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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308129
details
property
value
status
complete
benchmark
MYNAT_nokinds_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n130.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.21604 seconds
cpu usage
5.57711
user time
5.36192
system time
0.21519
max virtual memory
1.8277336E7
max residence set size
463864.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
5.46/2.16 WORST_CASE(NON_POLY, ?) 5.46/2.18 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 5.46/2.18 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 5.46/2.18 5.46/2.18 5.46/2.18 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 5.46/2.18 5.46/2.18 (0) CpxTRS 5.46/2.18 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 5.46/2.18 (2) TRS for Loop Detection 5.46/2.18 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 5.46/2.18 (4) BEST 5.46/2.18 (5) proven lower bound 5.46/2.18 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 5.46/2.18 (7) BOUNDS(n^1, INF) 5.46/2.18 (8) TRS for Loop Detection 5.46/2.18 (9) DecreasingLoopProof [FINISHED, 286 ms] 5.46/2.18 (10) BOUNDS(EXP, INF) 5.46/2.18 5.46/2.18 5.46/2.18 ---------------------------------------- 5.46/2.18 5.46/2.18 (0) 5.46/2.18 Obligation: 5.46/2.18 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 5.46/2.18 5.46/2.18 5.46/2.18 The TRS R consists of the following rules: 5.46/2.18 5.46/2.18 U11(tt, N) -> activate(N) 5.46/2.18 U21(tt, M, N) -> s(plus(activate(N), activate(M))) 5.46/2.18 U31(tt) -> 0 5.46/2.18 U41(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 5.46/2.18 and(tt, X) -> activate(X) 5.46/2.18 isNat(n__0) -> tt 5.46/2.18 isNat(n__plus(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) 5.46/2.18 isNat(n__s(V1)) -> isNat(activate(V1)) 5.46/2.18 isNat(n__x(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) 5.46/2.18 plus(N, 0) -> U11(isNat(N), N) 5.46/2.18 plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) 5.46/2.18 x(N, 0) -> U31(isNat(N)) 5.46/2.18 x(N, s(M)) -> U41(and(isNat(M), n__isNat(N)), M, N) 5.46/2.18 0 -> n__0 5.46/2.18 plus(X1, X2) -> n__plus(X1, X2) 5.46/2.18 isNat(X) -> n__isNat(X) 5.46/2.18 s(X) -> n__s(X) 5.46/2.18 x(X1, X2) -> n__x(X1, X2) 5.46/2.18 activate(n__0) -> 0 5.46/2.18 activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2)) 5.46/2.18 activate(n__isNat(X)) -> isNat(X) 5.46/2.18 activate(n__s(X)) -> s(activate(X)) 5.46/2.18 activate(n__x(X1, X2)) -> x(activate(X1), activate(X2)) 5.46/2.18 activate(X) -> X 5.46/2.18 5.46/2.18 S is empty. 5.46/2.18 Rewrite Strategy: FULL 5.46/2.18 ---------------------------------------- 5.46/2.18 5.46/2.18 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 5.46/2.18 Transformed a relative TRS into a decreasing-loop problem. 5.46/2.18 ---------------------------------------- 5.46/2.18 5.46/2.18 (2) 5.46/2.18 Obligation: 5.46/2.18 Analyzing the following TRS for decreasing loops: 5.46/2.18 5.46/2.18 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 5.46/2.18 5.46/2.18 5.46/2.18 The TRS R consists of the following rules: 5.46/2.18 5.46/2.18 U11(tt, N) -> activate(N) 5.46/2.18 U21(tt, M, N) -> s(plus(activate(N), activate(M))) 5.46/2.18 U31(tt) -> 0 5.46/2.18 U41(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 5.46/2.18 and(tt, X) -> activate(X) 5.46/2.18 isNat(n__0) -> tt 5.46/2.18 isNat(n__plus(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) 5.46/2.18 isNat(n__s(V1)) -> isNat(activate(V1)) 5.46/2.18 isNat(n__x(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) 5.46/2.18 plus(N, 0) -> U11(isNat(N), N) 5.46/2.18 plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) 5.46/2.18 x(N, 0) -> U31(isNat(N)) 5.46/2.18 x(N, s(M)) -> U41(and(isNat(M), n__isNat(N)), M, N) 5.46/2.18 0 -> n__0 5.46/2.18 plus(X1, X2) -> n__plus(X1, X2) 5.46/2.18 isNat(X) -> n__isNat(X) 5.46/2.18 s(X) -> n__s(X) 5.46/2.18 x(X1, X2) -> n__x(X1, X2) 5.46/2.18 activate(n__0) -> 0 5.46/2.18 activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2)) 5.46/2.18 activate(n__isNat(X)) -> isNat(X) 5.46/2.18 activate(n__s(X)) -> s(activate(X)) 5.46/2.18 activate(n__x(X1, X2)) -> x(activate(X1), activate(X2)) 5.46/2.18 activate(X) -> X 5.46/2.18 5.46/2.18 S is empty. 5.46/2.18 Rewrite Strategy: FULL 5.46/2.18 ---------------------------------------- 5.46/2.18
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