details

property	value
status	complete
benchmark	ExIntrod_Zan97_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.79421 seconds
cpu usage	22.8718
user time	21.5387
system time	1.33309
max virtual memory	3.7644776E7
max residence set size	3777264.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 10 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsTAProof [FINISHED, 100 ms] (6) BOUNDS(1, n^1) (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 419 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 94 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 21 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 92 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 83 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 73 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 108 ms] (30) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: active(fact(X)) -> mark(if(zero(X), s(0), prod(X, fact(p(X))))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(prod(0, X)) -> mark(0) active(prod(s(X), Y)) -> mark(add(Y, prod(X, Y))) active(if(true, X, Y)) -> mark(X) active(if(false, X, Y)) -> mark(Y) active(zero(0)) -> mark(true) active(zero(s(X))) -> mark(false) active(p(s(X))) -> mark(X) active(fact(X)) -> fact(active(X)) active(if(X1, X2, X3)) -> if(active(X1), X2, X3) active(zero(X)) -> zero(active(X)) active(s(X)) -> s(active(X)) active(prod(X1, X2)) -> prod(active(X1), X2) active(prod(X1, X2)) -> prod(X1, active(X2)) active(p(X)) -> p(active(X)) active(add(X1, X2)) -> add(active(X1), X2) active(add(X1, X2)) -> add(X1, active(X2)) fact(mark(X)) -> mark(fact(X)) if(mark(X1), X2, X3) -> mark(if(X1, X2, X3)) zero(mark(X)) -> mark(zero(X)) s(mark(X)) -> mark(s(X)) prod(mark(X1), X2) -> mark(prod(X1, X2)) prod(X1, mark(X2)) -> mark(prod(X1, X2)) p(mark(X)) -> mark(p(X)) add(mark(X1), X2) -> mark(add(X1, X2)) add(X1, mark(X2)) -> mark(add(X1, X2)) proper(fact(X)) -> fact(proper(X)) proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3)) proper(zero(X)) -> zero(proper(X)) proper(s(X)) -> s(proper(X)) proper(0) -> ok(0) proper(prod(X1, X2)) -> prod(proper(X1), proper(X2)) proper(p(X)) -> p(proper(X)) proper(add(X1, X2)) -> add(proper(X1), proper(X2)) proper(true) -> ok(true) proper(false) -> ok(false) fact(ok(X)) -> ok(fact(X)) if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3)) zero(ok(X)) -> ok(zero(X)) s(ok(X)) -> ok(s(X)) prod(ok(X1), ok(X2)) -> ok(prod(X1, X2)) p(ok(X)) -> ok(p(X)) add(ok(X1), ok(X2)) -> ok(add(X1, X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) S is empty. Rewrite Strategy: FULL ---------------------------------------- popout

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

job log

popout

actions

all output return to Runtime Complexity: TRS