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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308020
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
n062.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.614 seconds
cpu usage
1102.7
user time
1088.27
system time
14.4328
max virtual memory
3.7778568E7
max residence set size
1.5030532E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
1102.36/291.52 WORST_CASE(Omega(n^1), O(n^1)) 1102.58/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1102.58/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1102.58/291.54 1102.58/291.54 1102.58/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 1102.58/291.54 1102.58/291.54 (0) CpxTRS 1102.58/291.54 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 1102.58/291.54 (2) CpxTRS 1102.58/291.54 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 1102.58/291.54 (4) CpxTRS 1102.58/291.54 (5) CpxTrsMatchBoundsTAProof [FINISHED, 676 ms] 1102.58/291.54 (6) BOUNDS(1, n^1) 1102.58/291.54 (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1102.58/291.54 (8) CpxTRS 1102.58/291.54 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1102.58/291.54 (10) typed CpxTrs 1102.58/291.54 (11) OrderProof [LOWER BOUND(ID), 0 ms] 1102.58/291.54 (12) typed CpxTrs 1102.58/291.54 (13) RewriteLemmaProof [LOWER BOUND(ID), 541 ms] 1102.58/291.54 (14) BEST 1102.58/291.54 (15) proven lower bound 1102.58/291.54 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1102.58/291.54 (17) BOUNDS(n^1, INF) 1102.58/291.54 (18) typed CpxTrs 1102.58/291.54 (19) RewriteLemmaProof [LOWER BOUND(ID), 135 ms] 1102.58/291.54 (20) typed CpxTrs 1102.58/291.54 (21) RewriteLemmaProof [LOWER BOUND(ID), 106 ms] 1102.58/291.54 (22) typed CpxTrs 1102.58/291.54 (23) RewriteLemmaProof [LOWER BOUND(ID), 88 ms] 1102.58/291.54 (24) typed CpxTrs 1102.58/291.54 (25) RewriteLemmaProof [LOWER BOUND(ID), 86 ms] 1102.58/291.54 (26) typed CpxTrs 1102.58/291.54 1102.58/291.54 1102.58/291.54 ---------------------------------------- 1102.58/291.54 1102.58/291.54 (0) 1102.58/291.54 Obligation: 1102.58/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 1102.58/291.54 1102.58/291.54 1102.58/291.54 The TRS R consists of the following rules: 1102.58/291.54 1102.58/291.54 active(zeros) -> mark(cons(0, zeros)) 1102.58/291.54 active(U11(tt, L)) -> mark(U12(tt, L)) 1102.58/291.54 active(U12(tt, L)) -> mark(s(length(L))) 1102.58/291.54 active(length(nil)) -> mark(0) 1102.58/291.54 active(length(cons(N, L))) -> mark(U11(tt, L)) 1102.58/291.54 active(cons(X1, X2)) -> cons(active(X1), X2) 1102.58/291.54 active(U11(X1, X2)) -> U11(active(X1), X2) 1102.58/291.54 active(U12(X1, X2)) -> U12(active(X1), X2) 1102.58/291.54 active(s(X)) -> s(active(X)) 1102.58/291.54 active(length(X)) -> length(active(X)) 1102.58/291.54 cons(mark(X1), X2) -> mark(cons(X1, X2)) 1102.58/291.54 U11(mark(X1), X2) -> mark(U11(X1, X2)) 1102.58/291.54 U12(mark(X1), X2) -> mark(U12(X1, X2)) 1102.58/291.54 s(mark(X)) -> mark(s(X)) 1102.58/291.54 length(mark(X)) -> mark(length(X)) 1102.58/291.54 proper(zeros) -> ok(zeros) 1102.58/291.54 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 1102.58/291.54 proper(0) -> ok(0) 1102.58/291.54 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 1102.58/291.54 proper(tt) -> ok(tt) 1102.58/291.54 proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) 1102.58/291.54 proper(s(X)) -> s(proper(X)) 1102.58/291.54 proper(length(X)) -> length(proper(X)) 1102.58/291.54 proper(nil) -> ok(nil) 1102.58/291.54 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 1102.58/291.54 U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 1102.58/291.54 U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) 1102.58/291.54 s(ok(X)) -> ok(s(X)) 1102.58/291.54 length(ok(X)) -> ok(length(X)) 1102.58/291.54 top(mark(X)) -> top(proper(X)) 1102.58/291.54 top(ok(X)) -> top(active(X)) 1102.58/291.54 1102.58/291.54 S is empty. 1102.58/291.54 Rewrite Strategy: FULL 1102.58/291.54 ---------------------------------------- 1102.58/291.54 1102.58/291.54 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 1102.58/291.54 The following defined symbols can occur below the 0th argument of cons: active, proper, cons 1102.58/291.54 The following defined symbols can occur below the 1th argument of cons: active, proper, cons 1102.58/291.54 The following defined symbols can occur below the 0th argument of top: active, proper, cons 1102.58/291.54 The following defined symbols can occur below the 0th argument of proper: active, proper, cons 1102.58/291.54 The following defined symbols can occur below the 0th argument of active: active, proper, cons 1102.58/291.54 1102.58/291.54 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 1102.58/291.54 active(U11(tt, L)) -> mark(U12(tt, L)) 1102.58/291.54 active(U12(tt, L)) -> mark(s(length(L))) 1102.58/291.54 active(length(nil)) -> mark(0) 1102.58/291.54 active(length(cons(N, L))) -> mark(U11(tt, L)) 1102.58/291.54 active(U11(X1, X2)) -> U11(active(X1), X2) 1102.58/291.54 active(U12(X1, X2)) -> U12(active(X1), X2) 1102.58/291.54 active(s(X)) -> s(active(X)) 1102.58/291.54 active(length(X)) -> length(active(X)) 1102.58/291.54 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 1102.58/291.54 proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) 1102.58/291.54 proper(s(X)) -> s(proper(X))
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