TRS Standard pair #487072068

details

property	value
status	complete
benchmark	Ex2_Luc03b.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n174.star.cs.uiowa.edu
space	Strategy_removed_CSR_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.33804 seconds
cpu usage	5.1372
user time	4.89679
system time	0.240415
max virtual memory	1.8544088E7
max residence set size	385900.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 1 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) TransformationProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) TransformationProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) NonTerminationLoopProof [COMPLETE, 0 ms]
        (31) NO
    (32) QDP
        (33) UsableRulesProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QReductionProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (38) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   fst(0, Z) -> nil
   fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z))
   from(X) -> cons(X, from(s(X)))
   add(0, X) -> X
   add(s(X), Y) -> s(add(X, Y))
   len(nil) -> 0
   len(cons(X, Z)) -> s(len(Z))

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:

   fst(0, Z) -> nil
   fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z))
   from(X) -> cons(X, from(s(X)))
   add(0, X) -> X
   add(s(X), Y) -> s(add(X, Y))
   len(nil) -> 0
   len(cons(X, Z)) -> s(len(Z))

The set Q consists of the following terms:

   fst(0, x0)
   fst(s(x0), cons(x1, x2))
   from(x0)
   add(0, x0)
   add(s(x0), x1)
   len(nil)
   len(cons(x0, x1))


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(3) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
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