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Derivational Complexity: TRS Innermost pair #487108850
details
property
value
status
complete
benchmark
PALINDROME_complete_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
3.03007 seconds
cpu usage
9.0557
user time
8.68204
system time
0.373653
max virtual memory
1.8551104E7
max residence set size
735212.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(EXP, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 1487 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 4 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection (13) DecreasingLoopProof [FINISHED, 197 ms] (14) BOUNDS(EXP, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: __(__(X, Y), Z) -> __(X, __(Y, Z)) __(X, nil) -> X __(nil, X) -> X U11(tt, V) -> U12(isNeList(activate(V))) U12(tt) -> tt U21(tt, V1, V2) -> U22(isList(activate(V1)), activate(V2)) U22(tt, V2) -> U23(isList(activate(V2))) U23(tt) -> tt U31(tt, V) -> U32(isQid(activate(V))) U32(tt) -> tt U41(tt, V1, V2) -> U42(isList(activate(V1)), activate(V2)) U42(tt, V2) -> U43(isNeList(activate(V2))) U43(tt) -> tt U51(tt, V1, V2) -> U52(isNeList(activate(V1)), activate(V2)) U52(tt, V2) -> U53(isList(activate(V2))) U53(tt) -> tt U61(tt, V) -> U62(isQid(activate(V))) U62(tt) -> tt U71(tt, V) -> U72(isNePal(activate(V))) U72(tt) -> tt and(tt, X) -> activate(X) isList(V) -> U11(isPalListKind(activate(V)), activate(V)) isList(n__nil) -> tt isList(n____(V1, V2)) -> U21(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2)) isNeList(V) -> U31(isPalListKind(activate(V)), activate(V)) isNeList(n____(V1, V2)) -> U41(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2)) isNeList(n____(V1, V2)) -> U51(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2)) isNePal(V) -> U61(isPalListKind(activate(V)), activate(V)) isNePal(n____(I, n____(P, I))) -> and(and(isQid(activate(I)), n__isPalListKind(activate(I))), n__and(n__isPal(activate(P)), n__isPalListKind(activate(P)))) isPal(V) -> U71(isPalListKind(activate(V)), activate(V)) isPal(n__nil) -> tt isPalListKind(n__a) -> tt isPalListKind(n__e) -> tt isPalListKind(n__i) -> tt isPalListKind(n__nil) -> tt isPalListKind(n__o) -> tt isPalListKind(n__u) -> tt isPalListKind(n____(V1, V2)) -> and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))) isQid(n__a) -> tt isQid(n__e) -> tt isQid(n__i) -> tt isQid(n__o) -> tt isQid(n__u) -> tt nil -> n__nil __(X1, X2) -> n____(X1, X2) isPalListKind(X) -> n__isPalListKind(X) and(X1, X2) -> n__and(X1, X2) isPal(X) -> n__isPal(X) a -> n__a e -> n__e i -> n__i o -> n__o u -> n__u activate(n__nil) -> nil activate(n____(X1, X2)) -> __(activate(X1), activate(X2)) activate(n__isPalListKind(X)) -> isPalListKind(X) activate(n__and(X1, X2)) -> and(activate(X1), X2) activate(n__isPal(X)) -> isPal(X) activate(n__a) -> a activate(n__e) -> e activate(n__i) -> i activate(n__o) -> o activate(n__u) -> u activate(X) -> X S is empty. Rewrite Strategy: INNERMOST
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