details

property	value
status	complete
benchmark	Applicative_first_order_05__#3.22.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Uncurried_Applicative_11

run statistics

property	value
solver	Wanda 2.2a
configuration	default
runtime (wallclock)	0.339766 seconds
cpu usage	0.32695
user time	0.267742
system time	0.059208
max virtual memory	113188.0
max residence set size	10264.0

stage attributes

key	value
starexec-result	YES

output

YES We consider the system theBenchmark. Alphabet: 0 : [] --> a cons : [c * d] --> d false : [] --> b filter : [c -> b * d] --> d filter2 : [b * c -> b * c * d] --> d map : [c -> c * d] --> d nil : [] --> d plus : [a * a] --> a s : [a] --> a times : [a * a] --> a true : [] --> b Rules: times(x, plus(y, s(z))) => plus(times(x, plus(y, times(s(z), 0))), times(x, s(z))) times(x, 0) => 0 times(x, s(y)) => plus(times(x, y), x) plus(x, 0) => x plus(x, s(y)) => s(plus(x, y)) map(f, nil) => nil map(f, cons(x, y)) => cons(f x, map(f, y)) filter(f, nil) => nil filter(f, cons(x, y)) => filter2(f x, f, x, y) filter2(true, f, x, y) => cons(x, filter(f, y)) filter2(false, f, x, y) => filter(f, y) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We observe that the rules contain a first-order subset: times(X, plus(Y, s(Z))) => plus(times(X, plus(Y, times(s(Z), 0))), times(X, s(Z))) times(X, 0) => 0 times(X, s(Y)) => plus(times(X, Y), X) plus(X, 0) => X plus(X, s(Y)) => s(plus(X, Y)) Moreover, the system is finitely branching. Thus, by [Kop12, Thm. 7.55], we may omit all first-order dependency pairs from the dependency pair problem (DP(R), R) if this first-order part is Ce-terminating when seen as a many-sorted first-order TRS. According to the external first-order termination prover, this system is indeed Ce-terminating: || Input TRS: || 1: times(PeRCenTX,plus(PeRCenTY,s(PeRCenTZ))) -> plus(times(PeRCenTX,plus(PeRCenTY,times(s(PeRCenTZ),0()))),times(PeRCenTX,s(PeRCenTZ))) || 2: times(PeRCenTX,0()) -> 0() || 3: times(PeRCenTX,s(PeRCenTY)) -> plus(times(PeRCenTX,PeRCenTY),PeRCenTX) || 4: plus(PeRCenTX,0()) -> PeRCenTX || 5: plus(PeRCenTX,s(PeRCenTY)) -> s(plus(PeRCenTX,PeRCenTY)) || 6: TIlDePAIR(PeRCenTX,PeRCenTY) -> PeRCenTX || 7: TIlDePAIR(PeRCenTX,PeRCenTY) -> PeRCenTY || Number of strict rules: 7 || Direct POLO(bPol) ... failed. || Uncurrying ... failed. || Dependency Pairs: || #1: #plus(PeRCenTX,s(PeRCenTY)) -> #plus(PeRCenTX,PeRCenTY) || #2: #times(PeRCenTX,s(PeRCenTY)) -> #plus(times(PeRCenTX,PeRCenTY),PeRCenTX) || #3: #times(PeRCenTX,s(PeRCenTY)) -> #times(PeRCenTX,PeRCenTY) || #4: #times(PeRCenTX,plus(PeRCenTY,s(PeRCenTZ))) -> #plus(times(PeRCenTX,plus(PeRCenTY,times(s(PeRCenTZ),0()))),times(PeRCenTX,s(PeRCenTZ))) || #5: #times(PeRCenTX,plus(PeRCenTY,s(PeRCenTZ))) -> #times(PeRCenTX,plus(PeRCenTY,times(s(PeRCenTZ),0()))) || #6: #times(PeRCenTX,plus(PeRCenTY,s(PeRCenTZ))) -> #plus(PeRCenTY,times(s(PeRCenTZ),0())) || #7: #times(PeRCenTX,plus(PeRCenTY,s(PeRCenTZ))) -> #times(s(PeRCenTZ),0()) || #8: #times(PeRCenTX,plus(PeRCenTY,s(PeRCenTZ))) -> #times(PeRCenTX,s(PeRCenTZ)) || Number of SCCs: 2, DPs: 4 || SCC { #1 } || POLO(Sum)... succeeded. || TIlDePAIR w: 0 || s w: x1 + 1 || #plus w: x2 || #times w: 0 || 0 w: 0 || times w: 0 || #TIlDePAIR w: 0 || plus w: 0 || USABLE RULES: { } || Removed DPs: #1 || Number of SCCs: 1, DPs: 3 || SCC { #3 #5 #8 } || POLO(Sum)... succeeded. || TIlDePAIR w: 0 || s w: x1 + 2 || #plus w: 0 || #times w: x2 || 0 w: 1 || times w: 1 || #TIlDePAIR w: 0 || plus w: x1 + x2 + 1 || USABLE RULES: { 2 4 5 } || Removed DPs: #3 #5 #8 || Number of SCCs: 0, DPs: 0 || We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs and accessible arguments in [FuhKop19]). We thus obtain the following dependency pair problem (P_0, R_0, computable, formative): Dependency Pairs P_0: 0] map#(F, cons(X, Y)) =#> map#(F, Y) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Higher Order Rewriting Union Beta