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Runtime Complexity: TRS pair #487110264
details
property
value
status
complete
benchmark
PEANO_complete_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
14.535 seconds
cpu usage
39.3948
user time
37.6479
system time
1.7469
max virtual memory
1.9210684E7
max residence set size
3987488.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 4 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsTAProof [FINISHED, 895 ms] (6) BOUNDS(1, n^1) (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 8 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 443 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 149 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 125 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 107 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 106 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 103 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 92 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 132 ms] (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 222 ms] (36) typed CpxTrs (37) RewriteLemmaProof [LOWER BOUND(ID), 150 ms] (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 169 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 92 ms] (42) typed CpxTrs (43) RewriteLemmaProof [LOWER BOUND(ID), 61 ms] (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 160 ms] (46) typed CpxTrs (47) RewriteLemmaProof [LOWER BOUND(ID), 116 ms] (48) typed CpxTrs (49) RewriteLemmaProof [LOWER BOUND(ID), 112 ms] (50) typed CpxTrs (51) RewriteLemmaProof [LOWER BOUND(ID), 45 ms] (52) typed CpxTrs (53) RewriteLemmaProof [LOWER BOUND(ID), 113 ms] (54) typed CpxTrs (55) RewriteLemmaProof [LOWER BOUND(ID), 219 ms] (56) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: active(U11(tt, V1, V2)) -> mark(U12(isNatKind(V1), V1, V2)) active(U12(tt, V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)) active(U13(tt, V1, V2)) -> mark(U14(isNatKind(V2), V1, V2)) active(U14(tt, V1, V2)) -> mark(U15(isNat(V1), V2)) active(U15(tt, V2)) -> mark(U16(isNat(V2))) active(U16(tt)) -> mark(tt) active(U21(tt, V1)) -> mark(U22(isNatKind(V1), V1)) active(U22(tt, V1)) -> mark(U23(isNat(V1))) active(U23(tt)) -> mark(tt) active(U31(tt, V2)) -> mark(U32(isNatKind(V2))) active(U32(tt)) -> mark(tt) active(U41(tt)) -> mark(tt) active(U51(tt, N)) -> mark(U52(isNatKind(N), N)) active(U52(tt, N)) -> mark(N) active(U61(tt, M, N)) -> mark(U62(isNatKind(M), M, N)) active(U62(tt, M, N)) -> mark(U63(isNat(N), M, N)) active(U63(tt, M, N)) -> mark(U64(isNatKind(N), M, N)) active(U64(tt, M, N)) -> mark(s(plus(N, M))) active(isNat(0)) -> mark(tt) active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)) active(isNatKind(0)) -> mark(tt) active(isNatKind(plus(V1, V2))) -> mark(U31(isNatKind(V1), V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N, 0)) -> mark(U51(isNat(N), N))
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