TRS Standard pair #487069198

details

property	value
status	complete
benchmark	cade15.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n183.star.cs.uiowa.edu
space	GTSSK07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.71314 seconds
cpu usage	13.4692
user time	13.0534
system time	0.415799
max virtual memory	1.8822712E7
max residence set size	797404.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 4 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, 0 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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QReductionProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (34) YES
    (35) QDP
        (36) UsableRulesProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) QReductionProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) NonInfProof [EQUIVALENT, 95 ms]
        (41) QDP
        (42) DependencyGraphProof [EQUIVALENT, 0 ms]
        (43) TRUE


----------------------------------------

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

   sort(l) -> st(0, l)
   st(n, l) -> cond1(member(n, l), n, l)
   cond1(true, n, l) -> cons(n, st(s(n), l))
   cond1(false, n, l) -> cond2(gt(n, max(l)), n, l)
   cond2(true, n, l) -> nil
   cond2(false, n, l) -> st(s(n), l)
   member(n, nil) -> false
   member(n, cons(m, l)) -> or(equal(n, m), member(n, l))
   or(x, true) -> true
   or(x, false) -> x
   equal(0, 0) -> true
   equal(s(x), 0) -> false
   equal(0, s(y)) -> false
   equal(s(x), s(y)) -> equal(x, y)
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)
   max(nil) -> 0
   max(cons(u, l)) -> if(gt(u, max(l)), u, max(l))
   if(true, u, v) -> u
   if(false, u, v) -> v

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:

   sort(l) -> st(0, l)
   st(n, l) -> cond1(member(n, l), n, l)
   cond1(true, n, l) -> cons(n, st(s(n), l))
   cond1(false, n, l) -> cond2(gt(n, max(l)), n, l)
   cond2(true, n, l) -> nil

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