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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308279
details
property
value
status
complete
benchmark
Ex26_Luc03b_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n107.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.08265 seconds
cpu usage
25.8965
user time
24.1417
system time
1.75485
max virtual memory
3.7909112E7
max residence set size
4119232.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
25.41/8.01 WORST_CASE(Omega(n^1), O(n^1)) 25.41/8.03 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 25.41/8.03 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 25.41/8.03 25.41/8.03 25.41/8.03 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 25.41/8.03 25.41/8.03 (0) CpxTRS 25.41/8.03 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 25.41/8.03 (2) CpxTRS 25.41/8.03 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 25.41/8.03 (4) CpxTRS 25.41/8.03 (5) CpxTrsMatchBoundsTAProof [FINISHED, 112 ms] 25.41/8.03 (6) BOUNDS(1, n^1) 25.41/8.03 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 25.41/8.03 (8) TRS for Loop Detection 25.41/8.03 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 25.41/8.03 (10) BEST 25.41/8.03 (11) proven lower bound 25.41/8.03 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 25.41/8.03 (13) BOUNDS(n^1, INF) 25.41/8.03 (14) TRS for Loop Detection 25.41/8.03 25.41/8.03 25.41/8.03 ---------------------------------------- 25.41/8.03 25.41/8.03 (0) 25.41/8.03 Obligation: 25.41/8.03 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 25.41/8.03 25.41/8.03 25.41/8.03 The TRS R consists of the following rules: 25.41/8.03 25.41/8.03 active(terms(N)) -> mark(cons(recip(sqr(N)), terms(s(N)))) 25.41/8.03 active(sqr(0)) -> mark(0) 25.41/8.03 active(sqr(s(X))) -> mark(s(add(sqr(X), dbl(X)))) 25.41/8.03 active(dbl(0)) -> mark(0) 25.41/8.03 active(dbl(s(X))) -> mark(s(s(dbl(X)))) 25.41/8.03 active(add(0, X)) -> mark(X) 25.41/8.03 active(add(s(X), Y)) -> mark(s(add(X, Y))) 25.41/8.03 active(first(0, X)) -> mark(nil) 25.41/8.03 active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))) 25.41/8.03 active(terms(X)) -> terms(active(X)) 25.41/8.03 active(cons(X1, X2)) -> cons(active(X1), X2) 25.41/8.03 active(recip(X)) -> recip(active(X)) 25.41/8.03 active(sqr(X)) -> sqr(active(X)) 25.41/8.03 active(add(X1, X2)) -> add(active(X1), X2) 25.41/8.03 active(add(X1, X2)) -> add(X1, active(X2)) 25.41/8.03 active(dbl(X)) -> dbl(active(X)) 25.41/8.03 active(first(X1, X2)) -> first(active(X1), X2) 25.41/8.03 active(first(X1, X2)) -> first(X1, active(X2)) 25.41/8.03 terms(mark(X)) -> mark(terms(X)) 25.41/8.03 cons(mark(X1), X2) -> mark(cons(X1, X2)) 25.41/8.03 recip(mark(X)) -> mark(recip(X)) 25.41/8.03 sqr(mark(X)) -> mark(sqr(X)) 25.41/8.03 add(mark(X1), X2) -> mark(add(X1, X2)) 25.41/8.03 add(X1, mark(X2)) -> mark(add(X1, X2)) 25.41/8.03 dbl(mark(X)) -> mark(dbl(X)) 25.41/8.03 first(mark(X1), X2) -> mark(first(X1, X2)) 25.41/8.03 first(X1, mark(X2)) -> mark(first(X1, X2)) 25.41/8.03 proper(terms(X)) -> terms(proper(X)) 25.41/8.03 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 25.41/8.03 proper(recip(X)) -> recip(proper(X)) 25.41/8.03 proper(sqr(X)) -> sqr(proper(X)) 25.41/8.03 proper(s(X)) -> s(proper(X)) 25.41/8.03 proper(0) -> ok(0) 25.41/8.03 proper(add(X1, X2)) -> add(proper(X1), proper(X2)) 25.41/8.03 proper(dbl(X)) -> dbl(proper(X)) 25.41/8.03 proper(first(X1, X2)) -> first(proper(X1), proper(X2)) 25.41/8.03 proper(nil) -> ok(nil) 25.41/8.03 terms(ok(X)) -> ok(terms(X)) 25.41/8.03 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 25.41/8.03 recip(ok(X)) -> ok(recip(X)) 25.41/8.03 sqr(ok(X)) -> ok(sqr(X)) 25.41/8.03 s(ok(X)) -> ok(s(X)) 25.41/8.03 add(ok(X1), ok(X2)) -> ok(add(X1, X2)) 25.41/8.03 dbl(ok(X)) -> ok(dbl(X)) 25.41/8.03 first(ok(X1), ok(X2)) -> ok(first(X1, X2)) 25.41/8.03 top(mark(X)) -> top(proper(X)) 25.41/8.03 top(ok(X)) -> top(active(X)) 25.41/8.03 25.41/8.03 S is empty. 25.41/8.03 Rewrite Strategy: FULL 25.41/8.03 ---------------------------------------- 25.41/8.03 25.41/8.03 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 25.41/8.03 The following defined symbols can occur below the 0th argument of top: proper, active 25.41/8.03 The following defined symbols can occur below the 0th argument of proper: proper, active 25.41/8.03 The following defined symbols can occur below the 0th argument of active: proper, active 25.41/8.03 25.41/8.03 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 25.41/8.03 active(terms(N)) -> mark(cons(recip(sqr(N)), terms(s(N)))) 25.41/8.03 active(sqr(0)) -> mark(0) 25.41/8.03 active(sqr(s(X))) -> mark(s(add(sqr(X), dbl(X)))) 25.41/8.03 active(dbl(0)) -> mark(0) 25.41/8.03 active(dbl(s(X))) -> mark(s(s(dbl(X)))) 25.41/8.03 active(add(0, X)) -> mark(X) 25.41/8.03 active(add(s(X), Y)) -> mark(s(add(X, Y))) 25.41/8.03 active(first(0, X)) -> mark(nil) 25.41/8.03 active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
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