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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308268
details
property
value
status
complete
benchmark
Ex4_7_15_Bor03_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n133.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.33872 seconds
cpu usage
21.6715
user time
20.0522
system time
1.61934
max virtual memory
1.9143024E7
max residence set size
3882776.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
21.47/7.28 WORST_CASE(Omega(n^1), O(n^1)) 21.47/7.29 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 21.47/7.29 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 21.47/7.29 21.47/7.29 21.47/7.29 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 21.47/7.29 21.47/7.29 (0) CpxTRS 21.47/7.29 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 21.47/7.29 (2) CpxTRS 21.47/7.29 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 21.47/7.29 (4) CpxTRS 21.47/7.29 (5) CpxTrsMatchBoundsTAProof [FINISHED, 21 ms] 21.47/7.29 (6) BOUNDS(1, n^1) 21.47/7.29 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 21.47/7.29 (8) TRS for Loop Detection 21.47/7.29 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 21.47/7.29 (10) BEST 21.47/7.29 (11) proven lower bound 21.47/7.29 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 21.47/7.29 (13) BOUNDS(n^1, INF) 21.47/7.29 (14) TRS for Loop Detection 21.47/7.29 21.47/7.29 21.47/7.29 ---------------------------------------- 21.47/7.29 21.47/7.29 (0) 21.47/7.29 Obligation: 21.47/7.29 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 21.47/7.29 21.47/7.29 21.47/7.29 The TRS R consists of the following rules: 21.47/7.29 21.47/7.29 active(f(0)) -> mark(cons(0, f(s(0)))) 21.47/7.29 active(f(s(0))) -> mark(f(p(s(0)))) 21.47/7.29 active(p(s(0))) -> mark(0) 21.47/7.29 active(f(X)) -> f(active(X)) 21.47/7.29 active(cons(X1, X2)) -> cons(active(X1), X2) 21.47/7.29 active(s(X)) -> s(active(X)) 21.47/7.29 active(p(X)) -> p(active(X)) 21.47/7.29 f(mark(X)) -> mark(f(X)) 21.47/7.29 cons(mark(X1), X2) -> mark(cons(X1, X2)) 21.47/7.29 s(mark(X)) -> mark(s(X)) 21.47/7.29 p(mark(X)) -> mark(p(X)) 21.47/7.29 proper(f(X)) -> f(proper(X)) 21.47/7.29 proper(0) -> ok(0) 21.47/7.29 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 21.47/7.29 proper(s(X)) -> s(proper(X)) 21.47/7.29 proper(p(X)) -> p(proper(X)) 21.47/7.29 f(ok(X)) -> ok(f(X)) 21.47/7.29 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 21.47/7.29 s(ok(X)) -> ok(s(X)) 21.47/7.29 p(ok(X)) -> ok(p(X)) 21.47/7.29 top(mark(X)) -> top(proper(X)) 21.47/7.29 top(ok(X)) -> top(active(X)) 21.47/7.29 21.47/7.29 S is empty. 21.47/7.29 Rewrite Strategy: FULL 21.47/7.29 ---------------------------------------- 21.47/7.29 21.47/7.29 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 21.47/7.29 The following defined symbols can occur below the 0th argument of top: proper, active 21.47/7.29 The following defined symbols can occur below the 0th argument of proper: proper, active 21.47/7.29 The following defined symbols can occur below the 0th argument of active: proper, active 21.47/7.29 21.47/7.29 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 21.47/7.29 active(f(0)) -> mark(cons(0, f(s(0)))) 21.47/7.29 active(f(s(0))) -> mark(f(p(s(0)))) 21.47/7.29 active(p(s(0))) -> mark(0) 21.47/7.29 active(f(X)) -> f(active(X)) 21.47/7.29 active(cons(X1, X2)) -> cons(active(X1), X2) 21.47/7.29 active(s(X)) -> s(active(X)) 21.47/7.29 active(p(X)) -> p(active(X)) 21.47/7.29 proper(f(X)) -> f(proper(X)) 21.47/7.29 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 21.47/7.29 proper(s(X)) -> s(proper(X)) 21.47/7.29 proper(p(X)) -> p(proper(X)) 21.47/7.29 21.47/7.29 ---------------------------------------- 21.47/7.29 21.47/7.29 (2) 21.47/7.29 Obligation: 21.47/7.29 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 21.47/7.29 21.47/7.29 21.47/7.29 The TRS R consists of the following rules: 21.47/7.29 21.47/7.29 f(mark(X)) -> mark(f(X)) 21.47/7.29 cons(mark(X1), X2) -> mark(cons(X1, X2)) 21.47/7.29 s(mark(X)) -> mark(s(X)) 21.47/7.29 p(mark(X)) -> mark(p(X)) 21.47/7.29 proper(0) -> ok(0) 21.47/7.29 f(ok(X)) -> ok(f(X)) 21.47/7.29 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 21.47/7.29 s(ok(X)) -> ok(s(X)) 21.47/7.29 p(ok(X)) -> ok(p(X)) 21.47/7.29 top(mark(X)) -> top(proper(X)) 21.47/7.29 top(ok(X)) -> top(active(X)) 21.47/7.29 21.47/7.29 S is empty.
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