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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308353
details
property
value
status
complete
benchmark
ExAppendixB_AEL03_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
12.5237 seconds
cpu usage
42.8623
user time
40.5408
system time
2.32147
max virtual memory
3.7908656E7
max residence set size
4238308.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
42.49/12.43 WORST_CASE(Omega(n^1), O(n^1)) 42.49/12.44 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 42.49/12.44 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 42.49/12.44 42.49/12.44 42.49/12.44 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 42.49/12.44 42.49/12.44 (0) CpxTRS 42.49/12.44 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 6 ms] 42.49/12.44 (2) CpxTRS 42.49/12.44 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 42.49/12.44 (4) CpxTRS 42.49/12.44 (5) CpxTrsMatchBoundsTAProof [FINISHED, 258 ms] 42.49/12.44 (6) BOUNDS(1, n^1) 42.49/12.44 (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 42.49/12.44 (8) CpxTRS 42.49/12.44 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 42.49/12.44 (10) typed CpxTrs 42.49/12.44 (11) OrderProof [LOWER BOUND(ID), 0 ms] 42.49/12.44 (12) typed CpxTrs 42.49/12.44 (13) RewriteLemmaProof [LOWER BOUND(ID), 469 ms] 42.49/12.44 (14) BEST 42.49/12.44 (15) proven lower bound 42.49/12.44 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 42.49/12.44 (17) BOUNDS(n^1, INF) 42.49/12.44 (18) typed CpxTrs 42.49/12.44 (19) RewriteLemmaProof [LOWER BOUND(ID), 128 ms] 42.49/12.44 (20) typed CpxTrs 42.49/12.44 (21) RewriteLemmaProof [LOWER BOUND(ID), 104 ms] 42.49/12.44 (22) typed CpxTrs 42.49/12.44 (23) RewriteLemmaProof [LOWER BOUND(ID), 90 ms] 42.49/12.44 (24) typed CpxTrs 42.49/12.44 (25) RewriteLemmaProof [LOWER BOUND(ID), 66 ms] 42.49/12.44 (26) typed CpxTrs 42.49/12.44 (27) RewriteLemmaProof [LOWER BOUND(ID), 104 ms] 42.49/12.44 (28) typed CpxTrs 42.49/12.44 (29) RewriteLemmaProof [LOWER BOUND(ID), 103 ms] 42.49/12.44 (30) typed CpxTrs 42.49/12.44 (31) RewriteLemmaProof [LOWER BOUND(ID), 136 ms] 42.49/12.44 (32) typed CpxTrs 42.49/12.44 (33) RewriteLemmaProof [LOWER BOUND(ID), 70 ms] 42.49/12.44 (34) typed CpxTrs 42.49/12.44 (35) RewriteLemmaProof [LOWER BOUND(ID), 111 ms] 42.49/12.44 (36) typed CpxTrs 42.49/12.44 (37) RewriteLemmaProof [LOWER BOUND(ID), 82 ms] 42.49/12.44 (38) typed CpxTrs 42.49/12.44 (39) RewriteLemmaProof [LOWER BOUND(ID), 59 ms] 42.49/12.44 (40) typed CpxTrs 42.49/12.44 (41) RewriteLemmaProof [LOWER BOUND(ID), 116 ms] 42.49/12.44 (42) typed CpxTrs 42.49/12.44 42.49/12.44 42.49/12.44 ---------------------------------------- 42.49/12.44 42.49/12.44 (0) 42.49/12.44 Obligation: 42.49/12.44 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 42.49/12.44 42.49/12.44 42.49/12.44 The TRS R consists of the following rules: 42.49/12.44 42.49/12.44 active(from(X)) -> mark(cons(X, from(s(X)))) 42.49/12.44 active(2ndspos(0, Z)) -> mark(rnil) 42.49/12.44 active(2ndspos(s(N), cons(X, Z))) -> mark(2ndspos(s(N), cons2(X, Z))) 42.49/12.44 active(2ndspos(s(N), cons2(X, cons(Y, Z)))) -> mark(rcons(posrecip(Y), 2ndsneg(N, Z))) 42.49/12.44 active(2ndsneg(0, Z)) -> mark(rnil) 42.49/12.44 active(2ndsneg(s(N), cons(X, Z))) -> mark(2ndsneg(s(N), cons2(X, Z))) 42.49/12.44 active(2ndsneg(s(N), cons2(X, cons(Y, Z)))) -> mark(rcons(negrecip(Y), 2ndspos(N, Z))) 42.49/12.44 active(pi(X)) -> mark(2ndspos(X, from(0))) 42.49/12.44 active(plus(0, Y)) -> mark(Y) 42.49/12.44 active(plus(s(X), Y)) -> mark(s(plus(X, Y))) 42.49/12.44 active(times(0, Y)) -> mark(0) 42.49/12.44 active(times(s(X), Y)) -> mark(plus(Y, times(X, Y))) 42.49/12.44 active(square(X)) -> mark(times(X, X)) 42.49/12.44 active(s(X)) -> s(active(X)) 42.49/12.44 active(posrecip(X)) -> posrecip(active(X)) 42.49/12.44 active(negrecip(X)) -> negrecip(active(X)) 42.49/12.44 active(cons(X1, X2)) -> cons(active(X1), X2) 42.49/12.44 active(cons2(X1, X2)) -> cons2(X1, active(X2)) 42.49/12.44 active(rcons(X1, X2)) -> rcons(active(X1), X2) 42.49/12.44 active(rcons(X1, X2)) -> rcons(X1, active(X2)) 42.49/12.44 active(from(X)) -> from(active(X)) 42.49/12.44 active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2) 42.49/12.44 active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2)) 42.49/12.44 active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2) 42.49/12.44 active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2)) 42.49/12.44 active(pi(X)) -> pi(active(X)) 42.49/12.44 active(plus(X1, X2)) -> plus(active(X1), X2) 42.49/12.44 active(plus(X1, X2)) -> plus(X1, active(X2)) 42.49/12.44 active(times(X1, X2)) -> times(active(X1), X2) 42.49/12.44 active(times(X1, X2)) -> times(X1, active(X2)) 42.49/12.44 active(square(X)) -> square(active(X)) 42.49/12.44 s(mark(X)) -> mark(s(X)) 42.49/12.44 posrecip(mark(X)) -> mark(posrecip(X)) 42.49/12.44 negrecip(mark(X)) -> mark(negrecip(X)) 42.49/12.44 cons(mark(X1), X2) -> mark(cons(X1, X2)) 42.49/12.44 cons2(X1, mark(X2)) -> mark(cons2(X1, X2)) 42.49/12.44 rcons(mark(X1), X2) -> mark(rcons(X1, X2)) 42.49/12.44 rcons(X1, mark(X2)) -> mark(rcons(X1, X2)) 42.49/12.44 from(mark(X)) -> mark(from(X))
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