TRS Stand 20472 pair #381714898

details

property	value
status	complete
benchmark	Ex49_GM04_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n014.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.96017599106 seconds
cpu usage	11.559744813
max memory	7.38574336E8

stage attributes

key	value
output-size	48984
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) UsableRulesProof [EQUIVALENT, 0 ms]
        (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) UsableRulesProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) QDP
        (31) QDPOrderProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QDPOrderProof [EQUIVALENT, 17 ms]
        (34) QDP
        (35) QDPOrderProof [EQUIVALENT, 14 ms]
        (36) QDP
        (37) QDPOrderProof [EQUIVALENT, 21 ms]
        (38) QDP
        (39) QDPOrderProof [EQUIVALENT, 60 ms]
        (40) QDP
        (41) UsableRulesProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (44) QDP
        (45) DependencyGraphProof [EQUIVALENT, 0 ms]
        (46) TRUE


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

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

   active(minus(0, Y)) -> mark(0)
   active(minus(s(X), s(Y))) -> mark(minus(X, Y))
   active(geq(X, 0)) -> mark(true)
   active(geq(0, s(Y))) -> mark(false)
   active(geq(s(X), s(Y))) -> mark(geq(X, Y))
   active(div(0, s(Y))) -> mark(0)
   active(div(s(X), s(Y))) -> mark(if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0))
   active(if(true, X, Y)) -> mark(X)
   active(if(false, X, Y)) -> mark(Y)
   mark(minus(X1, X2)) -> active(minus(X1, X2))
   mark(0) -> active(0)
   mark(s(X)) -> active(s(mark(X)))
   mark(geq(X1, X2)) -> active(geq(X1, X2))
   mark(true) -> active(true)
   mark(false) -> active(false)
   mark(div(X1, X2)) -> active(div(mark(X1), X2))
   mark(if(X1, X2, X3)) -> active(if(mark(X1), X2, X3))
   minus(mark(X1), X2) -> minus(X1, X2)
   minus(X1, mark(X2)) -> minus(X1, X2)
   minus(active(X1), X2) -> minus(X1, X2)
   minus(X1, active(X2)) -> minus(X1, X2)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
   geq(mark(X1), X2) -> geq(X1, X2)
   geq(X1, mark(X2)) -> geq(X1, X2)
   geq(active(X1), X2) -> geq(X1, X2)
   geq(X1, active(X2)) -> geq(X1, X2)
   div(mark(X1), X2) -> div(X1, X2)
   div(X1, mark(X2)) -> div(X1, X2)
   div(active(X1), X2) -> div(X1, X2)
   div(X1, active(X2)) -> div(X1, X2)

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