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Derivational Complexity: TRS pair #487103392
details
property
value
status
complete
benchmark
85834.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
ICFP_2010
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
295.299 seconds
cpu usage
824.736
user time
817.048
system time
7.68823
max virtual memory
1.889534E7
max residence set size
1.522222E7
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 161 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 160 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(x1))) -> 1(3(2(x1))) 1(1(4(2(3(x1))))) -> 1(5(4(4(x1)))) 2(2(1(3(5(x1))))) -> 1(2(0(5(x1)))) 3(0(0(2(1(x1))))) -> 0(5(4(0(x1)))) 4(3(2(5(0(x1))))) -> 3(4(1(5(5(x1))))) 0(0(0(3(2(5(x1)))))) -> 2(0(5(5(4(5(x1)))))) 2(2(1(1(3(2(x1)))))) -> 2(1(4(0(0(x1))))) 3(3(1(1(2(2(x1)))))) -> 3(3(0(0(2(x1))))) 0(2(5(1(0(4(2(2(x1)))))))) -> 0(0(3(5(1(5(4(x1))))))) 4(0(5(3(5(1(3(5(x1)))))))) -> 4(0(0(1(3(0(1(5(x1)))))))) 4(4(4(3(5(1(4(0(x1)))))))) -> 3(0(2(2(2(2(3(2(x1)))))))) 0(0(5(3(2(2(5(0(3(x1))))))))) -> 2(5(5(4(2(2(5(0(3(x1))))))))) 3(2(2(0(0(0(0(3(1(0(5(x1))))))))))) -> 0(4(3(0(4(4(2(4(1(4(0(5(x1)))))))))))) 4(3(3(3(5(0(0(3(2(4(4(1(2(x1))))))))))))) -> 4(4(5(2(2(0(5(0(1(4(3(0(x1)))))))))))) 4(4(3(3(1(2(2(5(3(5(3(2(3(x1))))))))))))) -> 4(1(4(0(0(2(5(4(4(2(0(3(x1)))))))))))) 0(0(5(0(1(4(4(3(5(2(0(0(3(3(x1)))))))))))))) -> 2(1(2(1(2(0(4(0(2(2(4(3(3(5(4(x1))))))))))))))) 3(0(1(5(5(1(0(4(0(0(2(1(0(3(x1)))))))))))))) -> 3(4(0(1(2(5(2(2(0(3(0(4(5(1(x1)))))))))))))) 5(5(0(5(4(4(4(3(4(0(5(4(3(3(x1)))))))))))))) -> 2(4(5(0(2(0(3(0(2(5(3(1(3(3(x1)))))))))))))) 1(0(4(3(2(1(1(1(2(4(4(5(5(0(1(x1))))))))))))))) -> 1(0(2(4(5(5(0(1(1(4(4(5(0(1(x1)))))))))))))) 3(4(1(1(4(4(0(4(4(2(4(1(0(0(5(3(2(x1))))))))))))))))) -> 3(5(5(5(0(1(3(2(4(2(0(3(5(3(0(x1))))))))))))))) 0(2(1(3(5(3(4(1(1(4(4(0(4(3(4(1(0(2(x1)))))))))))))))))) -> 1(5(2(2(0(3(2(3(4(2(0(1(1(1(3(2(1(x1))))))))))))))))) 3(3(0(0(1(2(3(5(3(0(5(2(0(0(2(4(4(1(x1)))))))))))))))))) -> 2(2(4(1(4(4(2(5(2(2(5(1(4(2(5(2(0(4(1(x1))))))))))))))))))) 3(3(0(5(2(3(1(3(0(0(3(1(5(2(2(1(2(2(x1)))))))))))))))))) -> 1(0(3(0(4(2(4(3(2(0(4(2(1(5(5(2(2(x1))))))))))))))))) 4(5(4(0(1(1(5(5(4(5(3(2(1(3(2(4(4(2(x1)))))))))))))))))) -> 3(4(5(5(3(0(4(3(3(3(0(5(3(2(2(5(0(x1))))))))))))))))) 0(0(4(1(2(3(3(5(5(2(0(3(1(2(2(4(0(1(5(x1))))))))))))))))))) -> 2(2(0(1(0(1(5(0(1(0(0(5(0(1(1(4(5(x1))))))))))))))))) 0(5(0(3(2(3(2(3(0(1(5(5(5(3(4(0(0(2(2(x1))))))))))))))))))) -> 2(2(5(4(0(0(1(5(5(3(2(2(5(0(0(5(4(0(x1)))))))))))))))))) 4(0(3(4(1(3(2(0(0(0(2(1(0(1(1(3(1(5(1(x1))))))))))))))))))) -> 0(3(5(3(4(5(1(0(0(3(1(0(2(4(1(3(3(0(x1)))))))))))))))))) 4(4(5(4(5(4(3(1(2(2(0(2(5(4(2(0(4(1(2(x1))))))))))))))))))) -> 0(3(5(5(2(0(3(4(2(4(5(0(2(1(3(2(2(1(x1)))))))))))))))))) 3(3(3(5(2(0(0(3(3(1(2(5(2(1(3(1(0(5(2(2(x1)))))))))))))))))))) -> 3(4(5(0(5(3(1(3(5(5(5(4(0(4(1(2(5(5(0(x1))))))))))))))))))) 2(5(4(3(4(4(4(4(2(1(2(2(1(5(5(2(5(0(1(1(1(x1))))))))))))))))))))) -> 5(4(5(4(1(3(4(3(0(3(3(1(1(4(4(2(1(2(0(1(0(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(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(x1))) -> 1(3(2(x1))) 1(1(4(2(3(x1))))) -> 1(5(4(4(x1)))) 2(2(1(3(5(x1))))) -> 1(2(0(5(x1)))) 3(0(0(2(1(x1))))) -> 0(5(4(0(x1)))) 4(3(2(5(0(x1))))) -> 3(4(1(5(5(x1))))) 0(0(0(3(2(5(x1)))))) -> 2(0(5(5(4(5(x1)))))) 2(2(1(1(3(2(x1)))))) -> 2(1(4(0(0(x1))))) 3(3(1(1(2(2(x1)))))) -> 3(3(0(0(2(x1))))) 0(2(5(1(0(4(2(2(x1)))))))) -> 0(0(3(5(1(5(4(x1))))))) 4(0(5(3(5(1(3(5(x1)))))))) -> 4(0(0(1(3(0(1(5(x1)))))))) 4(4(4(3(5(1(4(0(x1)))))))) -> 3(0(2(2(2(2(3(2(x1)))))))) 0(0(5(3(2(2(5(0(3(x1))))))))) -> 2(5(5(4(2(2(5(0(3(x1)))))))))
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