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Runti Compl Full Rewri 10127 pair #381902714
details
property
value
status
complete
benchmark
Ex4_7_37_Bor03_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n039.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.9973139763 seconds
cpu usage
36.577349159
max memory
4.432166912E9
stage attributes
key
value
output-size
17567
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 136 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(from(X)) -> mark(cons(X, from(s(X)))) active(sel(0, cons(X, XS))) -> mark(X) active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) active(minus(X, 0)) -> mark(0) active(minus(s(X), s(Y))) -> mark(minus(X, Y)) active(quot(0, s(Y))) -> mark(0) active(quot(s(X), s(Y))) -> mark(s(quot(minus(X, Y), s(Y)))) active(zWquot(XS, nil)) -> mark(nil) active(zWquot(nil, XS)) -> mark(nil) active(zWquot(cons(X, XS), cons(Y, YS))) -> mark(cons(quot(X, Y), zWquot(XS, YS))) active(from(X)) -> from(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(s(X)) -> s(active(X)) active(sel(X1, X2)) -> sel(active(X1), X2) active(sel(X1, X2)) -> sel(X1, active(X2)) active(minus(X1, X2)) -> minus(active(X1), X2) active(minus(X1, X2)) -> minus(X1, active(X2)) active(quot(X1, X2)) -> quot(active(X1), X2) active(quot(X1, X2)) -> quot(X1, active(X2)) active(zWquot(X1, X2)) -> zWquot(active(X1), X2) active(zWquot(X1, X2)) -> zWquot(X1, active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) s(mark(X)) -> mark(s(X)) sel(mark(X1), X2) -> mark(sel(X1, X2)) sel(X1, mark(X2)) -> mark(sel(X1, X2)) minus(mark(X1), X2) -> mark(minus(X1, X2)) minus(X1, mark(X2)) -> mark(minus(X1, X2)) quot(mark(X1), X2) -> mark(quot(X1, X2)) quot(X1, mark(X2)) -> mark(quot(X1, X2)) zWquot(mark(X1), X2) -> mark(zWquot(X1, X2)) zWquot(X1, mark(X2)) -> mark(zWquot(X1, X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(s(X)) -> s(proper(X)) proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) proper(0) -> ok(0) proper(minus(X1, X2)) -> minus(proper(X1), proper(X2)) proper(quot(X1, X2)) -> quot(proper(X1), proper(X2)) proper(zWquot(X1, X2)) -> zWquot(proper(X1), proper(X2)) proper(nil) -> ok(nil) from(ok(X)) -> ok(from(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) s(ok(X)) -> ok(s(X)) sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) minus(ok(X1), ok(X2)) -> ok(minus(X1, X2)) quot(ok(X1), ok(X2)) -> ok(quot(X1, X2)) zWquot(ok(X1), ok(X2)) -> ok(zWquot(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:
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