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Derivational Complexity: TRS Innermost pair #487108916
details
property
value
status
complete
benchmark
Ex6_GM04_L.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n147.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
1.55368 seconds
cpu usage
3.33034
user time
3.17781
system time
0.152526
max virtual memory
1.8611228E7
max residence set size
233588.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(1))
output
WORST_CASE(?, O(1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, 1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 32 ms] (4) CpxRelTRS (5) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms] (6) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, 1). The TRS R consists of the following rules: c -> f f -> g 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(g) -> g encArg(cons_c) -> c encArg(cons_f) -> f encode_c -> c encode_f -> f encode_g -> g ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, 1). The TRS R consists of the following rules: c -> f f -> g The (relative) TRS S consists of the following rules: encArg(g) -> g encArg(cons_c) -> c encArg(cons_f) -> f encode_c -> c encode_f -> f encode_g -> g Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, 1). The TRS R consists of the following rules: c -> f f -> g The (relative) TRS S consists of the following rules: encArg(g) -> g encArg(cons_c) -> c encArg(cons_f) -> f encode_c -> c encode_f -> f encode_g -> g Rewrite Strategy: INNERMOST ---------------------------------------- (5) NarrowingOnBasicTermsTerminatesProof (FINISHED) Constant runtime complexity proven by termination of constructor-based narrowing. The maximal most general narrowing sequences give rise to the following rewrite sequences: encode_g ->^* g
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