TRS Inner 89993 pair #381733757

details

property	value
status	complete
benchmark	PEANO_nokinds_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n006.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.83550715446 seconds
cpu usage	4.407903362
max memory	2.60046848E8

stage attributes

key	value
output-size	17467
starexec-result	YES

output

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


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) QTRSToCSRProof [SOUND, 0 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 48 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 0 ms]
(6) CSR
(7) CSRRRRProof [EQUIVALENT, 8 ms]
(8) CSR
(9) CSRRRRProof [EQUIVALENT, 0 ms]
(10) CSR
(11) CSRRRRProof [EQUIVALENT, 0 ms]
(12) CSR
(13) CSRRRRProof [EQUIVALENT, 7 ms]
(14) CSR
(15) RisEmptyProof [EQUIVALENT, 0 ms]
(16) YES


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

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

   active(U11(tt, V2)) -> mark(U12(isNat(V2)))
   active(U12(tt)) -> mark(tt)
   active(U21(tt)) -> mark(tt)
   active(U31(tt, N)) -> mark(N)
   active(U41(tt, M, N)) -> mark(U42(isNat(N), M, N))
   active(U42(tt, M, N)) -> mark(s(plus(N, M)))
   active(isNat(0)) -> mark(tt)
   active(isNat(plus(V1, V2))) -> mark(U11(isNat(V1), V2))
   active(isNat(s(V1))) -> mark(U21(isNat(V1)))
   active(plus(N, 0)) -> mark(U31(isNat(N), N))
   active(plus(N, s(M))) -> mark(U41(isNat(M), M, N))
   active(U11(X1, X2)) -> U11(active(X1), X2)
   active(U12(X)) -> U12(active(X))
   active(U21(X)) -> U21(active(X))
   active(U31(X1, X2)) -> U31(active(X1), X2)
   active(U41(X1, X2, X3)) -> U41(active(X1), X2, X3)
   active(U42(X1, X2, X3)) -> U42(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))
   U11(mark(X1), X2) -> mark(U11(X1, X2))
   U12(mark(X)) -> mark(U12(X))
   U21(mark(X)) -> mark(U21(X))
   U31(mark(X1), X2) -> mark(U31(X1, X2))
   U41(mark(X1), X2, X3) -> mark(U41(X1, X2, X3))
   U42(mark(X1), X2, X3) -> mark(U42(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))
   proper(U11(X1, X2)) -> U11(proper(X1), proper(X2))
   proper(tt) -> ok(tt)
   proper(U12(X)) -> U12(proper(X))
   proper(isNat(X)) -> isNat(proper(X))
   proper(U21(X)) -> U21(proper(X))
   proper(U31(X1, X2)) -> U31(proper(X1), proper(X2))
   proper(U41(X1, X2, X3)) -> U41(proper(X1), proper(X2), proper(X3))
   proper(U42(X1, X2, X3)) -> U42(proper(X1), proper(X2), proper(X3))
   proper(s(X)) -> s(proper(X))
   proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
   proper(0) -> ok(0)
   U11(ok(X1), ok(X2)) -> ok(U11(X1, X2))
   U12(ok(X)) -> ok(U12(X))
   isNat(ok(X)) -> ok(isNat(X))
   U21(ok(X)) -> ok(U21(X))
   U31(ok(X1), ok(X2)) -> ok(U31(X1, X2))
   U41(ok(X1), ok(X2), ok(X3)) -> ok(U41(X1, X2, X3))
   U42(ok(X1), ok(X2), ok(X3)) -> ok(U42(X1, X2, X3))
   s(ok(X)) -> ok(s(X))
   plus(ok(X1), ok(X2)) -> ok(plus(X1, X2))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

The set Q consists of the following terms:

   active(isNat(0))
   active(isNat(plus(x0, x1)))
   active(isNat(s(x0)))
   active(U11(x0, x1))
   active(U12(x0))
   active(U21(x0))
   active(U31(x0, x1))

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