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Derivational Complexity: TRS pair #487104044
details
property
value
status
complete
benchmark
Ex1_Zan97_GM.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)
291.548 seconds
cpu usage
315.374
user time
312.274
system time
3.10007
max virtual memory
1.9111476E7
max residence set size
5169696.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
WORST_CASE(?, 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 83 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 17 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: a__g(X) -> a__h(X) a__c -> d a__h(d) -> a__g(c) mark(g(X)) -> a__g(X) mark(h(X)) -> a__h(X) mark(c) -> a__c mark(d) -> d a__g(X) -> g(X) a__h(X) -> h(X) a__c -> c 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(d) -> d encArg(c) -> c encArg(g(x_1)) -> g(encArg(x_1)) encArg(h(x_1)) -> h(encArg(x_1)) encArg(cons_a__g(x_1)) -> a__g(encArg(x_1)) encArg(cons_a__c) -> a__c encArg(cons_a__h(x_1)) -> a__h(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__g(x_1) -> a__g(encArg(x_1)) encode_a__h(x_1) -> a__h(encArg(x_1)) encode_a__c -> a__c encode_d -> d encode_c -> c encode_mark(x_1) -> mark(encArg(x_1)) encode_g(x_1) -> g(encArg(x_1)) encode_h(x_1) -> h(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: a__g(X) -> a__h(X) a__c -> d a__h(d) -> a__g(c) mark(g(X)) -> a__g(X) mark(h(X)) -> a__h(X) mark(c) -> a__c mark(d) -> d a__g(X) -> g(X) a__h(X) -> h(X) a__c -> c The (relative) TRS S consists of the following rules: encArg(d) -> d encArg(c) -> c encArg(g(x_1)) -> g(encArg(x_1)) encArg(h(x_1)) -> h(encArg(x_1)) encArg(cons_a__g(x_1)) -> a__g(encArg(x_1)) encArg(cons_a__c) -> a__c encArg(cons_a__h(x_1)) -> a__h(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__g(x_1) -> a__g(encArg(x_1)) encode_a__h(x_1) -> a__h(encArg(x_1)) encode_a__c -> a__c encode_d -> d encode_c -> c encode_mark(x_1) -> mark(encArg(x_1)) encode_g(x_1) -> g(encArg(x_1))
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