TRS Standard pair #487070963

details

property	value
status	complete
benchmark	Ex1_2_AEL03_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	48.6746 seconds
cpu usage	172.99
user time	169.585
system time	3.40445
max virtual memory	3.7379768E7
max residence set size	4025204.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) TransformationProof [EQUIVALENT, 17 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) QDP
(7) QDPOrderProof [EQUIVALENT, 288 ms]
(8) QDP
(9) QDPOrderProof [EQUIVALENT, 311 ms]
(10) QDP
(11) QDPOrderProof [EQUIVALENT, 375 ms]
(12) QDP
(13) QDPOrderProof [EQUIVALENT, 383 ms]
(14) QDP
(15) DependencyGraphProof [EQUIVALENT, 0 ms]
(16) QDP
(17) QDPOrderProof [EQUIVALENT, 346 ms]
(18) QDP
(19) DependencyGraphProof [EQUIVALENT, 0 ms]
(20) QDP
(21) QDPOrderProof [EQUIVALENT, 277 ms]
(22) QDP
(23) QDPOrderProof [EQUIVALENT, 260 ms]
(24) QDP
(25) DependencyGraphProof [EQUIVALENT, 0 ms]
(26) QDP
(27) QDPOrderProof [EQUIVALENT, 246 ms]
(28) QDP
(29) QDPOrderProof [EQUIVALENT, 336 ms]
(30) QDP
(31) QDPOrderProof [EQUIVALENT, 273 ms]
(32) QDP
(33) QDPOrderProof [EQUIVALENT, 280 ms]
(34) QDP
(35) QDPOrderProof [EQUIVALENT, 241 ms]
(36) QDP
(37) QDPOrderProof [EQUIVALENT, 312 ms]
(38) QDP
(39) QDPOrderProof [EQUIVALENT, 282 ms]
(40) QDP
(41) QDPOrderProof [EQUIVALENT, 369 ms]
(42) QDP
(43) DependencyGraphProof [EQUIVALENT, 0 ms]
(44) AND
    (45) QDP
        (46) QDPOrderProof [EQUIVALENT, 203 ms]
        (47) QDP
        (48) QDPOrderProof [EQUIVALENT, 201 ms]
        (49) QDP
        (50) QDPOrderProof [EQUIVALENT, 192 ms]
        (51) QDP
        (52) QDPOrderProof [EQUIVALENT, 74 ms]
        (53) QDP
        (54) QDPOrderProof [EQUIVALENT, 331 ms]
        (55) QDP
        (56) QDPOrderProof [EQUIVALENT, 226 ms]
        (57) QDP
        (58) PisEmptyProof [EQUIVALENT, 0 ms]
        (59) YES
    (60) QDP
        (61) QDPOrderProof [EQUIVALENT, 260 ms]
        (62) QDP
        (63) PisEmptyProof [EQUIVALENT, 0 ms]
        (64) YES


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

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

   a__from(X) -> cons(mark(X), from(s(X)))
   a__2ndspos(0, Z) -> rnil
   a__2ndspos(s(N), cons(X, cons(Y, Z))) -> rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
   a__2ndsneg(0, Z) -> rnil
   a__2ndsneg(s(N), cons(X, cons(Y, Z))) -> rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
   a__pi(X) -> a__2ndspos(mark(X), a__from(0))
   a__plus(0, Y) -> mark(Y)
   a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
   a__times(0, Y) -> 0
   a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
   a__square(X) -> a__times(mark(X), mark(X))
   mark(from(X)) -> a__from(mark(X))
   mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
   mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
   mark(pi(X)) -> a__pi(mark(X))
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
   mark(square(X)) -> a__square(mark(X))
   mark(0) -> 0

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