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TRS Standard pair #487072063
details
property
value
status
complete
benchmark
ExIntrod_GM99.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.34526 seconds
cpu usage
6.07383
user time
5.79423
system time
0.279601
max virtual memory
1.8675168E7
max residence set size
418948.0
stage attributes
key
value
starexec-result
NO
output
NO proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 2 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPOrderProof [EQUIVALENT, 39 ms] (13) QDP (14) PisEmptyProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) TransformationProof [EQUIVALENT, 0 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) NonTerminationLoopProof [COMPLETE, 0 ms] (26) NO ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: primes -> sieve(from(s(s(0)))) from(X) -> cons(X, from(s(X))) head(cons(X, Y)) -> X tail(cons(X, Y)) -> Y if(true, X, Y) -> X if(false, X, Y) -> Y filter(s(s(X)), cons(Y, Z)) -> if(divides(s(s(X)), Y), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))) sieve(cons(X, Y)) -> cons(X, filter(X, sieve(Y))) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: primes -> sieve(from(s(s(0)))) from(X) -> cons(X, from(s(X))) head(cons(X, Y)) -> X tail(cons(X, Y)) -> Y if(true, X, Y) -> X if(false, X, Y) -> Y filter(s(s(X)), cons(Y, Z)) -> if(divides(s(s(X)), Y), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))) sieve(cons(X, Y)) -> cons(X, filter(X, sieve(Y))) The set Q consists of the following terms: primes from(x0) head(cons(x0, x1)) tail(cons(x0, x1)) if(true, x0, x1) if(false, x0, x1) filter(s(s(x0)), cons(x1, x2)) sieve(cons(x0, x1)) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: PRIMES -> SIEVE(from(s(s(0)))) PRIMES -> FROM(s(s(0))) FROM(X) -> FROM(s(X))
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