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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313723
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
n109.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.965 seconds
cpu usage
1119.12
user time
1104.99
system time
14.131
max virtual memory
3.7923984E7
max residence set size
1.5047192E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1118.59/291.85 WORST_CASE(Omega(n^2), ?) 1118.92/291.87 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1118.92/291.87 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1118.92/291.87 1118.92/291.87 1118.92/291.87 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1118.92/291.87 1118.92/291.87 (0) CpxTRS 1118.92/291.87 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1118.92/291.87 (2) CpxTRS 1118.92/291.87 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1118.92/291.87 (4) typed CpxTrs 1118.92/291.87 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1118.92/291.87 (6) typed CpxTrs 1118.92/291.87 (7) RewriteLemmaProof [LOWER BOUND(ID), 265 ms] 1118.92/291.87 (8) BEST 1118.92/291.87 (9) proven lower bound 1118.92/291.87 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1118.92/291.87 (11) BOUNDS(n^1, INF) 1118.92/291.87 (12) typed CpxTrs 1118.92/291.87 (13) RewriteLemmaProof [LOWER BOUND(ID), 125 ms] 1118.92/291.87 (14) BEST 1118.92/291.87 (15) proven lower bound 1118.92/291.87 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1118.92/291.87 (17) BOUNDS(n^2, INF) 1118.92/291.87 (18) typed CpxTrs 1118.92/291.87 (19) RewriteLemmaProof [LOWER BOUND(ID), 58 ms] 1118.92/291.87 (20) typed CpxTrs 1118.92/291.87 1118.92/291.87 1118.92/291.87 ---------------------------------------- 1118.92/291.87 1118.92/291.87 (0) 1118.92/291.87 Obligation: 1118.92/291.87 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1118.92/291.87 1118.92/291.87 1118.92/291.87 The TRS R consists of the following rules: 1118.92/291.87 1118.92/291.87 car(cons(x, l)) -> x 1118.92/291.87 cddr(nil) -> nil 1118.92/291.87 cddr(cons(x, nil)) -> nil 1118.92/291.87 cddr(cons(x, cons(y, l))) -> l 1118.92/291.87 cadr(cons(x, cons(y, l))) -> y 1118.92/291.87 isZero(0) -> true 1118.92/291.87 isZero(s(x)) -> false 1118.92/291.87 plus(x, y) -> ifplus(isZero(x), x, y) 1118.92/291.87 ifplus(true, x, y) -> y 1118.92/291.87 ifplus(false, x, y) -> s(plus(p(x), y)) 1118.92/291.87 times(x, y) -> iftimes(isZero(x), x, y) 1118.92/291.87 iftimes(true, x, y) -> 0 1118.92/291.87 iftimes(false, x, y) -> plus(y, times(p(x), y)) 1118.92/291.87 p(s(x)) -> x 1118.92/291.87 p(0) -> 0 1118.92/291.87 shorter(nil, y) -> true 1118.92/291.87 shorter(cons(x, l), 0) -> false 1118.92/291.87 shorter(cons(x, l), s(y)) -> shorter(l, y) 1118.92/291.87 prod(l) -> if(shorter(l, 0), shorter(l, s(0)), l) 1118.92/291.87 if(true, b, l) -> s(0) 1118.92/291.87 if(false, b, l) -> if2(b, l) 1118.92/291.87 if2(true, l) -> car(l) 1118.92/291.87 if2(false, l) -> prod(cons(times(car(l), cadr(l)), cddr(l))) 1118.92/291.87 1118.92/291.87 S is empty. 1118.92/291.87 Rewrite Strategy: INNERMOST 1118.92/291.87 ---------------------------------------- 1118.92/291.87 1118.92/291.87 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1118.92/291.87 Renamed function symbols to avoid clashes with predefined symbol. 1118.92/291.87 ---------------------------------------- 1118.92/291.87 1118.92/291.87 (2) 1118.92/291.87 Obligation: 1118.92/291.87 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1118.92/291.87 1118.92/291.87 1118.92/291.87 The TRS R consists of the following rules: 1118.92/291.87 1118.92/291.87 car(cons(x, l)) -> x 1118.92/291.87 cddr(nil) -> nil 1118.92/291.87 cddr(cons(x, nil)) -> nil 1118.92/291.87 cddr(cons(x, cons(y, l))) -> l 1118.92/291.87 cadr(cons(x, cons(y, l))) -> y 1118.92/291.87 isZero(0') -> true 1118.92/291.87 isZero(s(x)) -> false 1118.92/291.87 plus(x, y) -> ifplus(isZero(x), x, y) 1118.92/291.87 ifplus(true, x, y) -> y 1118.92/291.87 ifplus(false, x, y) -> s(plus(p(x), y)) 1118.92/291.87 times(x, y) -> iftimes(isZero(x), x, y) 1118.92/291.87 iftimes(true, x, y) -> 0' 1118.92/291.87 iftimes(false, x, y) -> plus(y, times(p(x), y)) 1118.92/291.87 p(s(x)) -> x 1118.92/291.87 p(0') -> 0' 1118.92/291.87 shorter(nil, y) -> true 1118.92/291.87 shorter(cons(x, l), 0') -> false 1118.92/291.87 shorter(cons(x, l), s(y)) -> shorter(l, y) 1118.92/291.87 prod(l) -> if(shorter(l, 0'), shorter(l, s(0')), l) 1118.92/291.87 if(true, b, l) -> s(0') 1118.92/291.87 if(false, b, l) -> if2(b, l) 1118.92/291.87 if2(true, l) -> car(l)
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