TRS Innermost pair #487524659

details

property	value
status	complete
benchmark	wiehe14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n113.star.cs.uiowa.edu
space	Mixed_innermost

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.64272999763 seconds
cpu usage	6.748884542
max memory	4.6985216E8

stage attributes

key	value
output-size	38504
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 33 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QReductionProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QReductionProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) TransformationProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) TransformationProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QReductionProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) TransformationProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) TransformationProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) TransformationProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QReductionProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QDPOrderProof [EQUIVALENT, 5 ms]
        (36) QDP
        (37) QDPOrderProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) PisEmptyProof [EQUIVALENT, 0 ms]
        (40) YES
    (41) QDP
        (42) UsableRulesProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) QReductionProof [EQUIVALENT, 0 ms]
        (45) QDP
        (46) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (47) YES
    (48) QDP
        (49) UsableRulesProof [EQUIVALENT, 0 ms]
        (50) QDP
        (51) QReductionProof [EQUIVALENT, 0 ms]
        (52) QDP
        (53) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (54) YES
    (55) QDP
        (56) UsableRulesProof [EQUIVALENT, 0 ms]
        (57) QDP
        (58) QReductionProof [EQUIVALENT, 0 ms]
        (59) QDP
        (60) QDPOrderProof [EQUIVALENT, 74 ms]
        (61) QDP
        (62) QDPOrderProof [EQUIVALENT, 23 ms]
        (63) QDP
        (64) PisEmptyProof [EQUIVALENT, 0 ms]
        (65) YES


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

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

   even(0) -> true
   even(s(0)) -> false
   even(s(s(x))) -> even(x)
   half(0) -> 0
   half(s(s(x))) -> s(half(x))
   plus(s(x), s(y)) -> s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
   plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
   plus(zero, y) -> y
   plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y))))
   id(x) -> x
   if(true, x, y) -> x
   if(false, x, y) -> y

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