TRS Standard pair #516964435

details

property	value
status	complete
benchmark	test10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	Strategy_removed_mixed_05

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	9.22324919701 seconds
cpu usage	15.918083688
max memory	6.18799104E8

stage attributes

key	value
output-size	9259
starexec-result	NO

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) QTRSRRRProof [EQUIVALENT, 70 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 4 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) TransformationProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) TransformationProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) MRRProof [EQUIVALENT, 4 ms]
        (20) QDP
        (21) TransformationProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) NonTerminationLoopProof [COMPLETE, 0 ms]
        (24) NO


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

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

   h(X, Z) -> f(X, s(X), Z)
   f(X, Y, g(X, Y)) -> h(0, g(X, Y))
   g(0, Y) -> 0
   g(X, s(Y)) -> g(X, Y)

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0) = 0
   POL(f(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(g(x_1, x_2)) = 2 + 2*x_1 + x_2
   POL(h(x_1, x_2)) = 2*x_1 + x_2
   POL(s(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   g(0, Y) -> 0




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

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   h(X, Z) -> f(X, s(X), Z)
   f(X, Y, g(X, Y)) -> h(0, g(X, Y))
   g(X, s(Y)) -> g(X, Y)

Q is empty.

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

(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   H(X, Z) -> F(X, s(X), Z)
   F(X, Y, g(X, Y)) -> H(0, g(X, Y))
   G(X, s(Y)) -> G(X, Y)

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