details

property	value
status	complete
benchmark	MYNAT_nokinds_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n049.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.63820505142 seconds
cpu usage	25.636699526
max memory	4.008935424E9

stage attributes

key	value
output-size	18719
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsTAProof [FINISHED, 127 ms] (6) BOUNDS(1, n^1) (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (8) TRS for Loop Detection (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (10) BEST (11) proven lower bound (12) LowerBoundPropagationProof [FINISHED, 0 ms] (13) BOUNDS(n^1, INF) (14) TRS for Loop Detection ---------------------------------------- (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(U11(tt, N)) -> mark(N) active(U21(tt, M, N)) -> mark(s(plus(N, M))) active(U31(tt)) -> mark(0) active(U41(tt, M, N)) -> mark(plus(x(N, M), N)) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(isNat(s(V1))) -> mark(isNat(V1)) active(isNat(x(V1, V2))) -> mark(and(isNat(V1), isNat(V2))) active(plus(N, 0)) -> mark(U11(isNat(N), N)) active(plus(N, s(M))) -> mark(U21(and(isNat(M), isNat(N)), M, N)) active(x(N, 0)) -> mark(U31(isNat(N))) active(x(N, s(M))) -> mark(U41(and(isNat(M), isNat(N)), M, N)) active(U11(X1, X2)) -> U11(active(X1), X2) active(U21(X1, X2, X3)) -> U21(active(X1), X2, X3) active(s(X)) -> s(active(X)) active(plus(X1, X2)) -> plus(active(X1), X2) active(plus(X1, X2)) -> plus(X1, active(X2)) active(U31(X)) -> U31(active(X)) active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) active(x(X1, X2)) -> x(active(X1), X2) active(x(X1, X2)) -> x(X1, active(X2)) active(and(X1, X2)) -> and(active(X1), X2) U11(mark(X1), X2) -> mark(U11(X1, X2)) U21(mark(X1), X2, X3) -> mark(U21(X1, X2, X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1), X2) -> mark(plus(X1, X2)) plus(X1, mark(X2)) -> mark(plus(X1, X2)) U31(mark(X)) -> mark(U31(X)) U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) x(mark(X1), X2) -> mark(x(X1, X2)) x(X1, mark(X2)) -> mark(x(X1, X2)) and(mark(X1), X2) -> mark(and(X1, X2)) proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) proper(tt) -> ok(tt) proper(U21(X1, X2, X3)) -> U21(proper(X1), proper(X2), proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) proper(U31(X)) -> U31(proper(X)) proper(0) -> ok(0) proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) proper(x(X1, X2)) -> x(proper(X1), proper(X2)) proper(and(X1, X2)) -> and(proper(X1), proper(X2)) proper(isNat(X)) -> isNat(proper(X)) U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) U21(ok(X1), ok(X2), ok(X3)) -> ok(U21(X1, X2, X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) U31(ok(X)) -> ok(U31(X)) U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) x(ok(X1), ok(X2)) -> ok(x(X1, X2)) and(ok(X1), ok(X2)) -> ok(and(X1, X2)) isNat(ok(X)) -> ok(isNat(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) popout

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

job log

popout

actions

all output return to Runti Compl Full Rewri 10127