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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308200
details
property
value
status
complete
benchmark
MYNAT_complete-noand_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
3.56056 seconds
cpu usage
10.7105
user time
10.2193
system time
0.491138
max virtual memory
1.8279384E7
max residence set size
1516576.0
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
10.33/3.48 WORST_CASE(NON_POLY, ?) 10.33/3.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 10.33/3.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.33/3.49 10.33/3.49 10.33/3.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.33/3.49 10.33/3.49 (0) CpxTRS 10.33/3.49 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 10.33/3.49 (2) TRS for Loop Detection 10.33/3.49 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 10.33/3.49 (4) BEST 10.33/3.49 (5) proven lower bound 10.33/3.49 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 10.33/3.49 (7) BOUNDS(n^1, INF) 10.33/3.49 (8) TRS for Loop Detection 10.33/3.49 (9) DecreasingLoopProof [FINISHED, 1279 ms] 10.33/3.49 (10) BOUNDS(EXP, INF) 10.33/3.49 10.33/3.49 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (0) 10.33/3.49 Obligation: 10.33/3.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.33/3.49 10.33/3.49 10.33/3.49 The TRS R consists of the following rules: 10.33/3.49 10.33/3.49 U101(tt, M, N) -> U102(isNatKind(activate(M)), activate(M), activate(N)) 10.33/3.49 U102(tt, M, N) -> U103(isNat(activate(N)), activate(M), activate(N)) 10.33/3.49 U103(tt, M, N) -> U104(isNatKind(activate(N)), activate(M), activate(N)) 10.33/3.49 U104(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 10.33/3.49 U11(tt, V1, V2) -> U12(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 U12(tt, V1, V2) -> U13(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U13(tt, V1, V2) -> U14(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U14(tt, V1, V2) -> U15(isNat(activate(V1)), activate(V2)) 10.33/3.49 U15(tt, V2) -> U16(isNat(activate(V2))) 10.33/3.49 U16(tt) -> tt 10.33/3.49 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 10.33/3.49 U22(tt, V1) -> U23(isNat(activate(V1))) 10.33/3.49 U23(tt) -> tt 10.33/3.49 U31(tt, V1, V2) -> U32(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 U32(tt, V1, V2) -> U33(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U33(tt, V1, V2) -> U34(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U34(tt, V1, V2) -> U35(isNat(activate(V1)), activate(V2)) 10.33/3.49 U35(tt, V2) -> U36(isNat(activate(V2))) 10.33/3.49 U36(tt) -> tt 10.33/3.49 U41(tt, V2) -> U42(isNatKind(activate(V2))) 10.33/3.49 U42(tt) -> tt 10.33/3.49 U51(tt) -> tt 10.33/3.49 U61(tt, V2) -> U62(isNatKind(activate(V2))) 10.33/3.49 U62(tt) -> tt 10.33/3.49 U71(tt, N) -> U72(isNatKind(activate(N)), activate(N)) 10.33/3.49 U72(tt, N) -> activate(N) 10.33/3.49 U81(tt, M, N) -> U82(isNatKind(activate(M)), activate(M), activate(N)) 10.33/3.49 U82(tt, M, N) -> U83(isNat(activate(N)), activate(M), activate(N)) 10.33/3.49 U83(tt, M, N) -> U84(isNatKind(activate(N)), activate(M), activate(N)) 10.33/3.49 U84(tt, M, N) -> s(plus(activate(N), activate(M))) 10.33/3.49 U91(tt, N) -> U92(isNatKind(activate(N))) 10.33/3.49 U92(tt) -> 0 10.33/3.49 isNat(n__0) -> tt 10.33/3.49 isNat(n__plus(V1, V2)) -> U11(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 10.33/3.49 isNat(n__x(V1, V2)) -> U31(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 isNatKind(n__0) -> tt 10.33/3.49 isNatKind(n__plus(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V2)) 10.33/3.49 isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1))) 10.33/3.49 isNatKind(n__x(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)) 10.33/3.49 plus(N, 0) -> U71(isNat(N), N) 10.33/3.49 plus(N, s(M)) -> U81(isNat(M), M, N) 10.33/3.49 x(N, 0) -> U91(isNat(N), N) 10.33/3.49 x(N, s(M)) -> U101(isNat(M), M, N) 10.33/3.49 0 -> n__0 10.33/3.49 plus(X1, X2) -> n__plus(X1, X2) 10.33/3.49 s(X) -> n__s(X) 10.33/3.49 x(X1, X2) -> n__x(X1, X2) 10.33/3.49 activate(n__0) -> 0 10.33/3.49 activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2)) 10.33/3.49 activate(n__s(X)) -> s(activate(X)) 10.33/3.49 activate(n__x(X1, X2)) -> x(activate(X1), activate(X2)) 10.33/3.49 activate(X) -> X 10.33/3.49 10.33/3.49 S is empty. 10.33/3.49 Rewrite Strategy: FULL 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 10.33/3.49 Transformed a relative TRS into a decreasing-loop problem. 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (2) 10.33/3.49 Obligation: 10.33/3.49 Analyzing the following TRS for decreasing loops: 10.33/3.49 10.33/3.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.33/3.49 10.33/3.49 10.33/3.49 The TRS R consists of the following rules: 10.33/3.49
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