [556,557] --> Loop 250 * CEs [555] --> Loop 251 * CEs [554] --> Loop 252 * CEs [553] --> Loop 253 * CEs [552] --> Loop 254 * CEs [551] --> Loop 255 * CEs [549,550] --> Loop 256 * CEs [548] --> Loop 257 * CEs [547] --> Loop 258 * CEs [546] --> Loop 259 * CEs [545] --> Loop 260 * CEs [544] --> Loop 261 * CEs [542,543] --> Loop 262 * CEs [541] --> Loop 263 * CEs [540] --> Loop 264 * CEs [539] --> Loop 265 * CEs [538] --> Loop 266 * CEs [537] --> Loop 267 * CEs [535,536] --> Loop 268 * CEs [534] --> Loop 269 * CEs [526,533] --> Loop 270 * CEs [525,532] --> Loop 271 * CEs [524,531] --> Loop 272 * CEs [523,527,530] --> Loop 273 * CEs [521,528,529,563] --> Loop 274 * CEs [520] --> Loop 275 * CEs [519] --> Loop 276 * CEs [518] --> Loop 277 * CEs [517] --> Loop 278 * CEs [516] --> Loop 279 * CEs [473] --> Loop 280 * CEs [515] --> Loop 281 * CEs [513] --> Loop 282 * CEs [512] --> Loop 283 * CEs [511] --> Loop 284 * CEs [510] --> Loop 285 * CEs [509] --> Loop 286 * CEs [507,508] --> Loop 287 * CEs [506] --> Loop 288 * CEs [505] --> Loop 289 * CEs [504] --> Loop 290 * CEs [503] --> Loop 291 * CEs [502] --> Loop 292 * CEs [500,501] --> Loop 293 * CEs [499] --> Loop 294 * CEs [498] --> Loop 295 * CEs [497] --> Loop 296 * CEs [496] --> Loop 297 * CEs [495] --> Loop 298 * CEs [493,494] --> Loop 299 * CEs [492] --> Loop 300 * CEs [491] --> Loop 301 * CEs [490] --> Loop 302 * CEs [489] --> Loop 303 * CEs [488] --> Loop 304 * CEs [486,487] --> Loop 305 * CEs [485] --> Loop 306 * CEs [477,484] --> Loop 307 * CEs [476,483] --> Loop 308 * CEs [475,482] --> Loop 309 * CEs [474,478,481] --> Loop 310 * CEs [472,479,480,514] --> Loop 311 * CEs [471] --> Loop 312 * CEs [470] --> Loop 313 * CEs [469] --> Loop 314 * CEs [468] --> Loop 315 * CEs [467] --> Loop 316 * CEs [424] --> Loop 317 * CEs [466] --> Loop 318 * CEs [464] --> Loop 319 * CEs [463] --> Loop 320 * CEs [462] --> Loop 321 * CEs [461] --> Loop 322 * CEs [460] --> Loop 323 * CEs [458,459] --> Loop 324 * CEs [457] --> Loop 325 * CEs [456] --> Loop 326 * CEs [455] --> Loop 327 * CEs [454] --> Loop 328 * CEs [453] --> Loop 329 * CEs [451,452] --> Loop 330 * CEs [450] --> Loop 331 * CEs [449] --> Loop 332 * CEs [448] --> Loop 333 * CEs [447] --> Loop 334 * CEs [446] --> Loop 335 * CEs [444,445] --> Loop 336 * CEs [443] --> Loop 337 * CEs [442] --> Loop 338 * CEs [441] --> Loop 339 * CEs [440] --> Loop 340 * CEs [439] --> Loop 341 * CEs [437,438] --> Loop 342 * CEs [436] --> Loop 343 * CEs [428,435] --> Loop 344 * CEs [427,434] --> Loop 345 * CEs [426,433] --> Loop 346 * CEs [425,429,432] --> Loop 347 * CEs [423,430,431,465] --> Loop 348 * CEs [422] --> Loop 349 * CEs [421] --> Loop 350 * CEs [420] --> Loop 351 * CEs [419] --> Loop 352 * CEs [418] --> Loop 353 * CEs [375] --> Loop 354 * CEs [417] --> Loop 355 * CEs [415] --> Loop 356 * CEs [414] --> Loop 357 * CEs [413] --> Loop 358 * CEs [412] --> Loop 359 * CEs [411] --> Loop 360 * CEs [409,410] --> Loop 361 * CEs [408] --> Loop 362 * CEs [407] --> Loop 363 * CEs [406] --> Loop 364 * CEs [405] --> Loop 365 * CEs [404] --> Loop 366 * CEs [402,403] --> Loop 367 * CEs [401] --> Loop 368 * CEs [400] --> Loop 369 * CEs [399] --> Loop 370 * CEs [398] --> Loop 371 * CEs [397] --> Loop 372 * CEs [395,396] --> Loop 373 * CEs [394] --> Loop 374 * CEs [393] --> Loop 375 * CEs [392] --> Loop 376 * CEs [391] --> Loop 377 * CEs [390,572] --> Loop 378 * CEs [388,389] --> Loop 379 * CEs [387] --> Loop 380 * CEs [379,386] --> Loop 381 * CEs [378,385] --> Loop 382 * CEs [377,384] --> Loop 383 * CEs [376,380,383] --> Loop 384 * CEs [374,381,382,416] --> Loop 385 * CEs [373] --> Loop 386 * CEs [372] --> Loop 387 * CEs [371] --> Loop 388 * CEs [370] --> Loop 389 * CEs [278,320,369] --> Loop 390 * CEs [326,571] --> Loop 391 * CEs [277,319,368] --> Loop 392 * CEs [366] --> Loop 393 * CEs [316,365] --> Loop 394 * CEs [315,364] --> Loop 395 * CEs [314,363] --> Loop 396 * CEs [313,317,362] --> Loop 397 * CEs [311,360,361,605] --> Loop 398 * CEs [359] --> Loop 399 * CEs [309,358] --> Loop 400 * CEs [308,357] --> Loop 401 * CEs [307,356] --> Loop 402 * CEs [306,310,355] --> Loop 403 * CEs [304,353,354,598] --> Loop 404 * CEs [352] --> Loop 405 * CEs [302,351] --> Loop 406 * CEs [301,350] --> Loop 407 * CEs [300,349] --> Loop 408 * CEs [299,303,348] --> Loop 409 * CEs [297,346,347,591] --> Loop 410 * CEs [345] --> Loop 411 * CEs [295,323,344] --> Loop 412 * CEs [294,322,343] --> Loop 413 * CEs [293,321,342] --> Loop 414 * CEs [292,296,341] --> Loop 415 * CEs [290,339,340,584] --> Loop 416 * CEs [283,289,324,338] --> Loop 417 * CEs [281,330,337,575] --> Loop 418 * CEs [280,329,336,574] --> Loop 419 * CEs [279,328,335,573] --> Loop 420 * CEs [282,327,331,334,576] --> Loop 421 * CEs [276,318,325,332,333,367,570,612] --> Loop 422 ### Ranking functions of CR fun2(V1,V,V13,Out) #### Partial ranking functions of CR fun2(V1,V,V13,Out) ### Specialization of cost equations fun4/1 * CE 35 is refined into CE [620] * CE 36 is refined into CE [621] ### Cost equations --> "Loop" of fun4/1 * CEs [620] --> Loop 423 * CEs [621] --> Loop 424 ### Ranking functions of CR fun4(Out) #### Partial ranking functions of CR fun4(Out) ### Specialization of cost equations fun5/1 * CE 37 is refined into CE [622] * CE 38 is refined into CE [623] ### Cost equations --> "Loop" of fun5/1 * CEs [622] --> Loop 425 * CEs [623] --> Loop 426 ### Ranking functions of CR fun5(Out) #### Partial ranking functions of CR fun5(Out) ### Specialization of cost equations fun6/1 * CE 39 is refined into CE [624] * CE 40 is refined into CE [625] ### Cost equations --> "Loop" of fun6/1 * CEs [624] --> Loop 427 * CEs [625] --> Loop 428 ### Ranking functions of CR fun6(Out) #### Partial ranking functions of CR fun6(Out) ### Specialization of cost equations fun7/1 * CE 41 is refined into CE [626] * CE 42 is refined into CE [627] ### Cost equations --> "Loop" of fun7/1 * CEs [626] --> Loop 429 * CEs [627] --> Loop 430 ### Ranking functions of CR fun7(Out) #### Partial ranking functions of CR fun7(Out) ### Specialization of cost equations fun8/4 * CE 43 is refined into CE [628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970] * CE 44 is refined into CE [971] ### Cost equations --> "Loop" of fun8/4 * CEs [970] --> Loop 431 * CEs [971] --> Loop 432 * CEs [969] --> Loop 433 * CEs [968] --> Loop 434 * CEs [967] --> Loop 435 * CEs [966] --> Loop 436 * CEs [965] --> Loop 437 * CEs [963] --> Loop 438 * CEs [962] --> Loop 439 * CEs [961] --> Loop 440 * CEs [960] --> Loop 441 * CEs [959] --> Loop 442 * CEs [664] --> Loop 443 * CEs [958] --> Loop 444 * CEs [956] --> Loop 445 * CEs [955] --> Loop 446 * CEs [954] --> Loop 447 * CEs [953] --> Loop 448 * CEs [952] --> Loop 449 * CEs [657] --> Loop 450 * CEs [951] --> Loop 451 * CEs [949] --> Loop 452 * CEs [948] --> Loop 453 * CEs [947] --> Loop 454 * CEs [946] --> Loop 455 * CEs [945] --> Loop 456 * CEs [650] --> Loop 457 * CEs [944] --> Loop 458 * CEs [942] --> Loop 459 * CEs [941] --> Loop 460 * CEs [940] --> Loop 461 * CEs [939] --> Loop 462 * CEs [938] --> Loop 463 * CEs [643] --> Loop 464 * CEs [937] --> Loop 465 * CEs [935] --> Loop 466 * CEs [640] --> Loop 467 * CEs [934] --> Loop 468 * CEs [639] --> Loop 469 * CEs [933] --> Loop 470 * CEs [638] --> Loop 471 * CEs [932] --> Loop 472 * CEs [637] --> Loop 473 * CEs [931] --> Loop 474 * CEs [636] --> Loop 475 * CEs [929,930] --> Loop 476 * CEs [921] --> Loop 477 * CEs [920] --> Loop 478 * CEs [919] --> Loop 479 * CEs [918] --> Loop 480 * CEs [917] --> Loop 481 * CEs [874] --> Loop 482 * CEs [916] --> Loop 483 * CEs [914] --> Loop 484 * CEs [913] --> Loop 485 * CEs [912] --> Loop 486 * CEs [911] --> Loop 487 * CEs [910] --> Loop 488 * CEs [908,909] --> Loop 489 * CEs [907] --> Loop 490 * CEs [906] --> Loop 491 * CEs [905] --> Loop 492 * CEs [904] --> Loop 493 * CEs [903] --> Loop 494 * CEs [901,902] --> Loop 495 * CEs [900] --> Loop 496 * CEs [899] --> Loop 497 * CEs [898] --> Loop 498 * CEs [897] --> Loop 499 * CEs [896] --> Loop 500 * CEs [894,895] --> Loop 501 * CEs [893] --> Loop 502 * CEs [892] --> Loop 503 * CEs [891] --> Loop 504 * CEs [890] --> Loop 505 * CEs [889] --> Loop 506 * CEs [887,888] --> Loop 507 * CEs [886] --> Loop 508 * CEs [878,885] --> Loop 509 * CEs [877,884] --> Loop 510 * CEs [876,883] --> Loop 511 * CEs [875,879,882] --> Loop 512 * CEs [873,880,881,915] --> Loop 513 * CEs [872] --> Loop 514 * CEs [871] --> Loop 515 * CEs [870] --> Loop 516 * CEs [869] --> Loop 517 * CEs [868] --> Loop 518 * CEs [825] --> Loop 519 * CEs [867] --> Loop 520 * CEs [865] --> Loop 521 * CEs [864] --> Loop 522 * CEs [863] --> Loop 523 * CEs [862] --> Loop 524 * CEs [861] --> Loop 525 * CEs [859,860] --> Loop 526 * CEs [858] --> Loop 527 * CEs [857] --> Loop 528 * CEs [856] --> Loop 529 * CEs [855] --> Loop 530 * CEs [854] --> Loop 531 * CEs [852,853] --> Loop 532 * CEs [851] --> Loop 533 * CEs [850] --> Loop 534 * CEs [849] --> Loop 535 * CEs [848] --> Loop 536 * CEs [847] --> Loop 537 * CEs [845,846] --> Loop 538 * CEs [844] --> Loop 539 * CEs [843] --> Loop 540 * CEs [842] --> Loop 541 * CEs [841] --> Loop 542 * CEs [840] --> Loop 543 * CEs [838,839] --> Loop 544 * CEs [837] --> Loop 545 * CEs [829,836] --> Loop 546 * CEs [828,835] --> Loop 547 * CEs [827,834] --> Loop 548 * CEs [826,830,833] --> Loop 549 * CEs [824,831,832,866] --> Loop 550 * CEs [823] --> Loop 551 * CEs [822] --> Loop 552 * CEs [821] --> Loop 553 * CEs [820] --> Loop 554 * CEs [819] --> Loop 555 * CEs [776] --> Loop 556 * CEs [818] --> Loop 557 * CEs [816] --> Loop 558 * CEs [815] --> Loop 559 * CEs [814] --> Loop 560 * CEs [813] --> Loop 561 * CEs [812] --> Loop 562 * CEs [810,811] --> Loop 563 * CEs [809] --> Loop 564 * CEs [808] --> Loop 565 * CEs [807] --> Loop 566 * CEs [806] --> Loop 567 * CEs [805] --> Loop 568 * CEs [803,804] --> Loop 569 * CEs [802] --> Loop 570 * CEs [801] --> Loop 571 * CEs [800] --> Loop 572 * CEs [799] --> Loop 573 * CEs [798] --> Loop 574 * CEs [796,797] --> Loop 575 * CEs [795] --> Loop 576 * CEs [794] --> Loop 577 * CEs [793] --> Loop 578 * CEs [792] --> Loop 579 * CEs [791] --> Loop 580 * CEs [789,790] --> Loop 581 * CEs [788] --> Loop 582 * CEs [780,787] --> Loop 583 * CEs [779,786] --> Loop 584 * CEs [778,785] --> Loop 585 * CEs [777,781,784] --> Loop 586 * CEs [775,782,783,817] --> Loop 587 * CEs [774] --> Loop 588 * CEs [773] --> Loop 589 * CEs [772] --> Loop 590 * CEs [771] --> Loop 591 * CEs [770] --> Loop 592 * CEs [727] --> Loop 593 * CEs [769] --> Loop 594 * CEs [767] --> Loop 595 * CEs [766] --> Loop 596 * CEs [765] --> Loop 597 * CEs [764] --> Loop 598 * CEs [763] --> Loop 599 * CEs [761,762] --> Loop 600 * CEs [760] --> Loop 601 * CEs [759] --> Loop 602 * CEs [758] --> Loop 603 * CEs [757] --> Loop 604 * CEs [756] --> Loop 605 * CEs [754,755] --> Loop 606 * CEs [753] --> Loop 607 * CEs [752] --> Loop 608 * CEs [751] --> Loop 609 * CEs [750] --> Loop 610 * CEs [749] --> Loop 611 * CEs [747,748] --> Loop 612 * CEs [746] --> Loop 613 * CEs [745] --> Loop 614 * CEs [744] --> Loop 615 * CEs [743] --> Loop 616 * CEs [742,924] --> Loop 617 * CEs [740,741] --> Loop 618 * CEs [739] --> Loop 619 * CEs [731,738] --> Loop 620 * CEs [730,737] --> Loop 621 * CEs [729,736] --> Loop 622 * CEs [728,732,735] --> Loop 623 * CEs [726,733,734,768] --> Loop 624 * CEs [725] --> Loop 625 * CEs [724] --> Loop 626 * CEs [723] --> Loop 627 * CEs [722] --> Loop 628 * CEs [630,672,721] --> Loop 629 * CEs [678,923] --> Loop 630 * CEs [629,671,720] --> Loop 631 * CEs [718] --> Loop 632 * CEs [668,717] --> Loop 633 * CEs [667,716] --> Loop 634 * CEs [666,715] --> Loop 635 * CEs [665,669,714] --> Loop 636 * CEs [663,712,713,957] --> Loop 637 * CEs [711] --> Loop 638 * CEs [661,710] --> Loop 639 * CEs [660,709] --> Loop 640 * CEs [659,708] --> Loop 641 * CEs [658,662,707] --> Loop 642 * CEs [656,705,706,950] --> Loop 643 * CEs [704] --> Loop 644 * CEs [654,703] --> Loop 645 * CEs [653,702] --> Loop 646 * CEs [652,701] --> Loop 647 * CEs [651,655,700] --> Loop 648 * CEs [649,698,699,943] --> Loop 649 * CEs [697] --> Loop 650 * CEs [647,675,696] --> Loop 651 * CEs [646,674,695] --> Loop 652 * CEs [645,673,694] --> Loop 653 * CEs [644,648,693] --> Loop 654 * CEs [642,691,692,936] --> Loop 655 * CEs [635,641,676,690] --> Loop 656 * CEs [633,682,689,927] --> Loop 657 * CEs [632,681,688,926] --> Loop 658 * CEs [631,680,687,925] --> Loop 659 * CEs [634,679,683,686,928] --> Loop 660 * CEs [628,670,677,684,685,719,922,964] --> Loop 661 ### Ranking functions of CR fun8(V1,V,V13,Out) #### Partial ranking functions of CR fun8(V1,V,V13,Out) ### Specialization of cost equations fun9/1 * CE 45 is refined into CE [972] * CE 46 is refined into CE [973] ### Cost equations --> "Loop" of fun9/1 * CEs [972] --> Loop 662 * CEs [973] --> Loop 663 ### Ranking functions of CR fun9(Out) #### Partial ranking functions of CR fun9(Out) ### Specialization of cost equations start/3 * CE 1 is refined into CE [974,975,976] * CE 2 is refined into CE [977,978,979,980,981,982,983] * CE 3 is refined into CE [984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003] * CE 4 is refined into CE [1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032] * CE 5 is refined into CE [1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196] * CE 6 is refined into CE [1197] * CE 7 is refined into CE [1198,1199] * CE 8 is refined into CE [1200,1201] * CE 9 is refined into CE [1202,1203] * CE 10 is refined into CE [1204,1205] * CE 11 is refined into CE [1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369] * CE 12 is refined into CE [1370,1371] * CE 13 is refined into CE [1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400] * CE 14 is refined into CE [1401,1402] * CE 15 is refined into CE [1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431] ### Cost equations --> "Loop" of start/3 * CEs [974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431] --> Loop 664 ### Ranking functions of CR start(V1,V,V13) #### Partial ranking functions of CR start(V1,V,V13) Computing Bounds ===================================== #### Cost of chains of f(V1,V,Out): * Chain [34]: 0 with precondition: [Out=0,V1>=0,V>=0] * Chain [multiple(33,[[34],[multiple(32,[[34]])]])]: 3 with precondition: [V1=6,V=4,133>=8*Out,Out>=7] * Chain [multiple(32,[[34]])]: 1 with precondition: [V1=8,V=4,Out=7] #### Cost of chains of encArg(V1,Out): * Chain [46]: 0 with precondition: [V1=1,Out=1] * Chain [45]: 0 with precondition: [V1=2,Out=2] * Chain [44]: 0 with precondition: [V1=3,Out=3] * Chain [43]: 0 with precondition: [V1=4,Out=4] * Chain [42]: 0 with precondition: [V1=5,Out=5] * Chain [41]: 0 with precondition: [V1=6,Out=6] * Chain [40]: 0 with precondition: [Out=0,V1>=0] * Chain [multiple([35,36,37,38,39],[[46],[45],[44],[43],[42],[41],[40]])]: 4*it(37)+0 Such that:aux(1) =< V1 it(37) =< aux(1) with precondition: [V1>=1,Out>=0] #### Cost of chains of fun(V1,V,Out): * Chain [75]: 8*s(4)+12*s(6)+0 Such that:aux(3) =< V1 aux(4) =< V s(6) =< aux(4) s(4) =< aux(3) with precondition: [Out=0,V1>=0,V>=0] * Chain [74]: 4*s(14)+0 Such that:s(13) =< V1 s(14) =< s(13) with precondition: [V=3,Out=0,V1>=0] * Chain [73]: 4*s(16)+0 Such that:s(15) =< V1 s(16) =< s(15) with precondition: [V=4,Out=0,V1>=0] * Chain [72]: 4*s(18)+0 Such that:s(17) =< V1 s(18) =< s(17) with precondition: [V=5,Out=0,V1>=0] * Chain [71]: 4*s(20)+0 Such that:s(19) =< V1 s(20) =< s(19) with precondition: [V=6,Out=0,V1>=0] * Chain [70]: 4*s(22)+0 Such that:s(21) =< V s(22) =< s(21) with precondition: [V1=3,Out=0,V>=0] * Chain [69]: 0 with precondition: [V1=3,V=3,Out=0] * Chain [68]: 0 with precondition: [V1=3,V=4,Out=0] * Chain [67]: 0 with precondition: [V1=3,V=5,Out=0] * Chain [66]: 0 with precondition: [V1=3,V=6,Out=0] * Chain [65]: 4*s(24)+0 Such that:s(23) =< V s(24) =< s(23) with precondition: [V1=4,Out=0,V>=0] * Chain [64]: 0 with precondition: [V1=4,V=3,Out=0] * Chain [63]: 0 with precondition: [V1=4,V=4,Out=0] * Chain [62]: 0 with precondition: [V1=4,V=5,Out=0] * Chain [61]: 0 with precondition: [V1=4,V=6,Out=0] * Chain [60]: 4*s(26)+0 Such that:s(25) =< V s(26) =< s(25) with precondition: [V1=5,Out=0,V>=0] * Chain [59]: 0 with precondition: [V1=5,V=3,Out=0] * Chain [58]: 0 with precondition: [V1=5,V=4,Out=0] * Chain [57]: 0 with precondition: [V1=5,V=5,Out=0] * Chain [56]: 0 with precondition: [V1=5,V=6,Out=0] * Chain [55]: 4*s(28)+0 Such that:s(27) =< V s(28) =< s(27) with precondition: [V1=6,Out=0,V>=0] * Chain [54]: 0 with precondition: [V1=6,V=3,Out=0] * Chain [53]: 0 with precondition: [V1=6,V=4,Out=0] * Chain [52]: 4*s(30)+8*s(32)+3 Such that:s(29) =< V1 aux(5) =< V s(32) =< aux(5) s(30) =< s(29) with precondition: [133>=8*Out,V1>=1,V>=1,Out>=7] * Chain [51]: 0 with precondition: [V1=6,V=5,Out=0] * Chain [50]: 0 with precondition: [V1=6,V=6,Out=0] * Chain [49]: 4*s(36)+0 Such that:s(35) =< V1 s(36) =< s(35) with precondition: [V=2,Out=0,V1>=0] * Chain [48]: 8*s(38)+3 Such that:aux(6) =< V1 s(38) =< aux(6) with precondition: [V=4,133>=8*Out,V1>=1,Out>=7] * Chain [47]: 4*s(42)+4*s(44)+1 Such that:s(41) =< V1 s(43) =< V s(44) =< s(43) s(42) =< s(41) with precondition: [Out=7,V1>=1,V>=1] #### Cost of chains of fun1(V1,V,Out): * Chain [113]: 4*s(70)+12*s(72)+0 Such that:s(69) =< V1 aux(9) =< V s(72) =< aux(9) s(70) =< s(69) with precondition: [V1>=0,V>=1,Out>=1] * Chain [112]: 8*s(78)+0 Such that:aux(10) =< V1 s(78) =< aux(10) with precondition: [V1>=1,V>=0,Out>=1] * Chain [111]: 4*s(82)+0 Such that:s(81) =< V1 s(82) =< s(81) with precondition: [V=4,V1>=1,Out>=5] * Chain [110]: 4*s(84)+0 Such that:s(83) =< V1 s(84) =< s(83) with precondition: [V=5,V1>=1,Out>=6] * Chain [109]: 4*s(86)+0 Such that:s(85) =< V1 s(86) =< s(85) with precondition: [V=6,V1>=1,Out>=7] * Chain [108]: 0 with precondition: [V1=2,Out=3,V>=0] * Chain [107]: 4*s(88)+0 Such that:s(87) =< V s(88) =< s(87) with precondition: [V1=3,V>=1,Out>=4] * Chain [106]: 0 with precondition: [V1=3,V=3,Out=7] * Chain [105]: 0 with precondition: [V1=3,V=4,Out=8] * Chain [104]: 0 with precondition: [V1=3,V=5,Out=9] * Chain [103]: 0 with precondition: [V1=3,V=6,Out=10] * Chain [102]: 0 with precondition: [V1=3,Out=4,V>=0] * Chain [101]: 4*s(90)+0 Such that:s(89) =< V s(90) =< s(89) with precondition: [V1=4,V>=1,Out>=5] * Chain [100]: 0 with precondition: [V1=4,V=3,Out=8] * Chain [99]: 0 with precondition: [V1=4,V=4,Out=9] * Chain [98]: 0 with precondition: [V1=4,V=5,Out=10] * Chain [97]: 0 with precondition: [V1=4,V=6,Out=11] * Chain [96]: 0 with precondition: [V1=4,Out=5,V>=0] * Chain [95]: 4*s(92)+0 Such that:s(91) =< V s(92) =< s(91) with precondition: [V1=5,V>=1,Out>=6] * Chain [94]: 0 with precondition: [V1=5,V=3,Out=9] * Chain [93]: 0 with precondition: [V1=5,V=4,Out=10] * Chain [92]: 0 with precondition: [V1=5,V=5,Out=11] * Chain [91]: 0 with precondition: [V1=5,V=6,Out=12] * Chain [90]: 0 with precondition: [V1=5,Out=6,V>=0] * Chain [89]: 4*s(94)+0 Such that:s(93) =< V s(94) =< s(93) with precondition: [V1=6,V>=1,Out>=7] * Chain [88]: 0 with precondition: [V1=6,V=3,Out=10] * Chain [87]: 0 with precondition: [V1=6,V=4,Out=11] * Chain [86]: 0 with precondition: [V1=6,V=5,Out=12] * Chain [85]: 0 with precondition: [V1=6,V=6,Out=13] * Chain [84]: 0 with precondition: [V1=6,Out=7,V>=0] * Chain [83]: 0 with precondition: [V=2,Out=3,V1>=0] * Chain [82]: 4*s(96)+0 Such that:s(95) =< V1 s(96) =< s(95) with precondition: [V=2,V1>=1,Out>=3] * Chain [81]: 0 with precondition: [V=3,Out=4,V1>=0] * Chain [80]: 0 with precondition: [V=4,Out=5,V1>=0] * Chain [79]: 0 with precondition: [V=5,Out=6,V1>=0] * Chain [78]: 0 with precondition: [V=6,Out=7,V1>=0] * Chain [77]: 0 with precondition: [Out=0,V1>=0,V>=0] * Chain [76]: 0 with precondition: [Out=1,V1>=0,V>=0] #### Cost of chains of fun10(V1,V,Out): * Chain [151]: 4*s(118)+12*s(120)+0 Such that:s(117) =< V1 aux(12) =< V s(120) =< aux(12) s(118) =< s(117) with precondition: [V1>=0,V>=1,Out>=1] * Chain [150]: 8*s(126)+0 Such that:aux(13) =< V1 s(126) =< aux(13) with precondition: [V1>=1,V>=0,Out>=1] * Chain [149]: 4*s(130)+0 Such that:s(129) =< V1 s(130) =< s(129) with precondition: [V=4,V1>=1,Out>=5] * Chain [148]: 4*s(132)+0 Such that:s(131) =< V1 s(132) =< s(131) with precondition: [V=5,V1>=1,Out>=6] * Chain [147]: 4*s(134)+0 Such that:s(133) =< V1 s(134) =< s(133) with precondition: [V=6,V1>=1,Out>=7] * Chain [146]: 0 with precondition: [V1=2,Out=3,V>=0] * Chain [145]: 4*s(136)+0 Such that:s(135) =< V s(136) =< s(135) with precondition: [V1=3,V>=1,Out>=4] * Chain [144]: 0 with precondition: [V1=3,V=3,Out=7] * Chain [143]: 0 with precondition: [V1=3,V=4,Out=8] * Chain [142]: 0 with precondition: [V1=3,V=5,Out=9] * Chain [141]: 0 with precondition: [V1=3,V=6,Out=10] * Chain [140]: 0 with precondition: [V1=3,Out=4,V>=0] * Chain [139]: 4*s(138)+0 Such that:s(137) =< V s(138) =< s(137) with precondition: [V1=4,V>=1,Out>=5] * Chain [138]: 0 with precondition: [V1=4,V=3,Out=8] * Chain [137]: 0 with precondition: [V1=4,V=4,Out=9] * Chain [136]: 0 with precondition: [V1=4,V=5,Out=10] * Chain [135]: 0 with precondition: [V1=4,V=6,Out=11] * Chain [134]: 0 with precondition: [V1=4,Out=5,V>=0] * Chain [133]: 4*s(140)+0 Such that:s(139) =< V s(140) =< s(139) with precondition: [V1=5,V>=1,Out>=6] * Chain [132]: 0 with precondition: [V1=5,V=3,Out=9] * Chain [131]: 0 with precondition: [V1=5,V=4,Out=10] * Chain [130]: 0 with precondition: [V1=5,V=5,Out=11] * Chain [129]: 0 with precondition: [V1=5,V=6,Out=12] * Chain [128]: 0 with precondition: [V1=5,Out=6,V>=0] * Chain [127]: 4*s(142)+0 Such that:s(141) =< V s(142) =< s(141) with precondition: [V1=6,V>=1,Out>=7] * Chain [126]: 0 with precondition: [V1=6,V=3,Out=10] * Chain [125]: 0 with precondition: [V1=6,V=4,Out=11] * Chain [124]: 0 with precondition: [V1=6,V=5,Out=12] * Chain [123]: 0 with precondition: [V1=6,V=6,Out=13] * Chain [122]: 0 with precondition: [V1=6,Out=7,V>=0] * Chain [121]: 0 with precondition: [V=2,Out=3,V1>=0] * Chain [120]: 4*s(144)+0 Such that:s(143) =< V1 s(144) =< s(143) with precondition: [V=2,V1>=1,Out>=3] * Chain [119]: 0 with precondition: [V=3,Out=4,V1>=0] * Chain [118]: 0 with precondition: [V=4,Out=5,V1>=0] * Chain [117]: 0 with precondition: [V=5,Out=6,V1>=0] * Chain [116]: 0 with precondition: [V=6,Out=7,V1>=0] * Chain [115]: 0 with precondition: [Out=0,V1>=0,V>=0] * Chain [114]: 0 with precondition: [Out=1,V1>=0,V>=0] #### Cost of chains of fun11(Out): * Chain [153]: 0 with precondition: [Out=0] * Chain [152]: 0 with precondition: [Out=5] #### Cost of chains of fun12(V1,V,Out): * Chain [191]: 4*s(166)+12*s(168)+0 Such that:s(165) =< V1 aux(15) =< V s(168) =< aux(15) s(166) =< s(165) with precondition: [V1>=0,V>=1,Out>=1] * Chain [190]: 8*s(174)+0 Such that:aux(16) =< V1 s(174) =< aux(16) with precondition: [V1>=1,V>=0,Out>=1] * Chain [189]: 4*s(178)+0 Such that:s(177) =< V1 s(178) =< s(177) with precondition: [V=4,V1>=1,Out>=5] * Chain [188]: 4*s(180)+0 Such that:s(179) =< V1 s(180) =< s(179) with precondition: [V=5,V1>=1,Out>=6] * Chain [187]: 4*s(182)+0 Such that:s(181) =< V1 s(182) =< s(181) with precondition: [V=6,V1>=1,Out>=7] * Chain [186]: 0 with precondition: [V1=2,Out=3,V>=0] * Chain [185]: 4*s(184)+0 Such that:s(183) =< V s(184) =< s(183) with precondition: [V1=3,V>=1,Out>=4] * Chain [184]: 0 with precondition: [V1=3,V=3,Out=7] * Chain [183]: 0 with precondition: [V1=3,V=4,Out=8] * Chain [182]: 0 with precondition: [V1=3,V=5,Out=9] * Chain [181]: 0 with precondition: [V1=3,V=6,Out=10] * Chain [180]: 0 with precondition: [V1=3,Out=4,V>=0] * Chain [179]: 4*s(186)+0 Such that:s(185) =< V s(186) =< s(185) with precondition: [V1=4,V>=1,Out>=5] * Chain [178]: 0 with precondition: [V1=4,V=3,Out=8] * Chain [177]: 0 with precondition: [V1=4,V=4,Out=9] * Chain [176]: 0 with precondition: [V1=4,V=5,Out=10] * Chain [175]: 0 with precondition: [V1=4,V=6,Out=11] * Chain [174]: 0 with precondition: [V1=4,Out=5,V>=0] * Chain [173]: 4*s(188)+0 Such that:s(187) =< V s(188) =< s(187) with precondition: [V1=5,V>=1,Out>=6] * Chain [172]: 0 with precondition: [V1=5,V=3,Out=9] * Chain [171]: 0 with precondition: [V1=5,V=4,Out=10] * Chain [170]: 0 with precondition: [V1=5,V=5,Out=11] * Chain [169]: 0 with precondition: [V1=5,V=6,Out=12] * Chain [168]: 0 with precondition: [V1=5,Out=6,V>=0] * Chain [167]: 4*s(190)+0 Such that:s(189) =< V s(190) =< s(189) with precondition: [V1=6,V>=1,Out>=7] * Chain [166]: 0 with precondition: [V1=6,V=3,Out=10] * Chain [165]: 0 with precondition: [V1=6,V=4,Out=11] * Chain [164]: 0 with precondition: [V1=6,V=5,Out=12] * Chain [163]: 0 with precondition: [V1=6,V=6,Out=13] * Chain [162]: 0 with precondition: [V1=6,Out=7,V>=0] * Chain [161]: 0 with precondition: [V=2,Out=3,V1>=0] * Chain [160]: 4*s(192)+0 Such that:s(191) =< V1 s(192) =< s(191) with precondition: [V=2,V1>=1,Out>=3] * Chain [159]: 0 with precondition: [V=3,Out=4,V1>=0] * Chain [158]: 0 with precondition: [V=4,Out=5,V1>=0] * Chain [157]: 0 with precondition: [V=5,Out=6,V1>=0] * Chain [156]: 0 with precondition: [V=6,Out=7,V1>=0] * Chain [155]: 0 with precondition: [Out=0,V1>=0,V>=0] * Chain [154]: 0 with precondition: [Out=1,V1>=0,V>=0] #### Cost of chains of fun2(V1,V,V13,Out): * Chain [422]: 8*s(214)+12*s(216)+28*s(218)+0 Such that:aux(18) =< V1 aux(19) =< V aux(20) =< V13 s(218) =< aux(20) s(216) =< aux(19) s(214) =< aux(18) with precondition: [V1>=0,V>=0,V13>=1,Out>=1] * Chain [421]: 4*s(238)+16*s(240)+0 Such that:s(237) =< V1 aux(21) =< V s(240) =< aux(21) s(238) =< s(237) with precondition: [V1>=0,V>=1,V13>=0,Out>=1] * Chain [420]: 4*s(248)+12*s(250)+0 Such that:s(247) =< V1 aux(22) =< V s(250) =< aux(22) s(248) =< s(247) with precondition: [V13=4,V1>=0,V>=1,Out>=5] * Chain [419]: 4*s(256)+12*s(258)+0 Such that:s(255) =< V1 aux(23) =< V s(258) =< aux(23) s(256) =< s(255) with precondition: [V13=5,V1>=0,V>=1,Out>=6] * Chain [418]: 4*s(264)+12*s(266)+0 Such that:s(263) =< V1 aux(24) =< V s(266) =< aux(24) s(264) =< s(263) with precondition: [V13=6,V1>=0,V>=1,Out>=7] * Chain [417]: 12*s(272)+4*s(274)+0 Such that:s(273) =< V13 aux(25) =< V1 s(274) =< s(273) s(272) =< aux(25) with precondition: [V1>=1,V>=0,V13>=0,Out>=1] * Chain [416]: 4*s(280)+12*s(282)+0 Such that:s(279) =< V1 aux(26) =< V13 s(282) =< aux(26) s(280) =< s(279) with precondition: [V=3,V1>=0,V13>=1,Out>=4] * Chain [415]: 8*s(288)+0 Such that:aux(27) =< V1 s(288) =< aux(27) with precondition: [V=3,V1>=1,V13>=0,Out>=4] * Chain [414]: 8*s(292)+0 Such that:aux(28) =< V1 s(292) =< aux(28) with precondition: [V13=4,V1>=1,V>=0,Out>=5] * Chain [413]: 8*s(296)+0 Such that:aux(29) =< V1 s(296) =< aux(29) with precondition: [V13=5,V1>=1,V>=0,Out>=6] * Chain [412]: 8*s(300)+0 Such that:aux(30) =< V1 s(300) =< aux(30) with precondition: [V13=6,V1>=1,V>=0,Out>=7] * Chain [411]: 0 with precondition: [V1=2,V=3,Out=6,V13>=0] * Chain [410]: 4*s(304)+12*s(306)+0 Such that:s(303) =< V1 aux(31) =< V13 s(306) =< aux(31) s(304) =< s(303) with precondition: [V=4,V1>=0,V13>=1,Out>=5] * Chain [409]: 8*s(312)+0 Such that:aux(32) =< V1 s(312) =< aux(32) with precondition: [V=4,V1>=1,V13>=0,Out>=5] * Chain [408]: 4*s(316)+0 Such that:s(315) =< V1 s(316) =< s(315) with precondition: [V=4,V13=4,V1>=1,Out>=9] * Chain [407]: 4*s(318)+0 Such that:s(317) =< V1 s(318) =< s(317) with precondition: [V=4,V13=5,V1>=1,Out>=10] * Chain [406]: 4*s(320)+0 Such that:s(319) =< V1 s(320) =< s(319) with precondition: [V=4,V13=6,V1>=1,Out>=11] * Chain [405]: 0 with precondition: [V1=2,V=4,Out=7,V13>=0] * Chain [404]: 4*s(322)+12*s(324)+0 Such that:s(321) =< V1 aux(33) =< V13 s(324) =< aux(33) s(322) =< s(321) with precondition: [V=5,V1>=0,V13>=1,Out>=6] * Chain [403]: 8*s(330)+0 Such that:aux(34) =< V1 s(330) =< aux(34) with precondition: [V=5,V1>=1,V13>=0,Out>=6] * Chain [402]: 4*s(334)+0 Such that:s(333) =< V1 s(334) =< s(333) with precondition: [V=5,V13=4,V1>=1,Out>=10] * Chain [401]: 4*s(336)+0 Such that:s(335) =< V1 s(336) =< s(335) with precondition: [V=5,V13=5,V1>=1,Out>=11] * Chain [400]: 4*s(338)+0 Such that:s(337) =< V1 s(338) =< s(337) with precondition: [V=5,V13=6,V1>=1,Out>=12] * Chain [399]: 0 with precondition: [V1=2,V=5,Out=8,V13>=0] * Chain [398]: 4*s(340)+12*s(342)+0 Such that:s(339) =< V1 aux(35) =< V13 s(342) =< aux(35) s(340) =< s(339) with precondition: [V=6,V1>=0,V13>=1,Out>=7] * Chain [397]: 8*s(348)+0 Such that:aux(36) =< V1 s(348) =< aux(36) with precondition: [V=6,V1>=1,V13>=0,Out>=7] * Chain [396]: 4*s(352)+0 Such that:s(351) =< V1 s(352) =< s(351) with precondition: [V=6,V13=4,V1>=1,Out>=11] * Chain [395]: 4*s(354)+0 Such that:s(353) =< V1 s(354) =< s(353) with precondition: [V=6,V13=5,V1>=1,Out>=12] * Chain [394]: 4*s(356)+0 Such that:s(355) =< V1 s(356) =< s(355) with precondition: [V=6,V13=6,V1>=1,Out>=13] * Chain [393]: 0 with precondition: [V1=2,V=6,Out=9,V13>=0] * Chain [392]: 8*s(358)+4*s(360)+0 Such that:s(359) =< V aux(37) =< V1 s(360) =< s(359) s(358) =< aux(37) with precondition: [V13=2,V1>=1,V>=0,Out>=3] * Chain [391]: 8*s(364)+0 Such that:aux(38) =< V s(364) =< aux(38) with precondition: [V13=2,V1>=0,V>=1,Out>=3] * Chain [390]: 8*s(368)+4*s(370)+0 Such that:s(369) =< V aux(39) =< V1 s(370) =< s(369) s(368) =< aux(39) with precondition: [V13=3,V1>=1,V>=0,Out>=4] * Chain [389]: 0 with precondition: [V1=2,V13=4,Out=7,V>=0] * Chain [388]: 0 with precondition: [V1=2,V13=5,Out=8,V>=0] * Chain [387]: 0 with precondition: [V1=2,V13=6,Out=9,V>=0] * Chain [386]: 0 with precondition: [V1=2,Out=3,V>=0,V13>=0] * Chain [385]: 4*s(374)+12*s(376)+0 Such that:s(373) =< V aux(40) =< V13 s(376) =< aux(40) s(374) =< s(373) with precondition: [V1=3,V>=0,V13>=1,Out>=4] * Chain [384]: 8*s(382)+0 Such that:aux(41) =< V s(382) =< aux(41) with precondition: [V1=3,V>=1,V13>=0,Out>=4] * Chain [383]: 4*s(386)+0 Such that:s(385) =< V s(386) =< s(385) with precondition: [V1=3,V13=4,V>=1,Out>=8] * Chain [382]: 4*s(388)+0 Such that:s(387) =< V s(388) =< s(387) with precondition: [V1=3,V13=5,V>=1,Out>=9] * Chain [381]: 4*s(390)+0 Such that:s(389) =< V s(390) =< s(389) with precondition: [V1=3,V13=6,V>=1,Out>=10] * Chain [380]: 0 with precondition: [V1=3,V=2,Out=6,V13>=0] * Chain [379]: 4*s(392)+0 Such that:s(391) =< V13 s(392) =< s(391) with precondition: [V1=3,V=3,V13>=1,Out>=7] * Chain [378]: 4*s(394)+0 Such that:s(393) =< V s(394) =< s(393) with precondition: [V13=3,V1>=0,V>=1,Out>=4] * Chain [377]: 0 with precondition: [V1=3,V=3,V13=4,Out=11] * Chain [376]: 0 with precondition: [V1=3,V=3,V13=5,Out=12] * Chain [375]: 0 with precondition: [V1=3,V=3,V13=6,Out=13] * Chain [374]: 0 with precondition: [V1=3,V=3,Out=7,V13>=0] * Chain [373]: 4*s(396)+0 Such that:s(395) =< V13 s(396) =< s(395) with precondition: [V1=3,V=4,V13>=1,Out>=8] * Chain [372]: 0 with precondition: [V1=3,V=4,V13=3,Out=11] * Chain [371]: 0 with precondition: [V1=3,V=4,V13=4,Out=12] * Chain [370]: 0 with precondition: [V1=3,V=4,V13=5,Out=13] * Chain [369]: 0 with precondition: [V1=3,V=4,V13=6,Out=14] * Chain [368]: 0 with precondition: [V1=3,V=4,Out=8,V13>=0] * Chain [367]: 4*s(398)+0 Such that:s(397) =< V13 s(398) =< s(397) with precondition: [V1=3,V=5,V13>=1,Out>=9] * Chain [366]: 0 with precondition: [V1=3,V=5,V13=3,Out=12] * Chain [365]: 0 with precondition: [V1=3,V=5,V13=4,Out=13] * Chain [364]: 0 with precondition: [V1=3,V=5,V13=5,Out=14] * Chain [363]: 0 with precondition: [V1=3,V=5,V13=6,Out=15] * Chain [362]: 0 with precondition: [V1=3,V=5,Out=9,V13>=0] * Chain [361]: 4*s(400)+0 Such that:s(399) =< V13 s(400) =< s(399) with precondition: [V1=3,V=6,V13>=1,Out>=10] * Chain [360]: 0 with precondition: [V1=3,V=6,V13=3,Out=13] * Chain [359]: 0 with precondition: [V1=3,V=6,V13=4,Out=14] * Chain [358]: 0 with precondition: [V1=3,V=6,V13=5,Out=15] * Chain [357]: 0 with precondition: [V1=3,V=6,V13=6,Out=16] * Chain [356]: 0 with precondition: [V1=3,V=6,Out=10,V13>=0] * Chain [355]: 0 with precondition: [V1=3,V13=2,Out=6,V>=0] * Chain [354]: 4*s(402)+0 Such that:s(401) =< V s(402) =< s(401) with precondition: [V1=3,V13=2,V>=1,Out>=6] * Chain [353]: 0 with precondition: [V1=3,V13=3,Out=7,V>=0] * Chain [352]: 0 with precondition: [V1=3,V13=4,Out=8,V>=0] * Chain [351]: 0 with precondition: [V1=3,V13=5,Out=9,V>=0] * Chain [350]: 0 with precondition: [V1=3,V13=6,Out=10,V>=0] * Chain [349]: 0 with precondition: [V1=3,Out=4,V>=0,V13>=0] * Chain [348]: 4*s(404)+12*s(406)+0 Such that:s(403) =< V aux(42) =< V13 s(406) =< aux(42) s(404) =< s(403) with precondition: [V1=4,V>=0,V13>=1,Out>=5] * Chain [347]: 8*s(412)+0 Such that:aux(43) =< V s(412) =< aux(43) with precondition: [V1=4,V>=1,V13>=0,Out>=5] * Chain [346]: 4*s(416)+0 Such that:s(415) =< V s(416) =< s(415) with precondition: [V1=4,V13=4,V>=1,Out>=9] * Chain [345]: 4*s(418)+0 Such that:s(417) =< V s(418) =< s(417) with precondition: [V1=4,V13=5,V>=1,Out>=10] * Chain [344]: 4*s(420)+0 Such that:s(419) =< V s(420) =< s(419) with precondition: [V1=4,V13=6,V>=1,Out>=11] * Chain [343]: 0 with precondition: [V1=4,V=2,Out=7,V13>=0] * Chain [342]: 4*s(422)+0 Such that:s(421) =< V13 s(422) =< s(421) with precondition: [V1=4,V=3,V13>=1,Out>=8] * Chain [341]: 0 with precondition: [V1=4,V=3,V13=3,Out=11] * Chain [340]: 0 with precondition: [V1=4,V=3,V13=4,Out=12] * Chain [339]: 0 with precondition: [V1=4,V=3,V13=5,Out=13] * Chain [338]: 0 with precondition: [V1=4,V=3,V13=6,Out=14] * Chain [337]: 0 with precondition: [V1=4,V=3,Out=8,V13>=0] * Chain [336]: 4*s(424)+0 Such that:s(423) =< V13 s(424) =< s(423) with precondition: [V1=4,V=4,V13>=1,Out>=9] * Chain [335]: 0 with precondition: [V1=4,V=4,V13=3,Out=12] * Chain [334]: 0 with precondition: [V1=4,V=4,V13=4,Out=13] * Chain [333]: 0 with precondition: [V1=4,V=4,V13=5,Out=14] * Chain [332]: 0 with precondition: [V1=4,V=4,V13=6,Out=15] * Chain [331]: 0 with precondition: [V1=4,V=4,Out=9,V13>=0] * Chain [330]: 4*s(426)+0 Such that:s(425) =< V13 s(426) =< s(425) with precondition: [V1=4,V=5,V13>=1,Out>=10] * Chain [329]: 0 with precondition: [V1=4,V=5,V13=3,Out=13] * Chain [328]: 0 with precondition: [V1=4,V=5,V13=4,Out=14] * Chain [327]: 0 with precondition: [V1=4,V=5,V13=5,Out=15] * Chain [326]: 0 with precondition: [V1=4,V=5,V13=6,Out=16] * Chain [325]: 0 with precondition: [V1=4,V=5,Out=10,V13>=0] * Chain [324]: 4*s(428)+0 Such that:s(427) =< V13 s(428) =< s(427) with precondition: [V1=4,V=6,V13>=1,Out>=11] * Chain [323]: 0 with precondition: [V1=4,V=6,V13=3,Out=14] * Chain [322]: 0 with precondition: [V1=4,V=6,V13=4,Out=15] * Chain [321]: 0 with precondition: [V1=4,V=6,V13=5,Out=16] * Chain [320]: 0 with precondition: [V1=4,V=6,V13=6,Out=17] * Chain [319]: 0 with precondition: [V1=4,V=6,Out=11,V13>=0] * Chain [318]: 0 with precondition: [V1=4,V13=2,Out=7,V>=0] * Chain [317]: 4*s(430)+0 Such that:s(429) =< V s(430) =< s(429) with precondition: [V1=4,V13=2,V>=1,Out>=7] * Chain [316]: 0 with precondition: [V1=4,V13=3,Out=8,V>=0] * Chain [315]: 0 with precondition: [V1=4,V13=4,Out=9,V>=0] * Chain [314]: 0 with precondition: [V1=4,V13=5,Out=10,V>=0] * Chain [313]: 0 with precondition: [V1=4,V13=6,Out=11,V>=0] * Chain [312]: 0 with precondition: [V1=4,Out=5,V>=0,V13>=0] * Chain [311]: 4*s(432)+12*s(434)+0 Such that:s(431) =< V aux(44) =< V13 s(434) =< aux(44) s(432) =< s(431) with precondition: [V1=5,V>=0,V13>=1,Out>=6] * Chain [310]: 8*s(440)+0 Such that:aux(45) =< V s(440) =< aux(45) with precondition: [V1=5,V>=1,V13>=0,Out>=6] * Chain [309]: 4*s(444)+0 Such that:s(443) =< V s(444) =< s(443) with precondition: [V1=5,V13=4,V>=1,Out>=10] * Chain [308]: 4*s(446)+0 Such that:s(445) =< V s(446) =< s(445) with precondition: [V1=5,V13=5,V>=1,Out>=11] * Chain [307]: 4*s(448)+0 Such that:s(447) =< V s(448) =< s(447) with precondition: [V1=5,V13=6,V>=1,Out>=12] * Chain [306]: 0 with precondition: [V1=5,V=2,Out=8,V13>=0] * Chain [305]: 4*s(450)+0 Such that:s(449) =< V13 s(450) =< s(449) with precondition: [V1=5,V=3,V13>=1,Out>=9] * Chain [304]: 0 with precondition: [V1=5,V=3,V13=3,Out=12] * Chain [303]: 0 with precondition: [V1=5,V=3,V13=4,Out=13] * Chain [302]: 0 with precondition: [V1=5,V=3,V13=5,Out=14] * Chain [301]: 0 with precondition: [V1=5,V=3,V13=6,Out=15] * Chain [300]: 0 with precondition: [V1=5,V=3,Out=9,V13>=0] * Chain [299]: 4*s(452)+0 Such that:s(451) =< V13 s(452) =< s(451) with precondition: [V1=5,V=4,V13>=1,Out>=10] * Chain [298]: 0 with precondition: [V1=5,V=4,V13=3,Out=13] * Chain [297]: 0 with precondition: [V1=5,V=4,V13=4,Out=14] * Chain [296]: 0 with precondition: [V1=5,V=4,V13=5,Out=15] * Chain [295]: 0 with precondition: [V1=5,V=4,V13=6,Out=16] * Chain [294]: 0 with precondition: [V1=5,V=4,Out=10,V13>=0] * Chain [293]: 4*s(454)+0 Such that:s(453) =< V13 s(454) =< s(453) with precondition: [V1=5,V=5,V13>=1,Out>=11] * Chain [292]: 0 with precondition: [V1=5,V=5,V13=3,Out=14] * Chain [291]: 0 with precondition: [V1=5,V=5,V13=4,Out=15] * Chain [290]: 0 with precondition: [V1=5,V=5,V13=5,Out=16] * Chain [289]: 0 with precondition: [V1=5,V=5,V13=6,Out=17] * Chain [288]: 0 with precondition: [V1=5,V=5,Out=11,V13>=0] * Chain [287]: 4*s(456)+0 Such that:s(455) =< V13 s(456) =< s(455) with precondition: [V1=5,V=6,V13>=1,Out>=12] * Chain [286]: 0 with precondition: [V1=5,V=6,V13=3,Out=15] * Chain [285]: 0 with precondition: [V1=5,V=6,V13=4,Out=16] * Chain [284]: 0 with precondition: [V1=5,V=6,V13=5,Out=17] * Chain [283]: 0 with precondition: [V1=5,V=6,V13=6,Out=18] * Chain [282]: 0 with precondition: [V1=5,V=6,Out=12,V13>=0] * Chain [281]: 0 with precondition: [V1=5,V13=2,Out=8,V>=0] * Chain [280]: 4*s(458)+0 Such that:s(457) =< V s(458) =< s(457) with precondition: [V1=5,V13=2,V>=1,Out>=8] * Chain [279]: 0 with precondition: [V1=5,V13=3,Out=9,V>=0] * Chain [278]: 0 with precondition: [V1=5,V13=4,Out=10,V>=0] * Chain [277]: 0 with precondition: [V1=5,V13=5,Out=11,V>=0] * Chain [276]: 0 with precondition: [V1=5,V13=6,Out=12,V>=0] * Chain [275]: 0 with precondition: [V1=5,Out=6,V>=0,V13>=0] * Chain [274]: 4*s(460)+12*s(462)+0 Such that:s(459) =< V aux(46) =< V13 s(462) =< aux(46) s(460) =< s(459) with precondition: [V1=6,V>=0,V13>=1,Out>=7] * Chain [273]: 8*s(468)+0 Such that:aux(47) =< V s(468) =< aux(47) with precondition: [V1=6,V>=1,V13>=0,Out>=7] * Chain [272]: 4*s(472)+0 Such that:s(471) =< V s(472) =< s(471) with precondition: [V1=6,V13=4,V>=1,Out>=11] * Chain [271]: 4*s(474)+0 Such that:s(473) =< V s(474) =< s(473) with precondition: [V1=6,V13=5,V>=1,Out>=12] * Chain [270]: 4*s(476)+0 Such that:s(475) =< V s(476) =< s(475) with precondition: [V1=6,V13=6,V>=1,Out>=13] * Chain [269]: 0 with precondition: [V1=6,V=2,Out=9,V13>=0] * Chain [268]: 4*s(478)+0 Such that:s(477) =< V13 s(478) =< s(477) with precondition: [V1=6,V=3,V13>=1,Out>=10] * Chain [267]: 0 with precondition: [V1=6,V=3,V13=3,Out=13] * Chain [266]: 0 with precondition: [V1=6,V=3,V13=4,Out=14] * Chain [265]: 0 with precondition: [V1=6,V=3,V13=5,Out=15] * Chain [264]: 0 with precondition: [V1=6,V=3,V13=6,Out=16] * Chain [263]: 0 with precondition: [V1=6,V=3,Out=10,V13>=0] * Chain [262]: 4*s(480)+0 Such that:s(479) =< V13 s(480) =< s(479) with precondition: [V1=6,V=4,V13>=1,Out>=11] * Chain [261]: 0 with precondition: [V1=6,V=4,V13=3,Out=14] * Chain [260]: 0 with precondition: [V1=6,V=4,V13=4,Out=15] * Chain [259]: 0 with precondition: [V1=6,V=4,V13=5,Out=16] * Chain [258]: 0 with precondition: [V1=6,V=4,V13=6,Out=17] * Chain [257]: 0 with precondition: [V1=6,V=4,Out=11,V13>=0] * Chain [256]: 4*s(482)+0 Such that:s(481) =< V13 s(482) =< s(481) with precondition: [V1=6,V=5,V13>=1,Out>=12] * Chain [255]: 0 with precondition: [V1=6,V=5,V13=3,Out=15] * Chain [254]: 0 with precondition: [V1=6,V=5,V13=4,Out=16] * Chain [253]: 0 with precondition: [V1=6,V=5,V13=5,Out=17] * Chain [252]: 0 with precondition: [V1=6,V=5,V13=6,Out=18] * Chain [251]: 0 with precondition: [V1=6,V=5,Out=12,V13>=0] * Chain [250]: 4*s(484)+0 Such that:s(483) =< V13 s(484) =< s(483) with precondition: [V1=6,V=6,V13>=1,Out>=13] * Chain [249]: 0 with precondition: [V1=6,V=6,V13=3,Out=16] * Chain [248]: 0 with precondition: [V1=6,V=6,V13=4,Out=17] * Chain [247]: 0 with precondition: [V1=6,V=6,V13=5,Out=18] * Chain [246]: 0 with precondition: [V1=6,V=6,V13=6,Out=19] * Chain [245]: 0 with precondition: [V1=6,V=6,Out=13,V13>=0] * Chain [244]: 0 with precondition: [V1=6,V13=2,Out=9,V>=0] * Chain [243]: 4*s(486)+0 Such that:s(485) =< V s(486) =< s(485) with precondition: [V1=6,V13=2,V>=1,Out>=9] * Chain [242]: 0 with precondition: [V1=6,V13=3,Out=10,V>=0] * Chain [241]: 0 with precondition: [V1=6,V13=4,Out=11,V>=0] * Chain [240]: 0 with precondition: [V1=6,V13=5,Out=12,V>=0] * Chain [239]: 0 with precondition: [V1=6,V13=6,Out=13,V>=0] * Chain [238]: 0 with precondition: [V1=6,Out=7,V>=0,V13>=0] * Chain [237]: 4*s(488)+0 Such that:s(487) =< V13 s(488) =< s(487) with precondition: [V=2,V1>=0,V13>=1,Out>=3] * Chain [236]: 4*s(490)+0 Such that:s(489) =< V1 s(490) =< s(489) with precondition: [V=2,V13=2,V1>=1,Out>=5] * Chain [235]: 0 with precondition: [V=2,V13=3,Out=6,V1>=0] * Chain [234]: 4*s(492)+0 Such that:s(491) =< V1 s(492) =< s(491) with precondition: [V=2,V13=3,V1>=1,Out>=6] * Chain [233]: 0 with precondition: [V=2,V13=4,Out=7,V1>=0] * Chain [232]: 4*s(494)+0 Such that:s(493) =< V1 s(494) =< s(493) with precondition: [V=2,V13=4,V1>=1,Out>=7] * Chain [231]: 0 with precondition: [V=2,V13=5,Out=8,V1>=0] * Chain [230]: 4*s(496)+0 Such that:s(495) =< V1 s(496) =< s(495) with precondition: [V=2,V13=5,V1>=1,Out>=8] * Chain [229]: 0 with precondition: [V=2,V13=6,Out=9,V1>=0] * Chain [228]: 4*s(498)+0 Such that:s(497) =< V1 s(498) =< s(497) with precondition: [V=2,V13=6,V1>=1,Out>=9] * Chain [227]: 0 with precondition: [V=2,Out=3,V1>=0,V13>=0] * Chain [226]: 0 with precondition: [V=3,V13=2,Out=6,V1>=0] * Chain [225]: 4*s(500)+0 Such that:s(499) =< V1 s(500) =< s(499) with precondition: [V=3,V13=2,V1>=1,Out>=6] * Chain [224]: 0 with precondition: [V=3,V13=3,Out=7,V1>=0] * Chain [223]: 0 with precondition: [V=3,V13=4,Out=8,V1>=0] * Chain [222]: 0 with precondition: [V=3,V13=5,Out=9,V1>=0] * Chain [221]: 0 with precondition: [V=3,V13=6,Out=10,V1>=0] * Chain [220]: 0 with precondition: [V=3,Out=4,V1>=0,V13>=0] * Chain [219]: 0 with precondition: [V=4,V13=2,Out=7,V1>=0] * Chain [218]: 4*s(502)+0 Such that:s(501) =< V1 s(502) =< s(501) with precondition: [V=4,V13=2,V1>=1,Out>=7] * Chain [217]: 0 with precondition: [V=4,V13=3,Out=8,V1>=0] * Chain [216]: 0 with precondition: [V=4,V13=4,Out=9,V1>=0] * Chain [215]: 0 with precondition: [V=4,V13=5,Out=10,V1>=0] * Chain [214]: 0 with precondition: [V=4,V13=6,Out=11,V1>=0] * Chain [213]: 0 with precondition: [V=4,Out=5,V1>=0,V13>=0] * Chain [212]: 0 with precondition: [V=5,V13=2,Out=8,V1>=0] * Chain [211]: 4*s(504)+0 Such that:s(503) =< V1 s(504) =< s(503) with precondition: [V=5,V13=2,V1>=1,Out>=8] * Chain [210]: 0 with precondition: [V=5,V13=3,Out=9,V1>=0] * Chain [209]: 0 with precondition: [V=5,V13=4,Out=10,V1>=0] * Chain [208]: 0 with precondition: [V=5,V13=5,Out=11,V1>=0] * Chain [207]: 0 with precondition: [V=5,V13=6,Out=12,V1>=0] * Chain [206]: 0 with precondition: [V=5,Out=6,V1>=0,V13>=0] * Chain [205]: 0 with precondition: [V=6,V13=2,Out=9,V1>=0] * Chain [204]: 4*s(506)+0 Such that:s(505) =< V1 s(506) =< s(505) with precondition: [V=6,V13=2,V1>=1,Out>=9] * Chain [203]: 0 with precondition: [V=6,V13=3,Out=10,V1>=0] * Chain [202]: 0 with precondition: [V=6,V13=4,Out=11,V1>=0] * Chain [201]: 0 with precondition: [V=6,V13=5,Out=12,V1>=0] * Chain [200]: 0 with precondition: [V=6,V13=6,Out=13,V1>=0] * Chain [199]: 0 with precondition: [V=6,Out=7,V1>=0,V13>=0] * Chain [198]: 0 with precondition: [V13=2,Out=3,V1>=0,V>=0] * Chain [197]: 0 with precondition: [V13=3,Out=4,V1>=0,V>=0] * Chain [196]: 0 with precondition: [V13=4,Out=5,V1>=0,V>=0] * Chain [195]: 0 with precondition: [V13=5,Out=6,V1>=0,V>=0] * Chain [194]: 0 with precondition: [V13=6,Out=7,V1>=0,V>=0] * Chain [193]: 0 with precondition: [Out=0,V1>=0,V>=0,V13>=0] * Chain [192]: 0 with precondition: [Out=1,V1>=0,V>=0,V13>=0] #### Cost of chains of fun4(Out): * Chain [424]: 0 with precondition: [Out=0] * Chain [423]: 0 with precondition: [Out=1] #### Cost of chains of fun5(Out): * Chain [426]: 0 with precondition: [Out=0] * Chain [425]: 0 with precondition: [Out=2] #### Cost of chains of fun6(Out): * Chain [428]: 0 with precondition: [Out=0] * Chain [427]: 0 with precondition: [Out=3] #### Cost of chains of fun7(Out): * Chain [430]: 0 with precondition: [Out=0] * Chain [429]: 0 with precondition: [Out=4] #### Cost of chains of fun8(V1,V,V13,Out): * Chain [661]: 8*s(680)+12*s(682)+28*s(684)+0 Such that:aux(62) =< V1 aux(63) =< V aux(64) =< V13 s(684) =< aux(64) s(682) =< aux(63) s(680) =< aux(62) with precondition: [V1>=0,V>=0,V13>=1,Out>=1] * Chain [660]: 4*s(704)+16*s(706)+0 Such that:s(703) =< V1 aux(65) =< V s(706) =< aux(65) s(704) =< s(703) with precondition: [V1>=0,V>=1,V13>=0,Out>=1] * Chain [659]: 4*s(714)+12*s(716)+0 Such that:s(713) =< V1 aux(66) =< V s(716) =< aux(66) s(714) =< s(713) with precondition: [V13=4,V1>=0,V>=1,Out>=5] * Chain [658]: 4*s(722)+12*s(724)+0 Such that:s(721) =< V1 aux(67) =< V s(724) =< aux(67) s(722) =< s(721) with precondition: [V13=5,V1>=0,V>=1,Out>=6] * Chain [657]: 4*s(730)+12*s(732)+0 Such that:s(729) =< V1 aux(68) =< V s(732) =< aux(68) s(730) =< s(729) with precondition: [V13=6,V1>=0,V>=1,Out>=7] * Chain [656]: 12*s(738)+4*s(740)+0 Such that:s(739) =< V13 aux(69) =< V1 s(740) =< s(739) s(738) =< aux(69) with precondition: [V1>=1,V>=0,V13>=0,Out>=1] * Chain [655]: 4*s(746)+12*s(748)+0 Such that:s(745) =< V1 aux(70) =< V13 s(748) =< aux(70) s(746) =< s(745) with precondition: [V=3,V1>=0,V13>=1,Out>=4] * Chain [654]: 8*s(754)+0 Such that:aux(71) =< V1 s(754) =< aux(71) with precondition: [V=3,V1>=1,V13>=0,Out>=4] * Chain [653]: 8*s(758)+0 Such that:aux(72) =< V1 s(758) =< aux(72) with precondition: [V13=4,V1>=1,V>=0,Out>=5] * Chain [652]: 8*s(762)+0 Such that:aux(73) =< V1 s(762) =< aux(73) with precondition: [V13=5,V1>=1,V>=0,Out>=6] * Chain [651]: 8*s(766)+0 Such that:aux(74) =< V1 s(766) =< aux(74) with precondition: [V13=6,V1>=1,V>=0,Out>=7] * Chain [650]: 0 with precondition: [V1=2,V=3,Out=6,V13>=0] * Chain [649]: 4*s(770)+12*s(772)+0 Such that:s(769) =< V1 aux(75) =< V13 s(772) =< aux(75) s(770) =< s(769) with precondition: [V=4,V1>=0,V13>=1,Out>=5] * Chain [648]: 8*s(778)+0 Such that:aux(76) =< V1 s(778) =< aux(76) with precondition: [V=4,V1>=1,V13>=0,Out>=5] * Chain [647]: 4*s(782)+0 Such that:s(781) =< V1 s(782) =< s(781) with precondition: [V=4,V13=4,V1>=1,Out>=9] * Chain [646]: 4*s(784)+0 Such that:s(783) =< V1 s(784) =< s(783) with precondition: [V=4,V13=5,V1>=1,Out>=10] * Chain [645]: 4*s(786)+0 Such that:s(785) =< V1 s(786) =< s(785) with precondition: [V=4,V13=6,V1>=1,Out>=11] * Chain [644]: 0 with precondition: [V1=2,V=4,Out=7,V13>=0] * Chain [643]: 4*s(788)+12*s(790)+0 Such that:s(787) =< V1 aux(77) =< V13 s(790) =< aux(77) s(788) =< s(787) with precondition: [V=5,V1>=0,V13>=1,Out>=6] * Chain [642]: 8*s(796)+0 Such that:aux(78) =< V1 s(796) =< aux(78) with precondition: [V=5,V1>=1,V13>=0,Out>=6] * Chain [641]: 4*s(800)+0 Such that:s(799) =< V1 s(800) =< s(799) with precondition: [V=5,V13=4,V1>=1,Out>=10] * Chain [640]: 4*s(802)+0 Such that:s(801) =< V1 s(802) =< s(801) with precondition: [V=5,V13=5,V1>=1,Out>=11] * Chain [639]: 4*s(804)+0 Such that:s(803) =< V1 s(804) =< s(803) with precondition: [V=5,V13=6,V1>=1,Out>=12] * Chain [638]: 0 with precondition: [V1=2,V=5,Out=8,V13>=0] * Chain [637]: 4*s(806)+12*s(808)+0 Such that:s(805) =< V1 aux(79) =< V13 s(808) =< aux(79) s(806) =< s(805) with precondition: [V=6,V1>=0,V13>=1,Out>=7] * Chain [636]: 8*s(814)+0 Such that:aux(80) =< V1 s(814) =< aux(80) with precondition: [V=6,V1>=1,V13>=0,Out>=7] * Chain [635]: 4*s(818)+0 Such that:s(817) =< V1 s(818) =< s(817) with precondition: [V=6,V13=4,V1>=1,Out>=11] * Chain [634]: 4*s(820)+0 Such that:s(819) =< V1 s(820) =< s(819) with precondition: [V=6,V13=5,V1>=1,Out>=12] * Chain [633]: 4*s(822)+0 Such that:s(821) =< V1 s(822) =< s(821) with precondition: [V=6,V13=6,V1>=1,Out>=13] * Chain [632]: 0 with precondition: [V1=2,V=6,Out=9,V13>=0] * Chain [631]: 8*s(824)+4*s(826)+0 Such that:s(825) =< V aux(81) =< V1 s(826) =< s(825) s(824) =< aux(81) with precondition: [V13=2,V1>=1,V>=0,Out>=3] * Chain [630]: 8*s(830)+0 Such that:aux(82) =< V s(830) =< aux(82) with precondition: [V13=2,V1>=0,V>=1,Out>=3] * Chain [629]: 8*s(834)+4*s(836)+0 Such that:s(835) =< V aux(83) =< V1 s(836) =< s(835) s(834) =< aux(83) with precondition: [V13=3,V1>=1,V>=0,Out>=4] * Chain [628]: 0 with precondition: [V1=2,V13=4,Out=7,V>=0] * Chain [627]: 0 with precondition: [V1=2,V13=5,Out=8,V>=0] * Chain [626]: 0 with precondition: [V1=2,V13=6,Out=9,V>=0] * Chain [625]: 0 with precondition: [V1=2,Out=3,V>=0,V13>=0] * Chain [624]: 4*s(840)+12*s(842)+0 Such that:s(839) =< V aux(84) =< V13 s(842) =< aux(84) s(840) =< s(839) with precondition: [V1=3,V>=0,V13>=1,Out>=4] * Chain [623]: 8*s(848)+0 Such that:aux(85) =< V s(848) =< aux(85) with precondition: [V1=3,V>=1,V13>=0,Out>=4] * Chain [622]: 4*s(852)+0 Such that:s(851) =< V s(852) =< s(851) with precondition: [V1=3,V13=4,V>=1,Out>=8] * Chain [621]: 4*s(854)+0 Such that:s(853) =< V s(854) =< s(853) with precondition: [V1=3,V13=5,V>=1,Out>=9] * Chain [620]: 4*s(856)+0 Such that:s(855) =< V s(856) =< s(855) with precondition: [V1=3,V13=6,V>=1,Out>=10] * Chain [619]: 0 with precondition: [V1=3,V=2,Out=6,V13>=0] * Chain [618]: 4*s(858)+0 Such that:s(857) =< V13 s(858) =< s(857) with precondition: [V1=3,V=3,V13>=1,Out>=7] * Chain [617]: 4*s(860)+0 Such that:s(859) =< V s(860) =< s(859) with precondition: [V13=3,V1>=0,V>=1,Out>=4] * Chain [616]: 0 with precondition: [V1=3,V=3,V13=4,Out=11] * Chain [615]: 0 with precondition: [V1=3,V=3,V13=5,Out=12] * Chain [614]: 0 with precondition: [V1=3,V=3,V13=6,Out=13] * Chain [613]: 0 with precondition: [V1=3,V=3,Out=7,V13>=0] * Chain [612]: 4*s(862)+0 Such that:s(861) =< V13 s(862) =< s(861) with precondition: [V1=3,V=4,V13>=1,Out>=8] * Chain [611]: 0 with precondition: [V1=3,V=4,V13=3,Out=11] * Chain [610]: 0 with precondition: [V1=3,V=4,V13=4,Out=12] * Chain [609]: 0 with precondition: [V1=3,V=4,V13=5,Out=13] * Chain [608]: 0 with precondition: [V1=3,V=4,V13=6,Out=14] * Chain [607]: 0 with precondition: [V1=3,V=4,Out=8,V13>=0] * Chain [606]: 4*s(864)+0 Such that:s(863) =< V13 s(864) =< s(863) with precondition: [V1=3,V=5,V13>=1,Out>=9] * Chain [605]: 0 with precondition: [V1=3,V=5,V13=3,Out=12] * Chain [604]: 0 with precondition: [V1=3,V=5,V13=4,Out=13] * Chain [603]: 0 with precondition: [V1=3,V=5,V13=5,Out=14] * Chain [602]: 0 with precondition: [V1=3,V=5,V13=6,Out=15] * Chain [601]: 0 with precondition: [V1=3,V=5,Out=9,V13>=0] * Chain [600]: 4*s(866)+0 Such that:s(865) =< V13 s(866) =< s(865) with precondition: [V1=3,V=6,V13>=1,Out>=10] * Chain [599]: 0 with precondition: [V1=3,V=6,V13=3,Out=13] * Chain [598]: 0 with precondition: [V1=3,V=6,V13=4,Out=14] * Chain [597]: 0 with precondition: [V1=3,V=6,V13=5,Out=15] * Chain [596]: 0 with precondition: [V1=3,V=6,V13=6,Out=16] * Chain [595]: 0 with precondition: [V1=3,V=6,Out=10,V13>=0] * Chain [594]: 0 with precondition: [V1=3,V13=2,Out=6,V>=0] * Chain [593]: 4*s(868)+0 Such that:s(867) =< V s(868) =< s(867) with precondition: [V1=3,V13=2,V>=1,Out>=6] * Chain [592]: 0 with precondition: [V1=3,V13=3,Out=7,V>=0] * Chain [591]: 0 with precondition: [V1=3,V13=4,Out=8,V>=0] * Chain [590]: 0 with precondition: [V1=3,V13=5,Out=9,V>=0] * Chain [589]: 0 with precondition: [V1=3,V13=6,Out=10,V>=0] * Chain [588]: 0 with precondition: [V1=3,Out=4,V>=0,V13>=0] * Chain [587]: 4*s(870)+12*s(872)+0 Such that:s(869) =< V aux(86) =< V13 s(872) =< aux(86) s(870) =< s(869) with precondition: [V1=4,V>=0,V13>=1,Out>=5] * Chain [586]: 8*s(878)+0 Such that:aux(87) =< V s(878) =< aux(87) with precondition: [V1=4,V>=1,V13>=0,Out>=5] * Chain [585]: 4*s(882)+0 Such that:s(881) =< V s(882) =< s(881) with precondition: [V1=4,V13=4,V>=1,Out>=9] * Chain [584]: 4*s(884)+0 Such that:s(883) =< V s(884) =< s(883) with precondition: [V1=4,V13=5,V>=1,Out>=10] * Chain [583]: 4*s(886)+0 Such that:s(885) =< V s(886) =< s(885) with precondition: [V1=4,V13=6,V>=1,Out>=11] * Chain [582]: 0 with precondition: [V1=4,V=2,Out=7,V13>=0] * Chain [581]: 4*s(888)+0 Such that:s(887) =< V13 s(888) =< s(887) with precondition: [V1=4,V=3,V13>=1,Out>=8] * Chain [580]: 0 with precondition: [V1=4,V=3,V13=3,Out=11] * Chain [579]: 0 with precondition: [V1=4,V=3,V13=4,Out=12] * Chain [578]: 0 with precondition: [V1=4,V=3,V13=5,Out=13] * Chain [577]: 0 with precondition: [V1=4,V=3,V13=6,Out=14] * Chain [576]: 0 with precondition: [V1=4,V=3,Out=8,V13>=0] * Chain [575]: 4*s(890)+0 Such that:s(889) =< V13 s(890) =< s(889) with precondition: [V1=4,V=4,V13>=1,Out>=9] * Chain [574]: 0 with precondition: [V1=4,V=4,V13=3,Out=12] * Chain [573]: 0 with precondition: [V1=4,V=4,V13=4,Out=13] * Chain [572]: 0 with precondition: [V1=4,V=4,V13=5,Out=14] * Chain [571]: 0 with precondition: [V1=4,V=4,V13=6,Out=15] * Chain [570]: 0 with precondition: [V1=4,V=4,Out=9,V13>=0] * Chain [569]: 4*s(892)+0 Such that:s(891) =< V13 s(892) =< s(891) with precondition: [V1=4,V=5,V13>=1,Out>=10] * Chain [568]: 0 with precondition: [V1=4,V=5,V13=3,Out=13] * Chain [567]: 0 with precondition: [V1=4,V=5,V13=4,Out=14] * Chain [566]: 0 with precondition: [V1=4,V=5,V13=5,Out=15] * Chain [565]: 0 with precondition: [V1=4,V=5,V13=6,Out=16] * Chain [564]: 0 with precondition: [V1=4,V=5,Out=10,V13>=0] * Chain [563]: 4*s(894)+0 Such that:s(893) =< V13 s(894) =< s(893) with precondition: [V1=4,V=6,V13>=1,Out>=11] * Chain [562]: 0 with precondition: [V1=4,V=6,V13=3,Out=14] * Chain [561]: 0 with precondition: [V1=4,V=6,V13=4,Out=15] * Chain [560]: 0 with precondition: [V1=4,V=6,V13=5,Out=16] * Chain [559]: 0 with precondition: [V1=4,V=6,V13=6,Out=17] * Chain [558]: 0 with precondition: [V1=4,V=6,Out=11,V13>=0] * Chain [557]: 0 with precondition: [V1=4,V13=2,Out=7,V>=0] * Chain [556]: 4*s(896)+0 Such that:s(895) =< V s(896) =< s(895) with precondition: [V1=4,V13=2,V>=1,Out>=7] * Chain [555]: 0 with precondition: [V1=4,V13=3,Out=8,V>=0] * Chain [554]: 0 with precondition: [V1=4,V13=4,Out=9,V>=0] * Chain [553]: 0 with precondition: [V1=4,V13=5,Out=10,V>=0] * Chain [552]: 0 with precondition: [V1=4,V13=6,Out=11,V>=0] * Chain [551]: 0 with precondition: [V1=4,Out=5,V>=0,V13>=0] * Chain [550]: 4*s(898)+12*s(900)+0 Such that:s(897) =< V aux(88) =< V13 s(900) =< aux(88) s(898) =< s(897) with precondition: [V1=5,V>=0,V13>=1,Out>=6] * Chain [549]: 8*s(906)+0 Such that:aux(89) =< V s(906) =< aux(89) with precondition: [V1=5,V>=1,V13>=0,Out>=6] * Chain [548]: 4*s(910)+0 Such that:s(909) =< V s(910) =< s(909) with precondition: [V1=5,V13=4,V>=1,Out>=10] * Chain [547]: 4*s(912)+0 Such that:s(911) =< V s(912) =< s(911) with precondition: [V1=5,V13=5,V>=1,Out>=11] * Chain [546]: 4*s(914)+0 Such that:s(913) =< V s(914) =< s(913) with precondition: [V1=5,V13=6,V>=1,Out>=12] * Chain [545]: 0 with precondition: [V1=5,V=2,Out=8,V13>=0] * Chain [544]: 4*s(916)+0 Such that:s(915) =< V13 s(916) =< s(915) with precondition: [V1=5,V=3,V13>=1,Out>=9] * Chain [543]: 0 with precondition: [V1=5,V=3,V13=3,Out=12] * Chain [542]: 0 with precondition: [V1=5,V=3,V13=4,Out=13] * Chain [541]: 0 with precondition: [V1=5,V=3,V13=5,Out=14] * Chain [540]: 0 with precondition: [V1=5,V=3,V13=6,Out=15] * Chain [539]: 0 with precondition: [V1=5,V=3,Out=9,V13>=0] * Chain [538]: 4*s(918)+0 Such that:s(917) =< V13 s(918) =< s(917) with precondition: [V1=5,V=4,V13>=1,Out>=10] * Chain [537]: 0 with precondition: [V1=5,V=4,V13=3,Out=13] * Chain [536]: 0 with precondition: [V1=5,V=4,V13=4,Out=14] * Chain [535]: 0 with precondition: [V1=5,V=4,V13=5,Out=15] * Chain [534]: 0 with precondition: [V1=5,V=4,V13=6,Out=16] * Chain [533]: 0 with precondition: [V1=5,V=4,Out=10,V13>=0] * Chain [532]: 4*s(920)+0 Such that:s(919) =< V13 s(920) =< s(919) with precondition: [V1=5,V=5,V13>=1,Out>=11] * Chain [531]: 0 with precondition: [V1=5,V=5,V13=3,Out=14] * Chain [530]: 0 with precondition: [V1=5,V=5,V13=4,Out=15] * Chain [529]: 0 with precondition: [V1=5,V=5,V13=5,Out=16] * Chain [528]: 0 with precondition: [V1=5,V=5,V13=6,Out=17] * Chain [527]: 0 with precondition: [V1=5,V=5,Out=11,V13>=0] * Chain [526]: 4*s(922)+0 Such that:s(921) =< V13 s(922) =< s(921) with precondition: [V1=5,V=6,V13>=1,Out>=12] * Chain [525]: 0 with precondition: [V1=5,V=6,V13=3,Out=15] * Chain [524]: 0 with precondition: [V1=5,V=6,V13=4,Out=16] * Chain [523]: 0 with precondition: [V1=5,V=6,V13=5,Out=17] * Chain [522]: 0 with precondition: [V1=5,V=6,V13=6,Out=18] * Chain [521]: 0 with precondition: [V1=5,V=6,Out=12,V13>=0] * Chain [520]: 0 with precondition: [V1=5,V13=2,Out=8,V>=0] * Chain [519]: 4*s(924)+0 Such that:s(923) =< V s(924) =< s(923) with precondition: [V1=5,V13=2,V>=1,Out>=8] * Chain [518]: 0 with precondition: [V1=5,V13=3,Out=9,V>=0] * Chain [517]: 0 with precondition: [V1=5,V13=4,Out=10,V>=0] * Chain [516]: 0 with precondition: [V1=5,V13=5,Out=11,V>=0] * Chain [515]: 0 with precondition: [V1=5,V13=6,Out=12,V>=0] * Chain [514]: 0 with precondition: [V1=5,Out=6,V>=0,V13>=0] * Chain [513]: 4*s(926)+12*s(928)+0 Such that:s(925) =< V aux(90) =< V13 s(928) =< aux(90) s(926) =< s(925) with precondition: [V1=6,V>=0,V13>=1,Out>=7] * Chain [512]: 8*s(934)+0 Such that:aux(91) =< V s(934) =< aux(91) with precondition: [V1=6,V>=1,V13>=0,Out>=7] * Chain [511]: 4*s(938)+0 Such that:s(937) =< V s(938) =< s(937) with precondition: [V1=6,V13=4,V>=1,Out>=11] * Chain [510]: 4*s(940)+0 Such that:s(939) =< V s(940) =< s(939) with precondition: [V1=6,V13=5,V>=1,Out>=12] * Chain [509]: 4*s(942)+0 Such that:s(941) =< V s(942) =< s(941) with precondition: [V1=6,V13=6,V>=1,Out>=13] * Chain [508]: 0 with precondition: [V1=6,V=2,Out=9,V13>=0] * Chain [507]: 4*s(944)+0 Such that:s(943) =< V13 s(944) =< s(943) with precondition: [V1=6,V=3,V13>=1,Out>=10] * Chain [506]: 0 with precondition: [V1=6,V=3,V13=3,Out=13] * Chain [505]: 0 with precondition: [V1=6,V=3,V13=4,Out=14] * Chain [504]: 0 with precondition: [V1=6,V=3,V13=5,Out=15] * Chain [503]: 0 with precondition: [V1=6,V=3,V13=6,Out=16] * Chain [502]: 0 with precondition: [V1=6,V=3,Out=10,V13>=0] * Chain [501]: 4*s(946)+0 Such that:s(945) =< V13 s(946) =< s(945) with precondition: [V1=6,V=4,V13>=1,Out>=11] * Chain [500]: 0 with precondition: [V1=6,V=4,V13=3,Out=14] * Chain [499]: 0 with precondition: [V1=6,V=4,V13=4,Out=15] * Chain [498]: 0 with precondition: [V1=6,V=4,V13=5,Out=16] * Chain [497]: 0 with precondition: [V1=6,V=4,V13=6,Out=17] * Chain [496]: 0 with precondition: [V1=6,V=4,Out=11,V13>=0] * Chain [495]: 4*s(948)+0 Such that:s(947) =< V13 s(948) =< s(947) with precondition: [V1=6,V=5,V13>=1,Out>=12] * Chain [494]: 0 with precondition: [V1=6,V=5,V13=3,Out=15] * Chain [493]: 0 with precondition: [V1=6,V=5,V13=4,Out=16] * Chain [492]: 0 with precondition: [V1=6,V=5,V13=5,Out=17] * Chain [491]: 0 with precondition: [V1=6,V=5,V13=6,Out=18] * Chain [490]: 0 with precondition: [V1=6,V=5,Out=12,V13>=0] * Chain [489]: 4*s(950)+0 Such that:s(949) =< V13 s(950) =< s(949) with precondition: [V1=6,V=6,V13>=1,Out>=13] * Chain [488]: 0 with precondition: [V1=6,V=6,V13=3,Out=16] * Chain [487]: 0 with precondition: [V1=6,V=6,V13=4,Out=17] * Chain [486]: 0 with precondition: [V1=6,V=6,V13=5,Out=18] * Chain [485]: 0 with precondition: [V1=6,V=6,V13=6,Out=19] * Chain [484]: 0 with precondition: [V1=6,V=6,Out=13,V13>=0] * Chain [483]: 0 with precondition: [V1=6,V13=2,Out=9,V>=0] * Chain [482]: 4*s(952)+0 Such that:s(951) =< V s(952) =< s(951) with precondition: [V1=6,V13=2,V>=1,Out>=9] * Chain [481]: 0 with precondition: [V1=6,V13=3,Out=10,V>=0] * Chain [480]: 0 with precondition: [V1=6,V13=4,Out=11,V>=0] * Chain [479]: 0 with precondition: [V1=6,V13=5,Out=12,V>=0] * Chain [478]: 0 with precondition: [V1=6,V13=6,Out=13,V>=0] * Chain [477]: 0 with precondition: [V1=6,Out=7,V>=0,V13>=0] * Chain [476]: 4*s(954)+0 Such that:s(953) =< V13 s(954) =< s(953) with precondition: [V=2,V1>=0,V13>=1,Out>=3] * Chain [475]: 4*s(956)+0 Such that:s(955) =< V1 s(956) =< s(955) with precondition: [V=2,V13=2,V1>=1,Out>=5] * Chain [474]: 0 with precondition: [V=2,V13=3,Out=6,V1>=0] * Chain [473]: 4*s(958)+0 Such that:s(957) =< V1 s(958) =< s(957) with precondition: [V=2,V13=3,V1>=1,Out>=6] * Chain [472]: 0 with precondition: [V=2,V13=4,Out=7,V1>=0] * Chain [471]: 4*s(960)+0 Such that:s(959) =< V1 s(960) =< s(959) with precondition: [V=2,V13=4,V1>=1,Out>=7] * Chain [470]: 0 with precondition: [V=2,V13=5,Out=8,V1>=0] * Chain [469]: 4*s(962)+0 Such that:s(961) =< V1 s(962) =< s(961) with precondition: [V=2,V13=5,V1>=1,Out>=8] * Chain [468]: 0 with precondition: [V=2,V13=6,Out=9,V1>=0] * Chain [467]: 4*s(964)+0 Such that:s(963) =< V1 s(964) =< s(963) with precondition: [V=2,V13=6,V1>=1,Out>=9] * Chain [466]: 0 with precondition: [V=2,Out=3,V1>=0,V13>=0] * Chain [465]: 0 with precondition: [V=3,V13=2,Out=6,V1>=0] * Chain [464]: 4*s(966)+0 Such that:s(965) =< V1 s(966) =< s(965) with precondition: [V=3,V13=2,V1>=1,Out>=6] * Chain [463]: 0 with precondition: [V=3,V13=3,Out=7,V1>=0] * Chain [462]: 0 with precondition: [V=3,V13=4,Out=8,V1>=0] * Chain [461]: 0 with precondition: [V=3,V13=5,Out=9,V1>=0] * Chain [460]: 0 with precondition: [V=3,V13=6,Out=10,V1>=0] * Chain [459]: 0 with precondition: [V=3,Out=4,V1>=0,V13>=0] * Chain [458]: 0 with precondition: [V=4,V13=2,Out=7,V1>=0] * Chain [457]: 4*s(968)+0 Such that:s(967) =< V1 s(968) =< s(967) with precondition: [V=4,V13=2,V1>=1,Out>=7] * Chain [456]: 0 with precondition: [V=4,V13=3,Out=8,V1>=0] * Chain [455]: 0 with precondition: [V=4,V13=4,Out=9,V1>=0] * Chain [454]: 0 with precondition: [V=4,V13=5,Out=10,V1>=0] * Chain [453]: 0 with precondition: [V=4,V13=6,Out=11,V1>=0] * Chain [452]: 0 with precondition: [V=4,Out=5,V1>=0,V13>=0] * Chain [451]: 0 with precondition: [V=5,V13=2,Out=8,V1>=0] * Chain [450]: 4*s(970)+0 Such that:s(969) =< V1 s(970) =< s(969) with precondition: [V=5,V13=2,V1>=1,Out>=8] * Chain [449]: 0 with precondition: [V=5,V13=3,Out=9,V1>=0] * Chain [448]: 0 with precondition: [V=5,V13=4,Out=10,V1>=0] * Chain [447]: 0 with precondition: [V=5,V13=5,Out=11,V1>=0] * Chain [446]: 0 with precondition: [V=5,V13=6,Out=12,V1>=0] * Chain [445]: 0 with precondition: [V=5,Out=6,V1>=0,V13>=0] * Chain [444]: 0 with precondition: [V=6,V13=2,Out=9,V1>=0] * Chain [443]: 4*s(972)+0 Such that:s(971) =< V1 s(972) =< s(971) with precondition: [V=6,V13=2,V1>=1,Out>=9] * Chain [442]: 0 with precondition: [V=6,V13=3,Out=10,V1>=0] * Chain [441]: 0 with precondition: [V=6,V13=4,Out=11,V1>=0] * Chain [440]: 0 with precondition: [V=6,V13=5,Out=12,V1>=0] * Chain [439]: 0 with precondition: [V=6,V13=6,Out=13,V1>=0] * Chain [438]: 0 with precondition: [V=6,Out=7,V1>=0,V13>=0] * Chain [437]: 0 with precondition: [V13=2,Out=3,V1>=0,V>=0] * Chain [436]: 0 with precondition: [V13=3,Out=4,V1>=0,V>=0] * Chain [435]: 0 with precondition: [V13=4,Out=5,V1>=0,V>=0] * Chain [434]: 0 with precondition: [V13=5,Out=6,V1>=0,V>=0] * Chain [433]: 0 with precondition: [V13=6,Out=7,V1>=0,V>=0] * Chain [432]: 0 with precondition: [Out=0,V1>=0,V>=0,V13>=0] * Chain [431]: 0 with precondition: [Out=1,V1>=0,V>=0,V13>=0] #### Cost of chains of fun9(Out): * Chain [663]: 0 with precondition: [Out=0] * Chain [662]: 0 with precondition: [Out=6] #### Cost of chains of start(V1,V,V13): * Chain [664]: 524*s(1146)+516*s(1149)+392*s(1202)+3 Such that:aux(106) =< V1 aux(107) =< V aux(108) =< V13 s(1146) =< aux(106) s(1149) =< aux(107) s(1202) =< aux(108) with precondition: [] Closed-form bounds of start(V1,V,V13): ------------------------------------- * Chain [664] with precondition: [] - Upper bound: nat(V1)*524+3+nat(V)*516+nat(V13)*392 - Complexity: n ### Maximum cost of start(V1,V,V13): nat(V1)*524+3+nat(V)*516+nat(V13)*392 Asymptotic class: n * Total analysis performed in 5918 ms. ---------------------------------------- (16) BOUNDS(1, n^1)