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Derivational Complexity: TRS Innermost pair #487109132
details
property
value
status
complete
benchmark
Ex6_9_Luc02c_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
295.755 seconds
cpu usage
1148.09
user time
1134.11
system time
13.9883
max virtual memory
5.6017936E7
max residence set size
1.5077328E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 289 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: active(2nd(cons1(X, cons(Y, Z)))) -> mark(Y) active(2nd(cons(X, X1))) -> mark(2nd(cons1(X, X1))) active(from(X)) -> mark(cons(X, from(s(X)))) active(2nd(X)) -> 2nd(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(from(X)) -> from(active(X)) active(s(X)) -> s(active(X)) active(cons1(X1, X2)) -> cons1(active(X1), X2) active(cons1(X1, X2)) -> cons1(X1, active(X2)) 2nd(mark(X)) -> mark(2nd(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) from(mark(X)) -> mark(from(X)) s(mark(X)) -> mark(s(X)) cons1(mark(X1), X2) -> mark(cons1(X1, X2)) cons1(X1, mark(X2)) -> mark(cons1(X1, X2)) proper(2nd(X)) -> 2nd(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(from(X)) -> from(proper(X)) proper(s(X)) -> s(proper(X)) proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2)) 2nd(ok(X)) -> ok(2nd(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) from(ok(X)) -> ok(from(X)) s(ok(X)) -> ok(s(X)) cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) 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(mark(x_1)) -> mark(encArg(x_1)) encArg(ok(x_1)) -> ok(encArg(x_1)) encArg(cons_active(x_1)) -> active(encArg(x_1)) encArg(cons_2nd(x_1)) -> 2nd(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_cons1(x_1, x_2)) -> cons1(encArg(x_1), encArg(x_2)) encArg(cons_proper(x_1)) -> proper(encArg(x_1)) encArg(cons_top(x_1)) -> top(encArg(x_1)) encode_active(x_1) -> active(encArg(x_1)) encode_2nd(x_1) -> 2nd(encArg(x_1)) encode_cons1(x_1, x_2) -> cons1(encArg(x_1), encArg(x_2)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_mark(x_1) -> mark(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_proper(x_1) -> proper(encArg(x_1)) encode_ok(x_1) -> ok(encArg(x_1)) encode_top(x_1) -> top(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: active(2nd(cons1(X, cons(Y, Z)))) -> mark(Y) active(2nd(cons(X, X1))) -> mark(2nd(cons1(X, X1))) active(from(X)) -> mark(cons(X, from(s(X))))
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