TRS Standard pair #615303421

details

property	value
status	complete
benchmark	otto13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n052.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	9.99460291862 seconds
cpu usage	21.218134821
max memory	1.252773888E9

stage attributes

key	value
output-size	39449
starexec-result	"YES"

output

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


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YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished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) AAECC Innermost [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QReductionProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) NonInfProof [EQUIVALENT, 88 ms]
        (34) QDP
        (35) NonInfProof [EQUIVALENT, 22 ms]
        (36) QDP
        (37) PisEmptyProof [EQUIVALENT, 0 ms]
        (38) YES


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

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

   le(0, y, z) -> greater(y, z)
   le(s(x), 0, z) -> false
   le(s(x), s(y), 0) -> false
   le(s(x), s(y), s(z)) -> le(x, y, z)
   greater(x, 0) -> first
   greater(0, s(y)) -> second
   greater(s(x), s(y)) -> greater(x, y)
   double(0) -> 0
   double(s(x)) -> s(s(double(x)))
   triple(x) -> if(le(x, x, double(x)), x, 0, 0)
   if(false, x, y, z) -> true
   if(first, x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
   if(second, x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z)

Q is empty.

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(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   double(0) -> 0
   double(s(x)) -> s(s(double(x)))
   le(0, y, z) -> greater(y, z)
   le(s(x), 0, z) -> false
   le(s(x), s(y), 0) -> false
   le(s(x), s(y), s(z)) -> le(x, y, z)
   greater(x, 0) -> first
   greater(0, s(y)) -> second
   greater(s(x), s(y)) -> greater(x, y)

The TRS R 2 is 
   triple(x) -> if(le(x, x, double(x)), x, 0, 0)
   if(false, x, y, z) -> true
   if(first, x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
   if(second, x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z)

The signature Sigma is {triple_1, if_4, true}
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