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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313332
details
property
value
status
complete
benchmark
mss.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
hoca
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.574 seconds
cpu usage
940.877
user time
932.857
system time
8.01988
max virtual memory
3.7908656E7
max residence set size
7139764.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
940.44/291.48 WORST_CASE(Omega(n^1), ?) 940.44/291.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 940.44/291.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 940.44/291.49 940.44/291.49 940.44/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 940.44/291.49 940.44/291.49 (0) CpxTRS 940.44/291.49 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 940.44/291.49 (2) CpxTRS 940.44/291.49 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 940.44/291.49 (4) typed CpxTrs 940.44/291.49 (5) OrderProof [LOWER BOUND(ID), 0 ms] 940.44/291.49 (6) typed CpxTrs 940.44/291.49 (7) RewriteLemmaProof [LOWER BOUND(ID), 316 ms] 940.44/291.49 (8) BEST 940.44/291.49 (9) proven lower bound 940.44/291.49 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 940.44/291.49 (11) BOUNDS(n^1, INF) 940.44/291.49 (12) typed CpxTrs 940.44/291.49 (13) RewriteLemmaProof [LOWER BOUND(ID), 107 ms] 940.44/291.49 (14) typed CpxTrs 940.44/291.49 (15) RewriteLemmaProof [LOWER BOUND(ID), 124 ms] 940.44/291.49 (16) typed CpxTrs 940.44/291.49 (17) RewriteLemmaProof [LOWER BOUND(ID), 87 ms] 940.44/291.49 (18) typed CpxTrs 940.44/291.49 (19) RewriteLemmaProof [LOWER BOUND(ID), 12 ms] 940.44/291.49 (20) BOUNDS(1, INF) 940.44/291.49 940.44/291.49 940.44/291.49 ---------------------------------------- 940.44/291.49 940.44/291.49 (0) 940.44/291.49 Obligation: 940.44/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 940.44/291.49 940.44/291.49 940.44/291.49 The TRS R consists of the following rules: 940.44/291.49 940.44/291.49 cond_scanr_f_z_xs_1(Cons(0, x11), 0) -> Cons(0, Cons(0, x11)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(S(x2), x11), 0) -> Cons(S(x2), Cons(S(x2), x11)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(0, x11), M(x2)) -> Cons(0, Cons(0, x11)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(S(x40), x23), M(0)) -> Cons(S(x40), Cons(S(x40), x23)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(S(x8), x23), M(S(x4))) -> Cons(minus#2(x8, x4), Cons(S(x8), x23)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(0, x11), S(x2)) -> Cons(S(x2), Cons(0, x11)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(S(x2), x11), S(x4)) -> Cons(plus#2(S(x4), S(x2)), Cons(S(x2), x11)) 940.44/291.49 scanr#3(Nil) -> Cons(0, Nil) 940.44/291.49 scanr#3(Cons(x4, x2)) -> cond_scanr_f_z_xs_1(scanr#3(x2), x4) 940.44/291.49 foldl#3(x2, Nil) -> x2 940.44/291.49 foldl#3(x6, Cons(x4, x2)) -> foldl#3(max#2(x6, x4), x2) 940.44/291.49 minus#2(0, x16) -> 0 940.44/291.49 minus#2(S(x20), 0) -> S(x20) 940.44/291.49 minus#2(S(x4), S(x2)) -> minus#2(x4, x2) 940.44/291.49 plus#2(0, S(x2)) -> S(x2) 940.44/291.49 plus#2(S(x4), S(x2)) -> S(plus#2(x4, S(x2))) 940.44/291.49 max#2(0, x8) -> x8 940.44/291.49 max#2(S(x12), 0) -> S(x12) 940.44/291.49 max#2(S(x4), S(x2)) -> S(max#2(x4, x2)) 940.44/291.49 main(x1) -> foldl#3(0, scanr#3(x1)) 940.44/291.49 940.44/291.49 S is empty. 940.44/291.49 Rewrite Strategy: INNERMOST 940.44/291.49 ---------------------------------------- 940.44/291.49 940.44/291.49 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 940.44/291.49 Renamed function symbols to avoid clashes with predefined symbol. 940.44/291.49 ---------------------------------------- 940.44/291.49 940.44/291.49 (2) 940.44/291.49 Obligation: 940.44/291.49 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 940.44/291.49 940.44/291.49 940.44/291.49 The TRS R consists of the following rules: 940.44/291.49 940.44/291.49 cond_scanr_f_z_xs_1(Cons(0', x11), 0') -> Cons(0', Cons(0', x11)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(S(x2), x11), 0') -> Cons(S(x2), Cons(S(x2), x11)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(0', x11), M(x2)) -> Cons(0', Cons(0', x11)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(S(x40), x23), M(0')) -> Cons(S(x40), Cons(S(x40), x23)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(S(x8), x23), M(S(x4))) -> Cons(minus#2(x8, x4), Cons(S(x8), x23)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(0', x11), S(x2)) -> Cons(S(x2), Cons(0', x11)) 940.44/291.49 cond_scanr_f_z_xs_1(Cons(S(x2), x11), S(x4)) -> Cons(plus#2(S(x4), S(x2)), Cons(S(x2), x11)) 940.44/291.49 scanr#3(Nil) -> Cons(0', Nil) 940.44/291.49 scanr#3(Cons(x4, x2)) -> cond_scanr_f_z_xs_1(scanr#3(x2), x4) 940.44/291.49 foldl#3(x2, Nil) -> x2 940.44/291.49 foldl#3(x6, Cons(x4, x2)) -> foldl#3(max#2(x6, x4), x2) 940.44/291.49 minus#2(0', x16) -> 0' 940.44/291.49 minus#2(S(x20), 0') -> S(x20) 940.44/291.49 minus#2(S(x4), S(x2)) -> minus#2(x4, x2) 940.44/291.49 plus#2(0', S(x2)) -> S(x2) 940.44/291.49 plus#2(S(x4), S(x2)) -> S(plus#2(x4, S(x2))) 940.44/291.49 max#2(0', x8) -> x8 940.44/291.49 max#2(S(x12), 0') -> S(x12) 940.44/291.49 max#2(S(x4), S(x2)) -> S(max#2(x4, x2)) 940.44/291.49 main(x1) -> foldl#3(0', scanr#3(x1)) 940.44/291.49 940.44/291.49 S is empty. 940.44/291.49 Rewrite Strategy: INNERMOST 940.44/291.49 ---------------------------------------- 940.44/291.49
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