TRS Contextsensitive pair #487092615

details

property	value
status	complete
benchmark	csrdiv.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	Maude_06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.71514 seconds
cpu usage	14.9459
user time	14.1143
system time	0.831603
max virtual memory	3.710242E7
max residence set size	2139360.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Termination of the given CSR could be proven:

(0) CSR
(1) CSRInnermostProof [EQUIVALENT, 0 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 30 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QCSDP
        (8) QCSDPReductionPairProof [EQUIVALENT, 46 ms]
        (9) QCSDP
        (10) QCSDPInstantiationProcessor [EQUIVALENT, 2 ms]
        (11) QCSDP
        (12) QCSDPReductionPairProof [EQUIVALENT, 8 ms]
        (13) QCSDP
        (14) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
        (15) AND
            (16) QCSDP
                (17) QCSDPReductionPairProof [EQUIVALENT, 59 ms]
                (18) QCSDP
                (19) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
                (20) TRUE
            (21) QCSDP
                (22) QCSDPSubtermProof [EQUIVALENT, 0 ms]
                (23) QCSDP
                (24) PIsEmptyProof [EQUIVALENT, 0 ms]
                (25) YES
    (26) QCSDP
        (27) QCSDPReductionPairProof [EQUIVALENT, 7 ms]
        (28) QCSDP
        (29) PIsEmptyProof [EQUIVALENT, 0 ms]
        (30) YES
    (31) QCSDP
        (32) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (33) QCSDP
        (34) PIsEmptyProof [EQUIVALENT, 0 ms]
        (35) YES


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

(0)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   gt(0, Y) -> false
   gt(s(X), 0) -> true
   gt(s(X), s(Y)) -> gt(X, Y)
   p(0) -> 0
   p(s(X)) -> X
   if(true, X, Y) -> X
   if(false, X, Y) -> Y
   minus(X, Y) -> if(gt(Y, 0), minus(p(X), p(Y)), X)
   div(0, s(Y)) -> 0
   div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))

The replacement map contains the following entries:

gt: {1, 2}
0: empty set
false: empty set
s: {1}
true: empty set
p: {1}
if: {1}
minus: {1, 2}
div: {1, 2}

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

(1) CSRInnermostProof (EQUIVALENT)
The CSR is orthogonal. By [CS_Inn] we can switch to innermost.
----------------------------------------

(2)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   gt(0, Y) -> false
   gt(s(X), 0) -> true
   gt(s(X), s(Y)) -> gt(X, Y)
   p(0) -> 0
   p(s(X)) -> X
   if(true, X, Y) -> X
   if(false, X, Y) -> Y
   minus(X, Y) -> if(gt(Y, 0), minus(p(X), p(Y)), X)
   div(0, s(Y)) -> 0
   div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))

The replacement map contains the following entries:

gt: {1, 2}

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