TRS Standard pair #487072743

details

property	value
status	complete
benchmark	sumList.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.66493 seconds
cpu usage	16.6277
user time	16.0201
system time	0.607603
max virtual memory	1.8543288E7
max residence set size	449380.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1 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, 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) TransformationProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) UsableRulesProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) QReductionProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) TransformationProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) TransformationProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) TransformationProof [EQUIVALENT, 0 ms]
        (39) QDP
        (40) UsableRulesProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) QReductionProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) TransformationProof [EQUIVALENT, 0 ms]
        (45) QDP
        (46) UsableRulesProof [EQUIVALENT, 0 ms]
        (47) QDP
        (48) QReductionProof [EQUIVALENT, 0 ms]
        (49) QDP
        (50) TransformationProof [EQUIVALENT, 0 ms]
        (51) QDP
        (52) UsableRulesProof [EQUIVALENT, 0 ms]
        (53) QDP
        (54) QReductionProof [EQUIVALENT, 0 ms]
        (55) QDP
        (56) TransformationProof [EQUIVALENT, 0 ms]
        (57) QDP
        (58) UsableRulesProof [EQUIVALENT, 0 ms]
        (59) QDP
        (60) TransformationProof [EQUIVALENT, 0 ms]
        (61) QDP
        (62) QDPOrderProof [EQUIVALENT, 11 ms]
        (63) QDP
        (64) DependencyGraphProof [EQUIVALENT, 0 ms]
        (65) QDP
        (66) QDPOrderProof [EQUIVALENT, 5 ms]
        (67) QDP
        (68) DependencyGraphProof [EQUIVALENT, 0 ms]
        (69) TRUE


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

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

   isEmpty(cons(x, xs)) -> false
   isEmpty(nil) -> true
   isZero(0) -> true
   isZero(s(x)) -> false
   head(cons(x, xs)) -> x
   tail(cons(x, xs)) -> xs
   tail(nil) -> nil
   p(s(s(x))) -> s(p(s(x)))
   p(s(0)) -> 0
   p(0) -> 0
   inc(s(x)) -> s(inc(x))
   inc(0) -> s(0)
   sumList(xs, y) -> if(isEmpty(xs), isZero(head(xs)), y, tail(xs), cons(p(head(xs)), tail(xs)), inc(y))
   if(true, b, y, xs, ys, x) -> y

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