/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(NON_POLY, ?)
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).

(0) CpxTRS
(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(2) TRS for Loop Detection
(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
(4) BOUNDS(INF, INF)


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(0)
Obligation:
The Runtime Complexity (full) of the given CpxTRS 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: FULL
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(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
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(2)
Obligation:
Analyzing the following TRS for decreasing loops:

The Runtime Complexity (full) of the given CpxTRS 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: FULL
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(3) InfiniteLowerBoundProof (FINISHED)
The following loop proves infinite runtime complexity:

The rewrite sequence

isPalListKind ->^+ U91(isPalListKind)

gives rise to a decreasing loop by considering the right hand sides subterm at position [0].

The pumping substitution is [ ].

The result substitution is [ ].




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(4)
BOUNDS(INF, INF)