TRS Standard pair #615306221

details

property	value
status	complete
benchmark	14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n015.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	3.18727302551 seconds
cpu usage	9.970800852
max memory	5.92101376E8

stage attributes

key	value
output-size	34491
starexec-result	"YES"

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


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

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 247 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 80 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 117 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 25 ms]
(8) QTRS
(9) QTRSRRRProof [EQUIVALENT, 20 ms]
(10) QTRS
(11) QTRSRRRProof [EQUIVALENT, 32 ms]
(12) QTRS
(13) QTRSRRRProof [EQUIVALENT, 19 ms]
(14) QTRS
(15) DependencyPairsProof [EQUIVALENT, 0 ms]
(16) QDP
(17) DependencyGraphProof [EQUIVALENT, 0 ms]
(18) AND
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) UsableRulesProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (28) YES
    (29) QDP
        (30) UsableRulesProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) MRRProof [EQUIVALENT, 0 ms]
        (33) QDP
        (34) MNOCProof [EQUIVALENT, 4 ms]
        (35) QDP
        (36) MRRProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) PisEmptyProof [EQUIVALENT, 0 ms]
        (39) YES
    (40) QDP
        (41) UsableRulesProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) MRRProof [EQUIVALENT, 12 ms]
        (44) QDP
        (45) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (46) YES
    (47) QDP
        (48) UsableRulesProof [EQUIVALENT, 0 ms]
        (49) QDP
        (50) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (51) YES


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

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

   O(0) -> 0
   +(0, x) -> x
   +(x, 0) -> x
   +(O(x), O(y)) -> O(+(x, y))
   +(O(x), I(y)) -> I(+(x, y))
   +(I(x), O(y)) -> I(+(x, y))
   +(I(x), I(y)) -> O(+(+(x, y), I(0)))
   +(x, +(y, z)) -> +(+(x, y), z)
   -(x, 0) -> x
   -(0, x) -> 0
   -(O(x), O(y)) -> O(-(x, y))
   -(O(x), I(y)) -> I(-(-(x, y), I(1)))
   -(I(x), O(y)) -> I(-(x, y))
   -(I(x), I(y)) -> O(-(x, y))
   not(true) -> false
   not(false) -> true
   and(x, true) -> x
   and(x, false) -> false
   if(true, x, y) -> x
   if(false, x, y) -> y
   ge(O(x), O(y)) -> ge(x, y)
   ge(O(x), I(y)) -> not(ge(y, x))
   ge(I(x), O(y)) -> ge(x, y)
   ge(I(x), I(y)) -> ge(x, y)
   ge(x, 0) -> true
   ge(0, O(x)) -> ge(0, x)

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