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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308061
details
property
value
status
complete
benchmark
PALINDROME_complete_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n087.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.545 seconds
cpu usage
333.022
user time
330.927
system time
2.09517
max virtual memory
1.828184E7
max residence set size
5555384.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
332.90/291.50 WORST_CASE(Omega(n^1), ?) 332.90/291.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 332.90/291.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 332.90/291.51 332.90/291.51 332.90/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 332.90/291.51 332.90/291.51 (0) CpxTRS 332.90/291.51 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 332.90/291.51 (2) TRS for Loop Detection 332.90/291.51 (3) DecreasingLoopProof [LOWER BOUND(ID), 150 ms] 332.90/291.51 (4) BEST 332.90/291.51 (5) proven lower bound 332.90/291.51 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 332.90/291.51 (7) BOUNDS(n^1, INF) 332.90/291.51 (8) TRS for Loop Detection 332.90/291.51 332.90/291.51 332.90/291.51 ---------------------------------------- 332.90/291.51 332.90/291.51 (0) 332.90/291.51 Obligation: 332.90/291.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 332.90/291.51 332.90/291.51 332.90/291.51 The TRS R consists of the following rules: 332.90/291.51 332.90/291.51 __(__(X, Y), Z) -> __(X, __(Y, Z)) 332.90/291.51 __(X, nil) -> X 332.90/291.51 __(nil, X) -> X 332.90/291.51 U11(tt, V) -> U12(isNeList(activate(V))) 332.90/291.51 U12(tt) -> tt 332.90/291.51 U21(tt, V1, V2) -> U22(isList(activate(V1)), activate(V2)) 332.90/291.51 U22(tt, V2) -> U23(isList(activate(V2))) 332.90/291.51 U23(tt) -> tt 332.90/291.51 U31(tt, V) -> U32(isQid(activate(V))) 332.90/291.51 U32(tt) -> tt 332.90/291.51 U41(tt, V1, V2) -> U42(isList(activate(V1)), activate(V2)) 332.90/291.51 U42(tt, V2) -> U43(isNeList(activate(V2))) 332.90/291.51 U43(tt) -> tt 332.90/291.51 U51(tt, V1, V2) -> U52(isNeList(activate(V1)), activate(V2)) 332.90/291.51 U52(tt, V2) -> U53(isList(activate(V2))) 332.90/291.51 U53(tt) -> tt 332.90/291.51 U61(tt, V) -> U62(isQid(activate(V))) 332.90/291.51 U62(tt) -> tt 332.90/291.51 U71(tt, V) -> U72(isNePal(activate(V))) 332.90/291.51 U72(tt) -> tt 332.90/291.51 and(tt, X) -> activate(X) 332.90/291.51 isList(V) -> U11(isPalListKind(activate(V)), activate(V)) 332.90/291.51 isList(n__nil) -> tt 332.90/291.51 isList(n____(V1, V2)) -> U21(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2)) 332.90/291.51 isNeList(V) -> U31(isPalListKind(activate(V)), activate(V)) 332.90/291.51 isNeList(n____(V1, V2)) -> U41(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2)) 332.90/291.51 isNeList(n____(V1, V2)) -> U51(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2)) 332.90/291.51 isNePal(V) -> U61(isPalListKind(activate(V)), activate(V)) 332.90/291.51 isNePal(n____(I, __(P, I))) -> and(and(isQid(activate(I)), n__isPalListKind(activate(I))), n__and(isPal(activate(P)), n__isPalListKind(activate(P)))) 332.90/291.51 isPal(V) -> U71(isPalListKind(activate(V)), activate(V)) 332.90/291.51 isPal(n__nil) -> tt 332.90/291.51 isPalListKind(n__a) -> tt 332.90/291.51 isPalListKind(n__e) -> tt 332.90/291.51 isPalListKind(n__i) -> tt 332.90/291.51 isPalListKind(n__nil) -> tt 332.90/291.51 isPalListKind(n__o) -> tt 332.90/291.51 isPalListKind(n__u) -> tt 332.90/291.51 isPalListKind(n____(V1, V2)) -> and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))) 332.90/291.51 isQid(n__a) -> tt 332.90/291.51 isQid(n__e) -> tt 332.90/291.51 isQid(n__i) -> tt 332.90/291.51 isQid(n__o) -> tt 332.90/291.51 isQid(n__u) -> tt 332.90/291.51 nil -> n__nil 332.90/291.51 __(X1, X2) -> n____(X1, X2) 332.90/291.51 isPalListKind(X) -> n__isPalListKind(X) 332.90/291.51 and(X1, X2) -> n__and(X1, X2) 332.90/291.51 a -> n__a 332.90/291.51 e -> n__e 332.90/291.51 i -> n__i 332.90/291.51 o -> n__o 332.90/291.51 u -> n__u 332.90/291.51 activate(n__nil) -> nil 332.90/291.51 activate(n____(X1, X2)) -> __(X1, X2) 332.90/291.51 activate(n__isPalListKind(X)) -> isPalListKind(X) 332.90/291.51 activate(n__and(X1, X2)) -> and(X1, X2) 332.90/291.51 activate(n__a) -> a 332.90/291.51 activate(n__e) -> e 332.90/291.51 activate(n__i) -> i 332.90/291.51 activate(n__o) -> o 332.90/291.51 activate(n__u) -> u 332.90/291.51 activate(X) -> X 332.90/291.51 332.90/291.51 S is empty. 332.90/291.51 Rewrite Strategy: FULL 332.90/291.51 ---------------------------------------- 332.90/291.51 332.90/291.51 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 332.90/291.51 Transformed a relative TRS into a decreasing-loop problem. 332.90/291.51 ---------------------------------------- 332.90/291.51 332.90/291.51 (2) 332.90/291.51 Obligation:
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