details

property	value
status	complete
benchmark	Ex4_Zan97_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.581 seconds
cpu usage	1135.9
user time	1122.69
system time	13.2031
max virtual memory	3.7600764E7
max residence set size	1.4988148E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), ?)

output

WORST_CASE(Omega(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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 242 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 514 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 136 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 131 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 95 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 123 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 667 ms] (26) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: active(f(X)) -> mark(cons(X, f(g(X)))) active(g(0)) -> mark(s(0)) active(g(s(X))) -> mark(s(s(g(X)))) active(sel(0, cons(X, Y))) -> mark(X) active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)) active(f(X)) -> f(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(g(X)) -> g(active(X)) active(s(X)) -> s(active(X)) active(sel(X1, X2)) -> sel(active(X1), X2) active(sel(X1, X2)) -> sel(X1, active(X2)) f(mark(X)) -> mark(f(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) g(mark(X)) -> mark(g(X)) s(mark(X)) -> mark(s(X)) sel(mark(X1), X2) -> mark(sel(X1, X2)) sel(X1, mark(X2)) -> mark(sel(X1, X2)) proper(f(X)) -> f(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(g(X)) -> g(proper(X)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) f(ok(X)) -> ok(f(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) g(ok(X)) -> ok(g(X)) s(ok(X)) -> ok(s(X)) sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(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(mark(x_1)) -> mark(encArg(x_1)) encArg(0) -> 0 encArg(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_f(x_1)) -> f(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_g(x_1)) -> g(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_proper(x_1)) -> proper(encArg(x_1)) encArg(cons_top(x_1)) -> top(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_f(x_1) -> f(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_g(x_1) -> g(encArg(x_1)) encode_0 -> 0 popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost