TRS Standard pair #487070968

details

property	value
status	complete
benchmark	ExIntrod_Zan97_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n189.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.20423 seconds
cpu usage	5.24457
user time	5.02023
system time	0.224341
max virtual memory	1.8477524E7
max residence set size	379656.0

stage attributes

key	value
starexec-result	NO

output

NO
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 disproven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) UsableRulesProof [EQUIVALENT, 0 ms]
        (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) MNOCProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) TransformationProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) TransformationProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QReductionProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) NonTerminationLoopProof [COMPLETE, 0 ms]
        (29) NO


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

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

   fact(X) -> if(zero(X), n__s(0), n__prod(X, fact(p(X))))
   add(0, X) -> X
   add(s(X), Y) -> s(add(X, Y))
   prod(0, X) -> 0
   prod(s(X), Y) -> add(Y, prod(X, Y))
   if(true, X, Y) -> activate(X)
   if(false, X, Y) -> activate(Y)
   zero(0) -> true
   zero(s(X)) -> false
   p(s(X)) -> X
   s(X) -> n__s(X)
   prod(X1, X2) -> n__prod(X1, X2)
   activate(n__s(X)) -> s(X)
   activate(n__prod(X1, X2)) -> prod(X1, X2)
   activate(X) -> X

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   FACT(X) -> IF(zero(X), n__s(0), n__prod(X, fact(p(X))))
   FACT(X) -> ZERO(X)
   FACT(X) -> FACT(p(X))
   FACT(X) -> P(X)
   ADD(s(X), Y) -> S(add(X, Y))
   ADD(s(X), Y) -> ADD(X, Y)
   PROD(s(X), Y) -> ADD(Y, prod(X, Y))
   PROD(s(X), Y) -> PROD(X, Y)
   IF(true, X, Y) -> ACTIVATE(X)
   IF(false, X, Y) -> ACTIVATE(Y)
   ACTIVATE(n__s(X)) -> S(X)
   ACTIVATE(n__prod(X1, X2)) -> PROD(X1, X2)

The TRS R consists of the following rules:

   fact(X) -> if(zero(X), n__s(0), n__prod(X, fact(p(X))))
   add(0, X) -> X
   add(s(X), Y) -> s(add(X, Y))
   prod(0, X) -> 0
   prod(s(X), Y) -> add(Y, prod(X, Y))
   if(true, X, Y) -> activate(X)
   if(false, X, Y) -> activate(Y)
   zero(0) -> true
   zero(s(X)) -> false
   p(s(X)) -> X

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