TRS Innermost pair #487524319

details

property	value
status	complete
benchmark	MYNAT_nosorts_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n082.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.01447415352 seconds
cpu usage	3.779489584
max memory	2.29879808E8

stage attributes

key	value
output-size	10653
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) QTRSToCSRProof [SOUND, 0 ms]
(2) CSR
(3) CSRInnermostProof [EQUIVALENT, 0 ms]
(4) CSR
(5) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(6) QCSDP
(7) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QCSDP
        (10) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (11) QCSDP
        (12) PIsEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QCSDP
        (15) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (16) QCSDP
        (17) PIsEmptyProof [EQUIVALENT, 0 ms]
        (18) YES


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

   active(and(tt, X)) -> mark(X)
   active(plus(N, 0)) -> mark(N)
   active(plus(N, s(M))) -> mark(s(plus(N, M)))
   active(x(N, 0)) -> mark(0)
   active(x(N, s(M))) -> mark(plus(x(N, M), N))
   active(and(X1, X2)) -> and(active(X1), X2)
   active(plus(X1, X2)) -> plus(active(X1), X2)
   active(plus(X1, X2)) -> plus(X1, active(X2))
   active(s(X)) -> s(active(X))
   active(x(X1, X2)) -> x(active(X1), X2)
   active(x(X1, X2)) -> x(X1, active(X2))
   and(mark(X1), X2) -> mark(and(X1, X2))
   plus(mark(X1), X2) -> mark(plus(X1, X2))
   plus(X1, mark(X2)) -> mark(plus(X1, X2))
   s(mark(X)) -> mark(s(X))
   x(mark(X1), X2) -> mark(x(X1, X2))
   x(X1, mark(X2)) -> mark(x(X1, X2))
   proper(and(X1, X2)) -> and(proper(X1), proper(X2))
   proper(tt) -> ok(tt)
   proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
   proper(0) -> ok(0)
   proper(s(X)) -> s(proper(X))
   proper(x(X1, X2)) -> x(proper(X1), proper(X2))
   and(ok(X1), ok(X2)) -> ok(and(X1, X2))
   plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
   s(ok(X)) -> ok(s(X))
   x(ok(X1), ok(X2)) -> ok(x(X1, X2))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

The set Q consists of the following terms:

   active(and(x0, x1))
   active(plus(x0, x1))
   active(s(x0))
   active(x(x0, x1))
   and(mark(x0), x1)
   plus(mark(x0), x1)
   plus(x0, mark(x1))
   s(mark(x0))
   x(mark(x0), x1)
   x(x0, mark(x1))
   proper(and(x0, x1))
   proper(tt)
   proper(plus(x0, x1))
   proper(0)
   proper(s(x0))
   proper(x(x0, x1))
   and(ok(x0), ok(x1))
   plus(ok(x0), ok(x1))
   s(ok(x0))
   x(ok(x0), ok(x1))
   top(mark(x0))
   top(ok(x0))


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(1) QTRSToCSRProof (SOUND)

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