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TRS Contextsensitive pair #487092573
details
property
value
status
complete
benchmark
Ex7_BLR02.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.55683 seconds
cpu usage
3.67396
user time
3.5042
system time
0.169758
max virtual memory
1.8343376E7
max residence set size
215644.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRInnermostProof [EQUIVALENT, 0 ms] (2) CSR (3) CSDependencyPairsProof [EQUIVALENT, 0 ms] (4) QCSDP (5) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QCSDP (8) QCSDPSubtermProof [EQUIVALENT, 14 ms] (9) QCSDP (10) PIsEmptyProof [EQUIVALENT, 0 ms] (11) YES (12) QCSDP (13) QCSDPSubtermProof [EQUIVALENT, 0 ms] (14) QCSDP (15) PIsEmptyProof [EQUIVALENT, 0 ms] (16) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: from(X) -> cons(X, from(s(X))) head(cons(X, XS)) -> X 2nd(cons(X, XS)) -> head(XS) take(0, XS) -> nil take(s(N), cons(X, XS)) -> cons(X, take(N, XS)) sel(0, cons(X, XS)) -> X sel(s(N), cons(X, XS)) -> sel(N, XS) The replacement map contains the following entries: from: {1} cons: {1} s: {1} head: {1} 2nd: {1} take: {1, 2} 0: empty set nil: empty set sel: {1, 2} ---------------------------------------- (1) CSRInnermostProof (EQUIVALENT) The CSR is orthogonal. By [CS_Inn] we can switch to innermost. ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: from(X) -> cons(X, from(s(X))) head(cons(X, XS)) -> X 2nd(cons(X, XS)) -> head(XS) take(0, XS) -> nil take(s(N), cons(X, XS)) -> cons(X, take(N, XS)) sel(0, cons(X, XS)) -> X sel(s(N), cons(X, XS)) -> sel(N, XS) The replacement map contains the following entries: from: {1} cons: {1} s: {1} head: {1} 2nd: {1} take: {1, 2} 0: empty set nil: empty set sel: {1, 2} Innermost Strategy. ---------------------------------------- (3) CSDependencyPairsProof (EQUIVALENT) Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem. ---------------------------------------- (4) Obligation: Q-restricted context-sensitive dependency pair problem: The symbols in {from_1, s_1, head_1, 2nd_1, take_2, sel_2, HEAD_1, 2ND_1, SEL_2, FROM_1, TAKE_2} are replacing on all positions. For all symbols f in {cons_2} we have mu(f) = {1}. The symbols in {U_1} are not replacing on any position.
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