Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runti Compl Full Rewri 10127 pair #381903885
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
n037.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.52196407318 seconds
cpu usage
22.445587396
max memory
3.992612864E9
stage attributes
key
value
output-size
15585
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 130 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(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 ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of top: proper, active The following defined symbols can occur below the 0th argument of proper: proper, active The following defined symbols can occur below the 0th argument of active: proper, active Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 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)))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runti Compl Full Rewri 10127