TRS Standard pair #615300446

details

property	value
status	complete
benchmark	PEANO_complete_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n157.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	2.35604596138 seconds
cpu usage	6.912356248
max memory	3.44428544E8

stage attributes

key	value
output-size	28120
starexec-result	"YES"

output

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


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


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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished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) QTRSToCSRProof [EQUIVALENT, 0 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 87 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 6 ms]
(6) CSR
(7) CSRRRRProof [EQUIVALENT, 7 ms]
(8) CSR
(9) CSRRRRProof [EQUIVALENT, 10 ms]
(10) CSR
(11) CSRRRRProof [EQUIVALENT, 0 ms]
(12) CSR
(13) CSRRRRProof [EQUIVALENT, 7 ms]
(14) CSR
(15) CSRRRRProof [EQUIVALENT, 0 ms]
(16) CSR
(17) CSRRRRProof [EQUIVALENT, 9 ms]
(18) CSR
(19) CSRRRRProof [EQUIVALENT, 0 ms]
(20) CSR
(21) CSRRRRProof [EQUIVALENT, 0 ms]
(22) CSR
(23) RisEmptyProof [EQUIVALENT, 0 ms]
(24) YES


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

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

   active(U11(tt, V1, V2)) -> mark(U12(isNat(V1), V2))
   active(U12(tt, V2)) -> mark(U13(isNat(V2)))
   active(U13(tt)) -> mark(tt)
   active(U21(tt, V1)) -> mark(U22(isNat(V1)))
   active(U22(tt)) -> mark(tt)
   active(U31(tt, N)) -> mark(N)
   active(U41(tt, M, N)) -> mark(s(plus(N, M)))
   active(and(tt, X)) -> mark(X)
   active(isNat(0)) -> mark(tt)
   active(isNat(plus(V1, V2))) -> mark(U11(and(isNatKind(V1), isNatKind(V2)), V1, V2))
   active(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1))
   active(isNatKind(0)) -> mark(tt)
   active(isNatKind(plus(V1, V2))) -> mark(and(isNatKind(V1), isNatKind(V2)))
   active(isNatKind(s(V1))) -> mark(isNatKind(V1))
   active(plus(N, 0)) -> mark(U31(and(isNat(N), isNatKind(N)), N))
   active(plus(N, s(M))) -> mark(U41(and(and(isNat(M), isNatKind(M)), and(isNat(N), isNatKind(N))), M, N))
   active(U11(X1, X2, X3)) -> U11(active(X1), X2, X3)
   active(U12(X1, X2)) -> U12(active(X1), X2)
   active(U13(X)) -> U13(active(X))
   active(U21(X1, X2)) -> U21(active(X1), X2)
   active(U22(X)) -> U22(active(X))
   active(U31(X1, X2)) -> U31(active(X1), X2)
   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
   active(s(X)) -> s(active(X))
   active(plus(X1, X2)) -> plus(active(X1), X2)
   active(plus(X1, X2)) -> plus(X1, active(X2))
   active(and(X1, X2)) -> and(active(X1), X2)
   U11(mark(X1), X2, X3) -> mark(U11(X1, X2, X3))
   U12(mark(X1), X2) -> mark(U12(X1, X2))
   U13(mark(X)) -> mark(U13(X))
   U21(mark(X1), X2) -> mark(U21(X1, X2))
   U22(mark(X)) -> mark(U22(X))
   U31(mark(X1), X2) -> mark(U31(X1, X2))
   U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
   s(mark(X)) -> mark(s(X))
   plus(mark(X1), X2) -> mark(plus(X1, X2))
   plus(X1, mark(X2)) -> mark(plus(X1, X2))
   and(mark(X1), X2) -> mark(and(X1, X2))
   proper(U11(X1, X2, X3)) -> U11(proper(X1), proper(X2), proper(X3))
   proper(tt) -> ok(tt)
   proper(U12(X1, X2)) -> U12(proper(X1), proper(X2))
   proper(isNat(X)) -> isNat(proper(X))
   proper(U13(X)) -> U13(proper(X))
   proper(U21(X1, X2)) -> U21(proper(X1), proper(X2))
   proper(U22(X)) -> U22(proper(X))
   proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
   proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3))
   proper(s(X)) -> s(proper(X))
   proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
   proper(and(X1, X2)) -> and(proper(X1), proper(X2))
   proper(0) -> ok(0)
   proper(isNatKind(X)) -> isNatKind(proper(X))
   U11(ok(X1), ok(X2), ok(X3)) -> ok(U11(X1, X2, X3))

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job log

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actions all output return to TRS Standard