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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308088
details
property
value
status
complete
benchmark
PEANO_nokinds_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.91185 seconds
cpu usage
28.5807
user time
26.9983
system time
1.58243
max virtual memory
1.9471472E7
max residence set size
4123376.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
27.86/8.64 WORST_CASE(Omega(n^1), O(n^1)) 27.86/8.65 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 27.86/8.65 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 27.86/8.65 27.86/8.65 27.86/8.65 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 27.86/8.65 27.86/8.65 (0) CpxTRS 27.86/8.65 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 27.86/8.65 (2) CpxTRS 27.86/8.65 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 27.86/8.65 (4) CpxTRS 27.86/8.65 (5) CpxTrsMatchBoundsTAProof [FINISHED, 125 ms] 27.86/8.65 (6) BOUNDS(1, n^1) 27.86/8.65 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 27.86/8.65 (8) TRS for Loop Detection 27.86/8.65 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 27.86/8.65 (10) BEST 27.86/8.65 (11) proven lower bound 27.86/8.65 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 27.86/8.65 (13) BOUNDS(n^1, INF) 27.86/8.65 (14) TRS for Loop Detection 27.86/8.65 27.86/8.65 27.86/8.65 ---------------------------------------- 27.86/8.65 27.86/8.65 (0) 27.86/8.65 Obligation: 27.86/8.65 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 27.86/8.65 27.86/8.65 27.86/8.65 The TRS R consists of the following rules: 27.86/8.65 27.86/8.65 active(U11(tt, V2)) -> mark(U12(isNat(V2))) 27.86/8.65 active(U12(tt)) -> mark(tt) 27.86/8.65 active(U21(tt)) -> mark(tt) 27.86/8.65 active(U31(tt, N)) -> mark(N) 27.86/8.65 active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N)) 27.86/8.65 active(U42(tt, M, N)) -> mark(s(plus(N, M))) 27.86/8.65 active(isNat(0)) -> mark(tt) 27.86/8.65 active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2)) 27.86/8.65 active(isNat(s(V1))) -> mark(U21(isNat(V1))) 27.86/8.65 active(plus(N, 0)) -> mark(U31(isNat(N), N)) 27.86/8.65 active(plus(N, s(M))) -> mark(U41(isNat(M), M, N)) 27.86/8.65 active(U11(X1, X2)) -> U11(active(X1), X2) 27.86/8.65 active(U12(X)) -> U12(active(X)) 27.86/8.65 active(U21(X)) -> U21(active(X)) 27.86/8.65 active(U31(X1, X2)) -> U31(active(X1), X2) 27.86/8.65 active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3) 27.86/8.65 active(U42(X1, X2, X3)) -> U42(active(X1), X2, X3) 27.86/8.65 active(s(X)) -> s(active(X)) 27.86/8.65 active(plus(X1, X2)) -> plus(active(X1), X2) 27.86/8.65 active(plus(X1, X2)) -> plus(X1, active(X2)) 27.86/8.65 U11(mark(X1), X2) -> mark(U11(X1, X2)) 27.86/8.65 U12(mark(X)) -> mark(U12(X)) 27.86/8.65 U21(mark(X)) -> mark(U21(X)) 27.86/8.65 U31(mark(X1), X2) -> mark(U31(X1, X2)) 27.86/8.65 U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3)) 27.86/8.65 U42(mark(X1), X2, X3) -> mark(U42(X1, X2, X3)) 27.86/8.65 s(mark(X)) -> mark(s(X)) 27.86/8.65 plus(mark(X1), X2) -> mark(plus(X1, X2)) 27.86/8.65 plus(X1, mark(X2)) -> mark(plus(X1, X2)) 27.86/8.65 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 27.86/8.65 proper(tt) -> ok(tt) 27.86/8.65 proper(U12(X)) -> U12(proper(X)) 27.86/8.65 proper(isNat(X)) -> isNat(proper(X)) 27.86/8.65 proper(U21(X)) -> U21(proper(X)) 27.86/8.65 proper(U31(X1, X2)) -> U31(proper(X1), proper(X2)) 27.86/8.65 proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3)) 27.86/8.65 proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3)) 27.86/8.65 proper(s(X)) -> s(proper(X)) 27.86/8.65 proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 27.86/8.65 proper(0) -> ok(0) 27.86/8.65 U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 27.86/8.65 U12(ok(X)) -> ok(U12(X)) 27.86/8.65 isNat(ok(X)) -> ok(isNat(X)) 27.86/8.65 U21(ok(X)) -> ok(U21(X)) 27.86/8.65 U31(ok(X1), ok(X2)) -> ok(U31(X1, X2)) 27.86/8.65 U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3)) 27.86/8.65 U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3)) 27.86/8.65 s(ok(X)) -> ok(s(X)) 27.86/8.65 plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) 27.86/8.65 top(mark(X)) -> top(proper(X)) 27.86/8.65 top(ok(X)) -> top(active(X)) 27.86/8.65 27.86/8.65 S is empty. 27.86/8.65 Rewrite Strategy: FULL 27.86/8.65 ---------------------------------------- 27.86/8.65 27.86/8.65 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 27.86/8.65 The following defined symbols can occur below the 0th argument of top: proper, active 27.86/8.65 The following defined symbols can occur below the 0th argument of proper: proper, active 27.86/8.65 The following defined symbols can occur below the 0th argument of active: proper, active 27.86/8.65 27.86/8.65 Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: 27.86/8.65 active(U11(tt, V2)) -> mark(U12(isNat(V2))) 27.86/8.65 active(U12(tt)) -> mark(tt) 27.86/8.65 active(U21(tt)) -> mark(tt) 27.86/8.65 active(U31(tt, N)) -> mark(N) 27.86/8.65 active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N))
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