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Derivational Complexity: TRS Innermost pair #487105854
details
property
value
status
complete
benchmark
cime3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
296.463 seconds
cpu usage
1158.64
user time
1147.51
system time
11.1326
max virtual memory
3.7890084E7
max residence set size
1.4984208E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 617 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a__a -> a__c a__b -> a__c a__c -> e a__k -> l a__d -> m a__a -> a__d a__b -> a__d a__c -> l a__k -> m a__A -> a__h(a__f(a__a), a__f(a__b)) a__h(X, X) -> a__g(mark(X), mark(X), a__f(a__k)) a__g(d, X, X) -> a__A a__f(X) -> a__z(mark(X), X) a__z(e, X) -> mark(X) mark(A) -> a__A mark(a) -> a__a mark(b) -> a__b mark(c) -> a__c mark(d) -> a__d mark(k) -> a__k mark(z(X1, X2)) -> a__z(mark(X1), X2) mark(f(X)) -> a__f(mark(X)) mark(h(X1, X2)) -> a__h(mark(X1), mark(X2)) mark(g(X1, X2, X3)) -> a__g(mark(X1), mark(X2), mark(X3)) mark(e) -> e mark(l) -> l mark(m) -> m a__A -> A a__a -> a a__b -> b a__c -> c a__d -> d a__k -> k a__z(X1, X2) -> z(X1, X2) a__f(X) -> f(X) a__h(X1, X2) -> h(X1, X2) a__g(X1, X2, X3) -> g(X1, X2, X3) 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(e) -> e encArg(l) -> l encArg(m) -> m encArg(d) -> d encArg(A) -> A encArg(a) -> a encArg(b) -> b encArg(c) -> c encArg(k) -> k encArg(z(x_1, x_2)) -> z(encArg(x_1), encArg(x_2)) encArg(f(x_1)) -> f(encArg(x_1)) encArg(h(x_1, x_2)) -> h(encArg(x_1), encArg(x_2)) encArg(g(x_1, x_2, x_3)) -> g(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_a__a) -> a__a encArg(cons_a__b) -> a__b encArg(cons_a__c) -> a__c encArg(cons_a__k) -> a__k encArg(cons_a__d) -> a__d encArg(cons_a__A) -> a__A encArg(cons_a__h(x_1, x_2)) -> a__h(encArg(x_1), encArg(x_2)) encArg(cons_a__g(x_1, x_2, x_3)) -> a__g(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_a__f(x_1)) -> a__f(encArg(x_1)) encArg(cons_a__z(x_1, x_2)) -> a__z(encArg(x_1), encArg(x_2)) encArg(cons_mark(x_1)) -> mark(encArg(x_1))
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