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Derivational Complexity: TRS Innermost pair #487108344
details
property
value
status
complete
benchmark
PALINDROME_complete-noand_L.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
2.31276 seconds
cpu usage
6.1998
user time
5.94836
system time
0.251439
max virtual memory
1.8432412E7
max residence set size
407852.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 1210 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) InfiniteLowerBoundProof [FINISHED, 0 ms] (8) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: __(__(X, Y), Z) -> __(X, __(Y, Z)) __(X, nil) -> X __(nil, X) -> X U11(tt) -> U12(isPalListKind) U12(tt) -> U13(isNeList) U13(tt) -> tt U21(tt) -> U22(isPalListKind) U22(tt) -> U23(isPalListKind) U23(tt) -> U24(isPalListKind) U24(tt) -> U25(isList) U25(tt) -> U26(isList) U26(tt) -> tt U31(tt) -> U32(isPalListKind) U32(tt) -> U33(isQid) U33(tt) -> tt U41(tt) -> U42(isPalListKind) U42(tt) -> U43(isPalListKind) U43(tt) -> U44(isPalListKind) U44(tt) -> U45(isList) U45(tt) -> U46(isNeList) U46(tt) -> tt U51(tt) -> U52(isPalListKind) U52(tt) -> U53(isPalListKind) U53(tt) -> U54(isPalListKind) U54(tt) -> U55(isNeList) U55(tt) -> U56(isList) U56(tt) -> tt U61(tt) -> U62(isPalListKind) U62(tt) -> U63(isQid) U63(tt) -> tt U71(tt) -> U72(isPalListKind) U72(tt) -> U73(isPal) U73(tt) -> U74(isPalListKind) U74(tt) -> tt U81(tt) -> U82(isPalListKind) U82(tt) -> U83(isNePal) U83(tt) -> tt U91(tt) -> U92(isPalListKind) U92(tt) -> tt isList -> U11(isPalListKind) isList -> tt isList -> U21(isPalListKind) isNeList -> U31(isPalListKind) isNeList -> U41(isPalListKind) isNeList -> U51(isPalListKind) isNePal -> U61(isPalListKind) isNePal -> U71(isQid) isPal -> U81(isPalListKind) isPal -> tt isPalListKind -> tt isPalListKind -> U91(isPalListKind) isQid -> tt S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(nil) -> nil encArg(tt) -> tt encArg(cons___(x_1, x_2)) -> __(encArg(x_1), encArg(x_2)) encArg(cons_U11(x_1)) -> U11(encArg(x_1)) encArg(cons_U12(x_1)) -> U12(encArg(x_1)) encArg(cons_U13(x_1)) -> U13(encArg(x_1)) encArg(cons_U21(x_1)) -> U21(encArg(x_1)) encArg(cons_U22(x_1)) -> U22(encArg(x_1)) encArg(cons_U23(x_1)) -> U23(encArg(x_1)) encArg(cons_U24(x_1)) -> U24(encArg(x_1)) encArg(cons_U25(x_1)) -> U25(encArg(x_1)) encArg(cons_U26(x_1)) -> U26(encArg(x_1)) encArg(cons_U31(x_1)) -> U31(encArg(x_1))
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