TRS Standard pair #487066658

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	n185.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.00622 seconds
cpu usage	8.5806
user time	8.1277
system time	0.452902
max virtual memory	1.8677444E7
max residence set size	670840.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 187 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 100 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 55 ms]
(6) QTRS
(7) QTRSRRRProof [EQUIVALENT, 8 ms]
(8) QTRS
(9) QTRSRRRProof [EQUIVALENT, 3 ms]
(10) QTRS
(11) QTRSRRRProof [EQUIVALENT, 15 ms]
(12) QTRS
(13) QTRSRRRProof [EQUIVALENT, 29 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, 7 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, 0 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)
   ge(0, I(x)) -> false
   Log'(0) -> 0
   Log'(I(x)) -> +(Log'(x), I(0))
   Log'(O(x)) -> if(ge(x, I(0)), +(Log'(x), I(0)), 0)
   Log(x) -> -(Log'(x), I(0))
   Val(L(x)) -> x

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