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Derivational Complexity: TRS pair #487102948
details
property
value
status
complete
benchmark
212480.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
ICFP_2010
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
2.53367 seconds
cpu usage
7.19675
user time
6.87098
system time
0.325779
max virtual memory
1.8414844E7
max residence set size
823660.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 42 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 121 ms] (8) BOUNDS(1, n^1) (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (10) TRS for Loop Detection (11) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: 0(1(1(x1))) -> 1(2(1(2(0(x1))))) 0(3(1(x1))) -> 1(3(2(2(0(x1))))) 0(3(1(x1))) -> 3(2(1(2(0(x1))))) 0(3(1(x1))) -> 1(3(3(3(2(0(x1)))))) 0(4(1(x1))) -> 2(1(2(0(4(x1))))) 0(0(4(5(x1)))) -> 0(0(2(5(4(x1))))) 0(1(4(1(x1)))) -> 0(1(2(2(4(1(x1)))))) 0(1(4(5(x1)))) -> 4(0(1(2(5(4(x1)))))) 0(1(5(1(x1)))) -> 1(2(2(5(0(1(x1)))))) 0(1(5(3(x1)))) -> 0(5(3(2(1(x1))))) 0(2(4(1(x1)))) -> 1(3(3(2(0(4(x1)))))) 0(2(4(1(x1)))) -> 4(2(1(2(0(4(x1)))))) 0(2(4(5(x1)))) -> 0(2(2(5(0(4(x1)))))) 0(3(1(5(x1)))) -> 0(1(2(5(3(x1))))) 0(3(1(5(x1)))) -> 1(2(5(3(0(4(x1)))))) 0(3(5(1(x1)))) -> 1(2(5(3(0(x1))))) 0(3(5(1(x1)))) -> 0(5(2(1(2(3(x1)))))) 0(3(5(5(x1)))) -> 0(3(2(5(5(x1))))) 0(4(0(1(x1)))) -> 2(0(4(4(0(1(x1)))))) 0(4(1(5(x1)))) -> 1(2(5(0(4(x1))))) 0(4(3(5(x1)))) -> 0(4(3(2(5(4(x1)))))) 0(4(5(1(x1)))) -> 2(5(4(4(0(1(x1)))))) 3(0(1(5(x1)))) -> 3(1(4(0(5(4(x1)))))) 3(0(3(1(x1)))) -> 1(3(3(2(0(x1))))) 3(0(3(5(x1)))) -> 3(2(5(0(2(3(x1)))))) 3(3(0(1(x1)))) -> 0(1(3(2(2(3(x1)))))) 3(4(5(1(x1)))) -> 3(2(5(4(2(1(x1)))))) 4(1(3(5(x1)))) -> 1(2(5(3(4(4(x1)))))) 4(1(5(1(x1)))) -> 4(4(5(1(2(1(x1)))))) 4(4(1(5(x1)))) -> 4(1(2(5(4(x1))))) 0(1(4(5(5(x1))))) -> 0(5(1(4(2(5(x1)))))) 0(2(1(4(5(x1))))) -> 0(0(1(2(5(4(x1)))))) 0(2(1(5(5(x1))))) -> 0(1(2(2(5(5(x1)))))) 0(4(2(4(1(x1))))) -> 1(3(2(0(4(4(x1)))))) 0(4(5(4(3(x1))))) -> 2(5(0(4(4(3(x1)))))) 0(5(1(5(1(x1))))) -> 0(5(1(1(2(5(x1)))))) 0(5(2(1(5(x1))))) -> 1(2(5(5(0(4(x1)))))) 0(5(2(4(1(x1))))) -> 4(5(2(1(2(0(x1)))))) 3(0(1(4(1(x1))))) -> 0(4(4(1(3(1(x1)))))) 3(0(1(4(1(x1))))) -> 4(3(2(0(1(1(x1)))))) 3(0(3(5(5(x1))))) -> 3(3(2(5(0(5(x1)))))) 3(0(5(3(1(x1))))) -> 1(0(3(3(2(5(x1)))))) 4(0(1(4(1(x1))))) -> 4(4(0(1(3(1(x1)))))) 4(0(1(5(1(x1))))) -> 0(1(2(5(4(1(x1)))))) 4(0(2(4(5(x1))))) -> 4(0(2(5(0(4(x1)))))) 4(1(1(5(1(x1))))) -> 1(1(2(5(4(1(x1)))))) 4(5(1(4(1(x1))))) -> 4(4(1(2(1(5(x1)))))) 4(5(2(3(1(x1))))) -> 4(3(1(2(2(5(x1)))))) 4(5(4(3(1(x1))))) -> 4(1(2(5(3(4(x1)))))) 4(5(5(3(1(x1))))) -> 1(3(2(5(5(4(x1)))))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (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(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1))
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