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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307775
details
property
value
status
complete
benchmark
thiemann07.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.572 seconds
cpu usage
307.043
user time
305.378
system time
1.66474
max virtual memory
1.8279384E7
max residence set size
5171792.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
306.91/291.53 WORST_CASE(Omega(n^2), ?) 306.91/291.54 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 306.91/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 306.91/291.54 306.91/291.54 306.91/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 306.91/291.54 306.91/291.54 (0) CpxTRS 306.91/291.54 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 306.91/291.54 (2) CpxTRS 306.91/291.54 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 306.91/291.54 (4) typed CpxTrs 306.91/291.54 (5) OrderProof [LOWER BOUND(ID), 0 ms] 306.91/291.54 (6) typed CpxTrs 306.91/291.54 (7) RewriteLemmaProof [LOWER BOUND(ID), 286 ms] 306.91/291.54 (8) BEST 306.91/291.54 (9) proven lower bound 306.91/291.54 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 306.91/291.54 (11) BOUNDS(n^1, INF) 306.91/291.54 (12) typed CpxTrs 306.91/291.54 (13) RewriteLemmaProof [LOWER BOUND(ID), 89 ms] 306.91/291.54 (14) BEST 306.91/291.54 (15) proven lower bound 306.91/291.54 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 306.91/291.54 (17) BOUNDS(n^2, INF) 306.91/291.54 (18) typed CpxTrs 306.91/291.54 (19) RewriteLemmaProof [LOWER BOUND(ID), 79 ms] 306.91/291.54 (20) typed CpxTrs 306.91/291.54 306.91/291.54 306.91/291.54 ---------------------------------------- 306.91/291.54 306.91/291.54 (0) 306.91/291.54 Obligation: 306.91/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 306.91/291.54 306.91/291.54 306.91/291.54 The TRS R consists of the following rules: 306.91/291.54 306.91/291.54 car(cons(x, l)) -> x 306.91/291.54 cddr(nil) -> nil 306.91/291.54 cddr(cons(x, nil)) -> nil 306.91/291.54 cddr(cons(x, cons(y, l))) -> l 306.91/291.54 cadr(cons(x, cons(y, l))) -> y 306.91/291.54 isZero(0) -> true 306.91/291.54 isZero(s(x)) -> false 306.91/291.54 plus(x, y) -> ifplus(isZero(x), x, y) 306.91/291.54 ifplus(true, x, y) -> y 306.91/291.54 ifplus(false, x, y) -> s(plus(p(x), y)) 306.91/291.54 times(x, y) -> iftimes(isZero(x), x, y) 306.91/291.54 iftimes(true, x, y) -> 0 306.91/291.54 iftimes(false, x, y) -> plus(y, times(p(x), y)) 306.91/291.54 p(s(x)) -> x 306.91/291.54 p(0) -> 0 306.91/291.54 shorter(nil, y) -> true 306.91/291.54 shorter(cons(x, l), 0) -> false 306.91/291.54 shorter(cons(x, l), s(y)) -> shorter(l, y) 306.91/291.54 prod(l) -> if(shorter(l, 0), shorter(l, s(0)), l) 306.91/291.54 if(true, b, l) -> s(0) 306.91/291.54 if(false, b, l) -> if2(b, l) 306.91/291.54 if2(true, l) -> car(l) 306.91/291.54 if2(false, l) -> prod(cons(times(car(l), cadr(l)), cddr(l))) 306.91/291.54 306.91/291.54 S is empty. 306.91/291.54 Rewrite Strategy: FULL 306.91/291.54 ---------------------------------------- 306.91/291.54 306.91/291.54 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 306.91/291.54 Renamed function symbols to avoid clashes with predefined symbol. 306.91/291.54 ---------------------------------------- 306.91/291.54 306.91/291.54 (2) 306.91/291.54 Obligation: 306.91/291.54 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 306.91/291.54 306.91/291.54 306.91/291.54 The TRS R consists of the following rules: 306.91/291.54 306.91/291.54 car(cons(x, l)) -> x 306.91/291.54 cddr(nil) -> nil 306.91/291.54 cddr(cons(x, nil)) -> nil 306.91/291.54 cddr(cons(x, cons(y, l))) -> l 306.91/291.54 cadr(cons(x, cons(y, l))) -> y 306.91/291.54 isZero(0') -> true 306.91/291.54 isZero(s(x)) -> false 306.91/291.54 plus(x, y) -> ifplus(isZero(x), x, y) 306.91/291.54 ifplus(true, x, y) -> y 306.91/291.54 ifplus(false, x, y) -> s(plus(p(x), y)) 306.91/291.54 times(x, y) -> iftimes(isZero(x), x, y) 306.91/291.54 iftimes(true, x, y) -> 0' 306.91/291.54 iftimes(false, x, y) -> plus(y, times(p(x), y)) 306.91/291.54 p(s(x)) -> x 306.91/291.54 p(0') -> 0' 306.91/291.54 shorter(nil, y) -> true 306.91/291.54 shorter(cons(x, l), 0') -> false 306.91/291.54 shorter(cons(x, l), s(y)) -> shorter(l, y) 306.91/291.54 prod(l) -> if(shorter(l, 0'), shorter(l, s(0')), l) 306.91/291.54 if(true, b, l) -> s(0') 306.91/291.54 if(false, b, l) -> if2(b, l) 306.91/291.54 if2(true, l) -> car(l)
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