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Runtime Complexity: TRS pair #487109738
details
property
value
status
complete
benchmark
Ex4_Zan97_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
10.5593 seconds
cpu usage
25.5071
user time
23.8918
system time
1.61534
max virtual memory
1.9273284E7
max residence set size
3739832.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsTAProof [FINISHED, 65 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(f(X)) -> mark(cons(X, f(g(X)))) active(g(0)) -> mark(s(0)) active(g(s(X))) -> mark(s(s(g(X)))) active(sel(0, cons(X, Y))) -> mark(X) active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)) active(f(X)) -> f(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(g(X)) -> g(active(X)) active(s(X)) -> s(active(X)) active(sel(X1, X2)) -> sel(active(X1), X2) active(sel(X1, X2)) -> sel(X1, active(X2)) f(mark(X)) -> mark(f(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) g(mark(X)) -> mark(g(X)) s(mark(X)) -> mark(s(X)) sel(mark(X1), X2) -> mark(sel(X1, X2)) sel(X1, mark(X2)) -> mark(sel(X1, X2)) proper(f(X)) -> f(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(g(X)) -> g(proper(X)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) f(ok(X)) -> ok(f(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) g(ok(X)) -> ok(g(X)) s(ok(X)) -> ok(s(X)) sel(ok(X1), ok(X2)) -> ok(sel(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(f(X)) -> mark(cons(X, f(g(X)))) active(g(0)) -> mark(s(0)) active(g(s(X))) -> mark(s(s(g(X)))) active(sel(0, cons(X, Y))) -> mark(X) active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)) active(f(X)) -> f(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(g(X)) -> g(active(X)) active(s(X)) -> s(active(X)) active(sel(X1, X2)) -> sel(active(X1), X2) active(sel(X1, X2)) -> sel(X1, active(X2)) proper(f(X)) -> f(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(g(X)) -> g(proper(X)) proper(s(X)) -> s(proper(X)) proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules:
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