WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 210 ms] (4) CpxRelTRS (5) NonCtorToCtorProof [UPPER BOUND(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) NarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (14) CpxTypedWeightedCompleteTrs (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) InliningProof [UPPER BOUND(ID), 470 ms] (18) CpxRNTS (19) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRNTS (21) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 1 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 61 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 14 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 463 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 234 ms] (34) CpxRNTS (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 116 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 42 ms] (40) CpxRNTS (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 54 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 22 ms] (46) CpxRNTS (47) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 5 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 1 ms] (52) CpxRNTS (53) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (54) CpxRNTS (55) IntTrsBoundProof [UPPER BOUND(ID), 840 ms] (56) CpxRNTS (57) IntTrsBoundProof [UPPER BOUND(ID), 632 ms] (58) CpxRNTS (59) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (60) CpxRNTS (61) IntTrsBoundProof [UPPER BOUND(ID), 454 ms] (62) CpxRNTS (63) IntTrsBoundProof [UPPER BOUND(ID), 158 ms] (64) CpxRNTS (65) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (66) CpxRNTS (67) IntTrsBoundProof [UPPER BOUND(ID), 116 ms] (68) CpxRNTS (69) IntTrsBoundProof [UPPER BOUND(ID), 62 ms] (70) CpxRNTS (71) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (72) CpxRNTS (73) IntTrsBoundProof [UPPER BOUND(ID), 138 ms] (74) CpxRNTS (75) IntTrsBoundProof [UPPER BOUND(ID), 62 ms] (76) CpxRNTS (77) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (78) CpxRNTS (79) IntTrsBoundProof [UPPER BOUND(ID), 343 ms] (80) CpxRNTS (81) IntTrsBoundProof [UPPER BOUND(ID), 28 ms] (82) CpxRNTS (83) FinalProof [FINISHED, 0 ms] (84) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: h(X) -> g(X, X) g(a, X) -> f(b, activate(X)) f(X, X) -> h(a) a -> b activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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(b) -> b encArg(cons_h(x_1)) -> h(encArg(x_1)) encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encArg(cons_a) -> a encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_h(x_1) -> h(encArg(x_1)) encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_a -> a encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_b -> b encode_activate(x_1) -> activate(encArg(x_1)) ---------------------------------------- (2) 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: h(X) -> g(X, X) g(a, X) -> f(b, activate(X)) f(X, X) -> h(a) a -> b activate(X) -> X The (relative) TRS S consists of the following rules: encArg(b) -> b encArg(cons_h(x_1)) -> h(encArg(x_1)) encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encArg(cons_a) -> a encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_h(x_1) -> h(encArg(x_1)) encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_a -> a encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_b -> b encode_activate(x_1) -> activate(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) 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: h(X) -> g(X, X) g(a, X) -> f(b, activate(X)) f(X, X) -> h(a) a -> b activate(X) -> X The (relative) TRS S consists of the following rules: encArg(b) -> b encArg(cons_h(x_1)) -> h(encArg(x_1)) encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encArg(cons_a) -> a encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_h(x_1) -> h(encArg(x_1)) encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_a -> a encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_b -> b encode_activate(x_1) -> activate(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) NonCtorToCtorProof (UPPER BOUND(ID)) transformed non-ctor to ctor-system ---------------------------------------- (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: h(X) -> g(X, X) f(X, X) -> h(a) a -> b activate(X) -> X g(c_a, X) -> f(b, activate(X)) The (relative) TRS S consists of the following rules: encArg(b) -> b encArg(cons_h(x_1)) -> h(encArg(x_1)) encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encArg(cons_a) -> a encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_h(x_1) -> h(encArg(x_1)) encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) encode_a -> a encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_b -> b encode_activate(x_1) -> activate(encArg(x_1)) a -> c_a 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: h(X) -> g(X, X) [1] f(X, X) -> h(a) [1] a -> b [1] activate(X) -> X [1] g(c_a, X) -> f(b, activate(X)) [1] encArg(b) -> b [0] encArg(cons_h(x_1)) -> h(encArg(x_1)) [0] encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encArg(cons_a) -> a [0] encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0] encode_h(x_1) -> h(encArg(x_1)) [0] encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_b -> b [0] encode_activate(x_1) -> activate(encArg(x_1)) [0] a -> c_a [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: h(X) -> g(X, X) [1] f(X, X) -> h(a) [1] a -> b [1] activate(X) -> X [1] g(c_a, X) -> f(b, activate(X)) [1] encArg(b) -> b [0] encArg(cons_h(x_1)) -> h(encArg(x_1)) [0] encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encArg(cons_a) -> a [0] encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0] encode_h(x_1) -> h(encArg(x_1)) [0] encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_b -> b [0] encode_activate(x_1) -> activate(encArg(x_1)) [0] a -> c_a [0] The TRS has the following type information: h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate b :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate c_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate encArg :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate cons_h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate cons_g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate cons_f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate cons_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate cons_activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate encode_h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate encode_g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate encode_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate encode_f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate encode_b :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate encode_activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate Rewrite Strategy: INNERMOST ---------------------------------------- (11) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: activate_1 g_2 f_2 h_1 encArg_1 encode_h_1 encode_g_2 encode_a encode_f_2 encode_b encode_activate_1 a Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_h(v0) -> null_encode_h [0] encode_g(v0, v1) -> null_encode_g [0] encode_a -> null_encode_a [0] encode_f(v0, v1) -> null_encode_f [0] encode_b -> null_encode_b [0] encode_activate(v0) -> null_encode_activate [0] a -> null_a [0] g(v0, v1) -> null_g [0] f(v0, v1) -> null_f [0] And the following fresh constants: null_encArg, null_encode_h, null_encode_g, null_encode_a, null_encode_f, null_encode_b, null_encode_activate, null_a, null_g, null_f ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: h(X) -> g(X, X) [1] f(X, X) -> h(a) [1] a -> b [1] activate(X) -> X [1] g(c_a, X) -> f(b, activate(X)) [1] encArg(b) -> b [0] encArg(cons_h(x_1)) -> h(encArg(x_1)) [0] encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encArg(cons_a) -> a [0] encArg(cons_activate(x_1)) -> activate(encArg(x_1)) [0] encode_h(x_1) -> h(encArg(x_1)) [0] encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_b -> b [0] encode_activate(x_1) -> activate(encArg(x_1)) [0] a -> c_a [0] encArg(v0) -> null_encArg [0] encode_h(v0) -> null_encode_h [0] encode_g(v0, v1) -> null_encode_g [0] encode_a -> null_encode_a [0] encode_f(v0, v1) -> null_encode_f [0] encode_b -> null_encode_b [0] encode_activate(v0) -> null_encode_activate [0] a -> null_a [0] g(v0, v1) -> null_g [0] f(v0, v1) -> null_f [0] The TRS has the following type information: h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f b :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f c_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encArg :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f cons_h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f cons_g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f cons_f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f cons_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f cons_activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_b :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encArg :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_b :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f Rewrite Strategy: INNERMOST ---------------------------------------- (13) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (14) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: h(X) -> g(X, X) [1] f(X, X) -> h(b) [2] f(X, X) -> h(c_a) [1] f(X, X) -> h(null_a) [1] a -> b [1] activate(X) -> X [1] g(c_a, X) -> f(b, X) [2] encArg(b) -> b [0] encArg(cons_h(b)) -> h(b) [0] encArg(cons_h(cons_h(x_1'))) -> h(h(encArg(x_1'))) [0] encArg(cons_h(cons_g(x_1'', x_2'))) -> h(g(encArg(x_1''), encArg(x_2'))) [0] encArg(cons_h(cons_f(x_11, x_2''))) -> h(f(encArg(x_11), encArg(x_2''))) [0] encArg(cons_h(cons_a)) -> h(a) [0] encArg(cons_h(cons_activate(x_12))) -> h(activate(encArg(x_12))) [0] encArg(cons_h(x_1)) -> h(null_encArg) [0] encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encArg(cons_a) -> a [0] encArg(cons_activate(b)) -> activate(b) [0] encArg(cons_activate(cons_h(x_167))) -> activate(h(encArg(x_167))) [0] encArg(cons_activate(cons_g(x_168, x_233))) -> activate(g(encArg(x_168), encArg(x_233))) [0] encArg(cons_activate(cons_f(x_169, x_234))) -> activate(f(encArg(x_169), encArg(x_234))) [0] encArg(cons_activate(cons_a)) -> activate(a) [0] encArg(cons_activate(cons_activate(x_170))) -> activate(activate(encArg(x_170))) [0] encArg(cons_activate(x_1)) -> activate(null_encArg) [0] encode_h(b) -> h(b) [0] encode_h(cons_h(x_171)) -> h(h(encArg(x_171))) [0] encode_h(cons_g(x_172, x_235)) -> h(g(encArg(x_172), encArg(x_235))) [0] encode_h(cons_f(x_173, x_236)) -> h(f(encArg(x_173), encArg(x_236))) [0] encode_h(cons_a) -> h(a) [0] encode_h(cons_activate(x_174)) -> h(activate(encArg(x_174))) [0] encode_h(x_1) -> h(null_encArg) [0] encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_b -> b [0] encode_activate(b) -> activate(b) [0] encode_activate(cons_h(x_1139)) -> activate(h(encArg(x_1139))) [0] encode_activate(cons_g(x_1140, x_269)) -> activate(g(encArg(x_1140), encArg(x_269))) [0] encode_activate(cons_f(x_1141, x_270)) -> activate(f(encArg(x_1141), encArg(x_270))) [0] encode_activate(cons_a) -> activate(a) [0] encode_activate(cons_activate(x_1142)) -> activate(activate(encArg(x_1142))) [0] encode_activate(x_1) -> activate(null_encArg) [0] a -> c_a [0] encArg(v0) -> null_encArg [0] encode_h(v0) -> null_encode_h [0] encode_g(v0, v1) -> null_encode_g [0] encode_a -> null_encode_a [0] encode_f(v0, v1) -> null_encode_f [0] encode_b -> null_encode_b [0] encode_activate(v0) -> null_encode_activate [0] a -> null_a [0] g(v0, v1) -> null_g [0] f(v0, v1) -> null_f [0] The TRS has the following type information: h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f b :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f c_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encArg :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f cons_h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f cons_g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f cons_f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f cons_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f cons_activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_b :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f encode_activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f -> b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encArg :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_h :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_b :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_encode_activate :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_a :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_g :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f null_f :: b:c_a:cons_h:cons_g:cons_f:cons_a:cons_activate:null_encArg:null_encode_h:null_encode_g:null_encode_a:null_encode_f:null_encode_b:null_encode_activate:null_a:null_g:null_f Rewrite Strategy: INNERMOST ---------------------------------------- (15) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: b => 0 c_a => 1 cons_a => 2 null_encArg => 0 null_encode_h => 0 null_encode_g => 0 null_encode_a => 0 null_encode_f => 0 null_encode_b => 0 null_encode_activate => 0 null_a => 0 null_g => 0 null_f => 0 ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> X :|: X >= 0, z = X encArg(z) -{ 0 }-> h(h(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0 encArg(z) -{ 0 }-> h(a) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> h(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(x_167))) :|: z = 1 + (1 + x_167), x_167 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(x_170))) :|: z = 1 + (1 + x_170), x_170 >= 0 encArg(z) -{ 0 }-> activate(a) :|: z = 1 + 2 encArg(z) -{ 0 }-> activate(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> activate(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> a :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_a -{ 0 }-> a :|: encode_a -{ 0 }-> 0 :|: encode_activate(z) -{ 0 }-> activate(h(encArg(x_1139))) :|: z = 1 + x_1139, x_1139 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(x_1142))) :|: z = 1 + x_1142, x_1142 >= 0 encode_activate(z) -{ 0 }-> activate(a) :|: z = 2 encode_activate(z) -{ 0 }-> activate(0) :|: z = 0 encode_activate(z) -{ 0 }-> activate(0) :|: x_1 >= 0, z = x_1 encode_activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_b -{ 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 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_h(z) -{ 0 }-> h(h(encArg(x_171))) :|: z = 1 + x_171, x_171 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(x_174))) :|: x_174 >= 0, z = 1 + x_174 encode_h(z) -{ 0 }-> h(a) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 0 encode_h(z) -{ 0 }-> h(0) :|: x_1 >= 0, z = x_1 encode_h(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 f(z, z') -{ 1 }-> h(1) :|: z' = X, X >= 0, z = X f(z, z') -{ 2 }-> h(0) :|: z' = X, X >= 0, z = X f(z, z') -{ 1 }-> h(0) :|: z' = X, X >= 0, z = X f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 g(z, z') -{ 2 }-> f(0, X) :|: z' = X, z = 1, X >= 0 g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 h(z) -{ 1 }-> g(X, X) :|: X >= 0, z = X ---------------------------------------- (17) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> X :|: X >= 0, z = X ---------------------------------------- (18) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> X :|: X >= 0, z = X encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + x_1, x_1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 0 }-> h(h(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0 encArg(z) -{ 0 }-> h(1) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> h(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 1 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(x_167))) :|: z = 1 + (1 + x_167), x_167 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(x_170))) :|: z = 1 + (1 + x_170), x_170 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: x_1 >= 0, z = x_1, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(x_1139))) :|: z = 1 + x_1139, x_1139 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(x_1142))) :|: z = 1 + x_1142, x_1142 >= 0 encode_activate(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_b -{ 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 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_h(z) -{ 0 }-> h(h(encArg(x_171))) :|: z = 1 + x_171, x_171 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(x_174))) :|: x_174 >= 0, z = 1 + x_174 encode_h(z) -{ 0 }-> h(1) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 0 encode_h(z) -{ 0 }-> h(0) :|: x_1 >= 0, z = x_1 encode_h(z) -{ 1 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 f(z, z') -{ 1 }-> h(1) :|: z' = X, X >= 0, z = X f(z, z') -{ 2 }-> h(0) :|: z' = X, X >= 0, z = X f(z, z') -{ 1 }-> h(0) :|: z' = X, X >= 0, z = X f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 g(z, z') -{ 2 }-> f(0, X) :|: z' = X, z = 1, X >= 0 g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 h(z) -{ 1 }-> g(X, X) :|: X >= 0, z = X ---------------------------------------- (19) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (20) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(1) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> h(0) :|: z - 1 >= 0 encArg(z) -{ 1 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(1) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 0 encode_h(z) -{ 0 }-> h(0) :|: z >= 0 encode_h(z) -{ 1 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 1 }-> h(1) :|: z' >= 0, z = z' f(z, z') -{ 2 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 1 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 2 }-> f(0, z') :|: z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 1 }-> g(z, z) :|: z >= 0 ---------------------------------------- (21) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { encode_a } { f, h, g } { activate } { encode_b } { a } { encArg } { encode_activate } { encode_f } { encode_g } { encode_h } ---------------------------------------- (22) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(1) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> h(0) :|: z - 1 >= 0 encArg(z) -{ 1 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(1) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 0 encode_h(z) -{ 0 }-> h(0) :|: z >= 0 encode_h(z) -{ 1 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 1 }-> h(1) :|: z' >= 0, z = z' f(z, z') -{ 2 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 1 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 2 }-> f(0, z') :|: z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 1 }-> g(z, z) :|: z >= 0 Function symbols to be analyzed: {encode_a}, {f,h,g}, {activate}, {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} ---------------------------------------- (23) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (24) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(1) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> h(0) :|: z - 1 >= 0 encArg(z) -{ 1 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(1) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 0 encode_h(z) -{ 0 }-> h(0) :|: z >= 0 encode_h(z) -{ 1 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 1 }-> h(1) :|: z' >= 0, z = z' f(z, z') -{ 2 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 1 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 2 }-> f(0, z') :|: z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 1 }-> g(z, z) :|: z >= 0 Function symbols to be analyzed: {encode_a}, {f,h,g}, {activate}, {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} ---------------------------------------- (25) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: encode_a after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(1) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> h(0) :|: z - 1 >= 0 encArg(z) -{ 1 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(1) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 0 encode_h(z) -{ 0 }-> h(0) :|: z >= 0 encode_h(z) -{ 1 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 1 }-> h(1) :|: z' >= 0, z = z' f(z, z') -{ 2 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 1 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 2 }-> f(0, z') :|: z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 1 }-> g(z, z) :|: z >= 0 Function symbols to be analyzed: {encode_a}, {f,h,g}, {activate}, {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: ?, size: O(1) [1] ---------------------------------------- (27) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: encode_a after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(1) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> h(0) :|: z - 1 >= 0 encArg(z) -{ 1 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(1) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 0 encode_h(z) -{ 0 }-> h(0) :|: z >= 0 encode_h(z) -{ 1 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 1 }-> h(1) :|: z' >= 0, z = z' f(z, z') -{ 2 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 1 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 2 }-> f(0, z') :|: z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 1 }-> g(z, z) :|: z >= 0 Function symbols to be analyzed: {f,h,g}, {activate}, {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] ---------------------------------------- (29) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(1) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> h(0) :|: z - 1 >= 0 encArg(z) -{ 1 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(1) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 0 encode_h(z) -{ 0 }-> h(0) :|: z >= 0 encode_h(z) -{ 1 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 1 }-> h(1) :|: z' >= 0, z = z' f(z, z') -{ 2 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 1 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 2 }-> f(0, z') :|: z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 1 }-> g(z, z) :|: z >= 0 Function symbols to be analyzed: {f,h,g}, {activate}, {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] ---------------------------------------- (31) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: f after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 Computed SIZE bound using CoFloCo for: h after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 Computed SIZE bound using CoFloCo for: g after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(1) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> h(0) :|: z - 1 >= 0 encArg(z) -{ 1 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(1) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 0 encode_h(z) -{ 0 }-> h(0) :|: z >= 0 encode_h(z) -{ 1 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 1 }-> h(1) :|: z' >= 0, z = z' f(z, z') -{ 2 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 1 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 2 }-> f(0, z') :|: z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 1 }-> g(z, z) :|: z >= 0 Function symbols to be analyzed: {f,h,g}, {activate}, {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: ?, size: O(1) [0] h: runtime: ?, size: O(1) [0] g: runtime: ?, size: O(1) [0] ---------------------------------------- (33) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: f after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 4 Computed RUNTIME bound using CoFloCo for: h after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 7 Computed RUNTIME bound using CoFloCo for: g after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 6 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(1) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 0 encArg(z) -{ 0 }-> h(0) :|: z - 1 >= 0 encArg(z) -{ 1 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> h(0) :|: z = 1 + 2 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(1) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 0 encode_h(z) -{ 0 }-> h(0) :|: z >= 0 encode_h(z) -{ 1 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> h(0) :|: z = 2 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 1 }-> h(1) :|: z' >= 0, z = z' f(z, z') -{ 2 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 1 }-> h(0) :|: z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 2 }-> f(0, z') :|: z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 1 }-> g(z, z) :|: z >= 0 Function symbols to be analyzed: {activate}, {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] ---------------------------------------- (35) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {activate}, {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] ---------------------------------------- (37) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: activate after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {activate}, {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: ?, size: O(n^1) [z] ---------------------------------------- (39) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: activate after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (41) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (42) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (43) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: encode_b after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_b}, {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: ?, size: O(1) [0] ---------------------------------------- (45) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: encode_b after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (46) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] ---------------------------------------- (47) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] ---------------------------------------- (49) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: a after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (50) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {a}, {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: ?, size: O(1) [1] ---------------------------------------- (51) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: a after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (52) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] ---------------------------------------- (53) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] ---------------------------------------- (55) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: encArg after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encArg}, {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: ?, size: O(1) [1] ---------------------------------------- (57) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: encArg after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 8 + 14*z ---------------------------------------- (58) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> h(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> h(g(encArg(x_1''), encArg(x_2'))) :|: x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 0 }-> h(f(encArg(x_11), encArg(x_2''))) :|: x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> h(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 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 }-> activate(h(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> activate(g(encArg(x_168), encArg(x_233))) :|: x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 0 }-> activate(f(encArg(x_169), encArg(x_234))) :|: x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ 0 }-> activate(activate(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 0 }-> activate(h(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> activate(g(encArg(x_1140), encArg(x_269))) :|: x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 0 }-> activate(f(encArg(x_1141), encArg(x_270))) :|: z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ 0 }-> activate(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 0 }-> h(h(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> h(g(encArg(x_172), encArg(x_235))) :|: x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 0 }-> h(f(encArg(x_173), encArg(x_236))) :|: x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 0 }-> h(activate(encArg(z - 1))) :|: z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] ---------------------------------------- (59) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (60) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] ---------------------------------------- (61) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: encode_activate after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_activate}, {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: ?, size: O(1) [1] ---------------------------------------- (63) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: encode_activate after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 9 + 14*z ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: O(n^1) [9 + 14*z], size: O(1) [1] ---------------------------------------- (65) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (66) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: O(n^1) [9 + 14*z], size: O(1) [1] ---------------------------------------- (67) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: encode_f after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (68) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_f}, {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: O(n^1) [9 + 14*z], size: O(1) [1] encode_f: runtime: ?, size: O(1) [0] ---------------------------------------- (69) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: encode_f after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 20 + 14*z + 14*z' ---------------------------------------- (70) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: O(n^1) [9 + 14*z], size: O(1) [1] encode_f: runtime: O(n^1) [20 + 14*z + 14*z'], size: O(1) [0] ---------------------------------------- (71) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (72) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: O(n^1) [9 + 14*z], size: O(1) [1] encode_f: runtime: O(n^1) [20 + 14*z + 14*z'], size: O(1) [0] ---------------------------------------- (73) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: encode_g after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (74) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_g}, {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: O(n^1) [9 + 14*z], size: O(1) [1] encode_f: runtime: O(n^1) [20 + 14*z + 14*z'], size: O(1) [0] encode_g: runtime: ?, size: O(1) [0] ---------------------------------------- (75) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: encode_g after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 22 + 14*z + 14*z' ---------------------------------------- (76) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: O(n^1) [9 + 14*z], size: O(1) [1] encode_f: runtime: O(n^1) [20 + 14*z + 14*z'], size: O(1) [0] encode_g: runtime: O(n^1) [22 + 14*z + 14*z'], size: O(1) [0] ---------------------------------------- (77) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (78) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: O(n^1) [9 + 14*z], size: O(1) [1] encode_f: runtime: O(n^1) [20 + 14*z + 14*z'], size: O(1) [0] encode_g: runtime: O(n^1) [22 + 14*z + 14*z'], size: O(1) [0] ---------------------------------------- (79) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: encode_h after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (80) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: {encode_h} Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: O(n^1) [9 + 14*z], size: O(1) [1] encode_f: runtime: O(n^1) [20 + 14*z + 14*z'], size: O(1) [0] encode_g: runtime: O(n^1) [22 + 14*z + 14*z'], size: O(1) [0] encode_h: runtime: ?, size: O(1) [0] ---------------------------------------- (81) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: encode_h after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 15 + 14*z ---------------------------------------- (82) Obligation: Complexity RNTS consisting of the following rules: a -{ 0 }-> 1 :|: a -{ 1 }-> 0 :|: a -{ 0 }-> 0 :|: activate(z) -{ 1 }-> z :|: z >= 0 encArg(z) -{ 1 }-> X :|: z = 1 + 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z - 1 >= 0, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 1 = X encArg(z) -{ 2 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ 1 }-> X :|: z = 1 + 2, X >= 0, 0 = X encArg(z) -{ -6 + 14*z }-> s15 :|: s13 >= 0, s13 <= 1, s14 >= 0, s14 <= 0, s15 >= 0, s15 <= 0, z - 2 >= 0 encArg(z) -{ 29 + 14*x_1'' + 14*x_2' }-> s19 :|: s16 >= 0, s16 <= 1, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= 0, x_1'' >= 0, z = 1 + (1 + x_1'' + x_2'), x_2' >= 0 encArg(z) -{ 27 + 14*x_11 + 14*x_2'' }-> s23 :|: s20 >= 0, s20 <= 1, s21 >= 0, s21 <= 1, s22 >= 0, s22 <= 0, s23 >= 0, s23 <= 0, x_11 >= 0, z = 1 + (1 + x_11 + x_2''), x_2'' >= 0 encArg(z) -{ 22 + 14*x_1 + 14*x_2 }-> s26 :|: s24 >= 0, s24 <= 1, s25 >= 0, s25 <= 1, s26 >= 0, s26 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 20 + 14*x_1 + 14*x_2 }-> s29 :|: s27 >= 0, s27 <= 1, s28 >= 0, s28 <= 1, s29 >= 0, s29 <= 0, x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 7 }-> s3 :|: s3 >= 0, s3 <= 0, z = 1 + 0 encArg(z) -{ 7 }-> s4 :|: s4 >= 0, s4 <= 0, z - 1 >= 0 encArg(z) -{ -12 + 14*z }-> s49 :|: s47 >= 0, s47 <= 1, s48 >= 0, s48 <= s47, s49 >= 0, s49 <= 0, z - 2 >= 0 encArg(z) -{ -12 + 14*z }-> s52 :|: s50 >= 0, s50 <= 1, s51 >= 0, s51 <= 0, s52 >= 0, s52 <= s51, z - 2 >= 0 encArg(z) -{ 23 + 14*x_168 + 14*x_233 }-> s56 :|: s53 >= 0, s53 <= 1, s54 >= 0, s54 <= 1, s55 >= 0, s55 <= 0, s56 >= 0, s56 <= s55, x_233 >= 0, x_168 >= 0, z = 1 + (1 + x_168 + x_233) encArg(z) -{ 21 + 14*x_169 + 14*x_234 }-> s60 :|: s57 >= 0, s57 <= 1, s58 >= 0, s58 <= 1, s59 >= 0, s59 <= 0, s60 >= 0, s60 <= s59, x_234 >= 0, z = 1 + (1 + x_169 + x_234), x_169 >= 0 encArg(z) -{ -18 + 14*z }-> s63 :|: s61 >= 0, s61 <= 1, s62 >= 0, s62 <= s61, s63 >= 0, s63 <= s62, z - 2 >= 0 encArg(z) -{ 7 }-> s7 :|: s7 >= 0, s7 <= 0, z = 1 + 2 encArg(z) -{ 8 }-> s8 :|: s8 >= 0, s8 <= 0, z = 1 + 2 encArg(z) -{ 7 }-> s9 :|: s9 >= 0, s9 <= 0, z = 1 + 2 encArg(z) -{ 0 }-> 1 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 1 }-> 0 :|: z = 2 encArg(z) -{ 0 }-> 0 :|: z = 2 encode_a -{ 0 }-> 1 :|: encode_a -{ 0 }-> 0 :|: encode_a -{ 1 }-> 0 :|: encode_activate(z) -{ 1 }-> X :|: z = 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z >= 0, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 1 = X encode_activate(z) -{ 2 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 1 }-> X :|: z = 2, X >= 0, 0 = X encode_activate(z) -{ 2 + 14*z }-> s69 :|: s67 >= 0, s67 <= 1, s68 >= 0, s68 <= 0, s69 >= 0, s69 <= s68, z - 1 >= 0 encode_activate(z) -{ 23 + 14*x_1140 + 14*x_269 }-> s73 :|: s70 >= 0, s70 <= 1, s71 >= 0, s71 <= 1, s72 >= 0, s72 <= 0, s73 >= 0, s73 <= s72, x_269 >= 0, x_1140 >= 0, z = 1 + x_1140 + x_269 encode_activate(z) -{ 21 + 14*x_1141 + 14*x_270 }-> s77 :|: s74 >= 0, s74 <= 1, s75 >= 0, s75 <= 1, s76 >= 0, s76 <= 0, s77 >= 0, s77 <= s76, z = 1 + x_1141 + x_270, x_1141 >= 0, x_270 >= 0 encode_activate(z) -{ -4 + 14*z }-> s80 :|: s78 >= 0, s78 <= 1, s79 >= 0, s79 <= s78, s80 >= 0, s80 <= s79, z - 1 >= 0 encode_activate(z) -{ 0 }-> 0 :|: z >= 0 encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 20 + 14*z + 14*z' }-> s46 :|: s44 >= 0, s44 <= 1, s45 >= 0, s45 <= 1, s46 >= 0, s46 <= 0, z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_g(z, z') -{ 22 + 14*z + 14*z' }-> s43 :|: s41 >= 0, s41 <= 1, s42 >= 0, s42 <= 1, s43 >= 0, s43 <= 0, z >= 0, z' >= 0 encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_h(z) -{ 7 }-> s10 :|: s10 >= 0, s10 <= 0, z = 2 encode_h(z) -{ 8 }-> s11 :|: s11 >= 0, s11 <= 0, z = 2 encode_h(z) -{ 7 }-> s12 :|: s12 >= 0, s12 <= 0, z = 2 encode_h(z) -{ 8 + 14*z }-> s32 :|: s30 >= 0, s30 <= 1, s31 >= 0, s31 <= 0, s32 >= 0, s32 <= 0, z - 1 >= 0 encode_h(z) -{ 29 + 14*x_172 + 14*x_235 }-> s36 :|: s33 >= 0, s33 <= 1, s34 >= 0, s34 <= 1, s35 >= 0, s35 <= 0, s36 >= 0, s36 <= 0, x_172 >= 0, x_235 >= 0, z = 1 + x_172 + x_235 encode_h(z) -{ 27 + 14*x_173 + 14*x_236 }-> s40 :|: s37 >= 0, s37 <= 1, s38 >= 0, s38 <= 1, s39 >= 0, s39 <= 0, s40 >= 0, s40 <= 0, x_173 >= 0, z = 1 + x_173 + x_236, x_236 >= 0 encode_h(z) -{ 7 }-> s5 :|: s5 >= 0, s5 <= 0, z = 0 encode_h(z) -{ 7 }-> s6 :|: s6 >= 0, s6 <= 0, z >= 0 encode_h(z) -{ 2 + 14*z }-> s66 :|: s64 >= 0, s64 <= 1, s65 >= 0, s65 <= s64, s66 >= 0, s66 <= 0, z - 1 >= 0 encode_h(z) -{ 0 }-> 0 :|: z >= 0 f(z, z') -{ 9 }-> s' :|: s' >= 0, s' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s'' :|: s'' >= 0, s'' <= 0, z' >= 0, z = z' f(z, z') -{ 8 }-> s1 :|: s1 >= 0, s1 <= 0, z' >= 0, z = z' f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 g(z, z') -{ 6 }-> s2 :|: s2 >= 0, s2 <= 0, z = 1, z' >= 0 g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 h(z) -{ 7 }-> s :|: s >= 0, s <= 0, z >= 0 Function symbols to be analyzed: Previous analysis results are: encode_a: runtime: O(1) [1], size: O(1) [1] f: runtime: O(1) [4], size: O(1) [0] h: runtime: O(1) [7], size: O(1) [0] g: runtime: O(1) [6], size: O(1) [0] activate: runtime: O(1) [1], size: O(n^1) [z] encode_b: runtime: O(1) [0], size: O(1) [0] a: runtime: O(1) [1], size: O(1) [1] encArg: runtime: O(n^1) [8 + 14*z], size: O(1) [1] encode_activate: runtime: O(n^1) [9 + 14*z], size: O(1) [1] encode_f: runtime: O(n^1) [20 + 14*z + 14*z'], size: O(1) [0] encode_g: runtime: O(n^1) [22 + 14*z + 14*z'], size: O(1) [0] encode_h: runtime: O(n^1) [15 + 14*z], size: O(1) [0] ---------------------------------------- (83) FinalProof (FINISHED) Computed overall runtime complexity ---------------------------------------- (84) BOUNDS(1, n^1)