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Runti Compl Full Rewri 10127 pair #381903158
details
property
value
status
complete
benchmark
LengthOfFiniteLists_nosorts_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n048.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.505697012 seconds
cpu usage
1114.95005705
max memory
1.5459557376E10
stage attributes
key
value
output-size
13078
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 569 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(zeros) -> mark(cons(0, zeros)) active(U11(tt, L)) -> mark(U12(tt, L)) active(U12(tt, L)) -> mark(s(length(L))) active(length(nil)) -> mark(0) active(length(cons(N, L))) -> mark(U11(tt, L)) active(cons(X1, X2)) -> cons(active(X1), X2) active(U11(X1, X2)) -> U11(active(X1), X2) active(U12(X1, X2)) -> U12(active(X1), X2) active(s(X)) -> s(active(X)) active(length(X)) -> length(active(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) U11(mark(X1), X2) -> mark(U11(X1, X2)) U12(mark(X1), X2) -> mark(U12(X1, X2)) s(mark(X)) -> mark(s(X)) length(mark(X)) -> mark(length(X)) proper(zeros) -> ok(zeros) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(0) -> ok(0) proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) proper(tt) -> ok(tt) proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) proper(s(X)) -> s(proper(X)) proper(length(X)) -> length(proper(X)) proper(nil) -> ok(nil) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) s(ok(X)) -> ok(s(X)) length(ok(X)) -> ok(length(X)) 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 cons: active, proper, cons The following defined symbols can occur below the 1th argument of cons: active, proper, cons The following defined symbols can occur below the 0th argument of top: active, proper, cons The following defined symbols can occur below the 0th argument of proper: active, proper, cons The following defined symbols can occur below the 0th argument of active: active, proper, cons Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: active(U11(tt, L)) -> mark(U12(tt, L)) active(U12(tt, L)) -> mark(s(length(L))) active(length(nil)) -> mark(0) active(length(cons(N, L))) -> mark(U11(tt, L)) active(U11(X1, X2)) -> U11(active(X1), X2) active(U12(X1, X2)) -> U12(active(X1), X2) active(s(X)) -> s(active(X)) active(length(X)) -> length(active(X)) proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) proper(s(X)) -> s(proper(X)) proper(length(X)) -> length(proper(X)) ---------------------------------------- (2) Obligation:
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