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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308329
details
property
value
status
complete
benchmark
Ex8_BLR02_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n037.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.33976 seconds
cpu usage
24.2797
user time
22.5849
system time
1.69481
max virtual memory
5.6516992E7
max residence set size
3944436.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
24.08/8.28 WORST_CASE(Omega(n^1), O(n^1)) 24.08/8.29 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 24.08/8.29 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 24.08/8.29 24.08/8.29 24.08/8.29 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 24.08/8.29 24.08/8.29 (0) CpxTRS 24.08/8.29 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 6 ms] 24.08/8.29 (2) CpxTRS 24.08/8.29 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 24.08/8.29 (4) CpxTRS 24.08/8.29 (5) CpxTrsMatchBoundsTAProof [FINISHED, 58 ms] 24.08/8.29 (6) BOUNDS(1, n^1) 24.08/8.29 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 24.08/8.29 (8) TRS for Loop Detection 24.08/8.29 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 24.08/8.29 (10) BEST 24.08/8.29 (11) proven lower bound 24.08/8.29 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 24.08/8.29 (13) BOUNDS(n^1, INF) 24.08/8.29 (14) TRS for Loop Detection 24.08/8.29 24.08/8.29 24.08/8.29 ---------------------------------------- 24.08/8.29 24.08/8.29 (0) 24.08/8.29 Obligation: 24.08/8.29 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 24.08/8.29 24.08/8.29 24.08/8.29 The TRS R consists of the following rules: 24.08/8.29 24.08/8.29 active(fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) 24.08/8.29 active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) 24.08/8.29 active(add(0, X)) -> mark(X) 24.08/8.29 active(add(s(X), Y)) -> mark(s(add(X, Y))) 24.08/8.29 active(sel(0, cons(X, XS))) -> mark(X) 24.08/8.29 active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) 24.08/8.29 active(fib(X)) -> fib(active(X)) 24.08/8.29 active(sel(X1, X2)) -> sel(active(X1), X2) 24.08/8.29 active(sel(X1, X2)) -> sel(X1, active(X2)) 24.08/8.29 active(fib1(X1, X2)) -> fib1(active(X1), X2) 24.08/8.29 active(fib1(X1, X2)) -> fib1(X1, active(X2)) 24.08/8.29 active(s(X)) -> s(active(X)) 24.08/8.29 active(cons(X1, X2)) -> cons(active(X1), X2) 24.08/8.29 active(add(X1, X2)) -> add(active(X1), X2) 24.08/8.29 active(add(X1, X2)) -> add(X1, active(X2)) 24.08/8.29 fib(mark(X)) -> mark(fib(X)) 24.08/8.29 sel(mark(X1), X2) -> mark(sel(X1, X2)) 24.08/8.29 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 24.08/8.29 fib1(mark(X1), X2) -> mark(fib1(X1, X2)) 24.08/8.29 fib1(X1, mark(X2)) -> mark(fib1(X1, X2)) 24.08/8.29 s(mark(X)) -> mark(s(X)) 24.08/8.29 cons(mark(X1), X2) -> mark(cons(X1, X2)) 24.08/8.29 add(mark(X1), X2) -> mark(add(X1, X2)) 24.08/8.29 add(X1, mark(X2)) -> mark(add(X1, X2)) 24.08/8.29 proper(fib(X)) -> fib(proper(X)) 24.08/8.29 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 24.08/8.29 proper(fib1(X1, X2)) -> fib1(proper(X1), proper(X2)) 24.08/8.29 proper(s(X)) -> s(proper(X)) 24.08/8.29 proper(0) -> ok(0) 24.08/8.29 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 24.08/8.29 proper(add(X1, X2)) -> add(proper(X1), proper(X2)) 24.08/8.29 fib(ok(X)) -> ok(fib(X)) 24.08/8.29 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 24.08/8.29 fib1(ok(X1), ok(X2)) -> ok(fib1(X1, X2)) 24.08/8.29 s(ok(X)) -> ok(s(X)) 24.08/8.29 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 24.08/8.29 add(ok(X1), ok(X2)) -> ok(add(X1, X2)) 24.08/8.29 top(mark(X)) -> top(proper(X)) 24.08/8.29 top(ok(X)) -> top(active(X)) 24.08/8.29 24.08/8.29 S is empty. 24.08/8.29 Rewrite Strategy: FULL 24.08/8.29 ---------------------------------------- 24.08/8.29 24.08/8.29 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 24.08/8.29 The following defined symbols can occur below the 0th argument of top: proper, active 24.08/8.29 The following defined symbols can occur below the 0th argument of proper: proper, active 24.08/8.29 The following defined symbols can occur below the 0th argument of active: proper, active 24.08/8.29 24.08/8.29 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 24.08/8.29 active(fib(N)) -> mark(sel(N, fib1(s(0), s(0)))) 24.08/8.29 active(fib1(X, Y)) -> mark(cons(X, fib1(Y, add(X, Y)))) 24.08/8.29 active(add(0, X)) -> mark(X) 24.08/8.29 active(add(s(X), Y)) -> mark(s(add(X, Y))) 24.08/8.29 active(sel(0, cons(X, XS))) -> mark(X) 24.08/8.29 active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) 24.08/8.29 active(fib(X)) -> fib(active(X)) 24.08/8.29 active(sel(X1, X2)) -> sel(active(X1), X2) 24.08/8.29 active(sel(X1, X2)) -> sel(X1, active(X2)) 24.08/8.29 active(fib1(X1, X2)) -> fib1(active(X1), X2) 24.08/8.29 active(fib1(X1, X2)) -> fib1(X1, active(X2)) 24.08/8.29 active(s(X)) -> s(active(X)) 24.08/8.29 active(cons(X1, X2)) -> cons(active(X1), X2) 24.08/8.29 active(add(X1, X2)) -> add(active(X1), X2) 24.08/8.29 active(add(X1, X2)) -> add(X1, active(X2)) 24.08/8.29 proper(fib(X)) -> fib(proper(X)) 24.08/8.29 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
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